PROCESSES IN BIOLOGICAL VISION: including,

ELECTROCHEMISTRY OF THE NEURON

This material is excerpted from the full β-version of the text. The final printed version will be more concise due to further editing and economical constraints. A Table of Contents and an index are located at the end of this paper.

James T. Fulton Vision Concepts [email protected]

April 30, 2017 Copyright 2003 James T. Fulton Performance Descriptors 17- 1

[xxx reconfirm all Section references to or in 17.2.2, etc. ] [xxx reword references to constant quantum efficiency ] 17 Performance descriptors of Vision1

Probably more error has crept into the subject of colour vision from inexact description of experimental conditions and the nature of the stimuli employed than from any other cause. Sir John Parsons, 1915

Because of the amount of artwork in this chapter, it has been necessary to divide it into three parts for distribution over the INTERNET. PART 1A: INTRO, LUMINANCE & NEW DIAGRAM PART 1B: EXTENSIONS TO THE NEW CHROMATICITY DIAGRAM PART 2: TEMPORAL AND SPATIAL DESCRIPTORS OF VISION

PART 1A: INTRO. LUMINANCE &

The press of work on other parts of the manuscript may delay the final cleanup of this PART but it is too valuable to delay its release for comment. Any comments are welcome at [email protected]. 17.1 Introduction

This Chapter and Chapter 16 form a pair. While the last Chapter developed equations that are applicable to any animal, this Chapter will concentrate on the most highly developed performance descriptors, those applicable to the human. The is considerably more capable, more flexible and more complex than reflected in even the scientific literature. To understand the operation of the visual system has required the development of a considerably more advanced model of the visual system than previously available. This model has defined many of the operating modes of the visual system for the first time. It has also indicated that considerably more sophisticated instrumentation is required than was used in the past.

Discussions of the shortcomings of the instrumentation and many of the current theories based on inductive reasoning and floating models used in vision research were originally included in the main body of this Chapter. This material has now been moved to Chapter 19. The material stresses the many degrees of freedom that have not been adequately controlled in most experiments. It also stresses the inadequacies of the theory of vision adopted by the C.I.E. based almost entirely on the inductive approach2. This approach did not call for rigorous experiments to verify the theory.

This chapter will concentrate on the descriptors of vision that can be formulated from the electrophysiology of the actual system as presented earlier in this work. While much of this electrophysiology has developed and can be confirmed using psychophysical experiments, it is extremely difficult to develop precise descriptors based on psychophysics alone. This is due to the very large number of uncontrolled variables encountered in the experiments reported in the literature. Section 17.8 of this chapter provides a discussion of this problem. It also provides an initial experimental framework that can be used to pars the description of an experiment provided by the author of a

1Released April 30, 2017

2[CIE-- Commission Internationale de l’Eclairage or International Commission on Illumination; responsible for standards in this area. Most well known for the CIE Chromaticity Diagram of 1924 (2 degree Standard Observer), the CIE Photopic Observer Curve of 1924 (2 degree Standard Observer) and the CIE Scotopic Observer curve of 1951 (2 degree Standard Observer) The Science of Color says they were adopted to aid in color measurement (i.e., not for use in color research) 2 Processes in Biological Vision

published paper. More usefully, it can be used to define their future experiments and report their results more precisely.

The primary descriptors are; the luminance, chrominance and temporal performance descriptors. A brief discussion of a combined luminance/chrominance descriptor solid will be presented; however, this concept is shown to have limited utility. The noise limiting and spatial performance descriptors of vision will only be discussed briefly in this document. Stochastic noise plays a remarkably small role in vision. Many of the major descriptors are compatible with other members of the animal kingdom format-wise but require different scales.

Using the temporal descriptors with other animals is primarily a matter of incorporating the appropriate time constants. The first known theoretical derivation of the waveforms found in the Electroretinogram will be presented here. After-images, a primarily temporal effect, are based on the state of adaptation of the various chromatic photodetection channels, the performance of the vascular system and the background illumination during the after image. After images will be discussed in Chapter 18.

To appreciate this Chapter, the reader must recognize the previously poorly documented fact that the human visual system is fundamentally tetrachromatic. As shown in Chapter 5, the fundamental photochemistry of all biological vision is tetrachromatic. Goldsmith has also pointed out that virtually all vertebrate vision is tetrachromatic3, at least as some time during the species lifetime. Chapter 11 shows how the signaling architecture of the visual system is designed to exploit this tetrachromatic capability. Less capable visual system appear to have evolved as an adaptation to a specific habitat. In the case of humans, and other large chordates, ultraviolet sensitivity has been lost as a traded-off with physical size. The tetrachromatic capability of the of humans is easily demonstrated in the case of aphakic eyes. The retina in such an eye exhibits the precise tetrachromatic sensitivity function predicted by this theory. As a result of its growth in physical size, the lens of the human eye exhibits an optical density of 3.5 in the ultraviolet spectrum between 325 and 395 nm. Because of this absorption by the lens, the human visual system can be considered a degenerate tetrachromatic system. More specifically, it could be described as a ultraviolet blocked tetrachromatic system. Less specifically, it could be described as a long wavelength trichromatic system.

The use of the term tetrachromatic in this Chapter does not include the proposed variants on human vision described by Gavrik4 or similar variants suggested in women due to a genetic mutation5. In both cases, the authors suggest the presence of a fourth in the region between the normal M– and L– channel photoreceptors. However, the proposal is based on psychophysical testing and does not include any electro-physical or other physiological. data..

17.1.1 Baseline human visual system required to understand this chapter

17.1.1.1 Historical Background

Beginning in the very early 1900's, significant effort was expended in attempting to characterize the performance of the human eye. These efforts can be described in terms of three areas; the luminance response, the chrominance

3Goldsmith, T. (1990) Optimization, constraint, and history in the evolution of eyes. Quart. Rev. Biol. vol. 65, no. 9, pp 281-322

4Gavrik, V. (2002) Tetrachromacy of human vision: spectral channels and primary SPIE Proc vol 2241, pp 315-318

5Greenwood, V. (2012) Super human vison Discover Special Issue, Jul/Aug pp 29-31 Performance Descriptors 17- 3

response, and the temporal response of the eye. Much of the effort was concentrated in the first two areas.

Because of the complexity of the visual system and the lack of a model, debate raged in the vision community with regard to the adequacy of many workers efforts. This led to considerable social difficulty and historically interesting statements by many leaders and groups of leaders of the day. Several of these positions were incorporated into official documents because of the positions occupied by some of these leaders in the scientific societies.

By the 1950's, the leadership had changed but the official text, The Science of Color, of the Committee on of the Optical Society of America, L. A. Jones Chairman, took a number of very defensive positions. As an example, on page 242-243, it stated under the heading

“Data independent of all theories of . Theories of color vision purport to explain the phenomenon in terms of retinal structure and function, nerve action, and cerebral projection. Color-mixture data on which are based computations of color specifications are independent of all theories.”

Unfortunately, most of their work is based on a theoretical foundation which employs linear addition of spectral component data using the human eye as a null detector and mixing illuminants on an energy basis instead of a photon flux basis. These assumptions lead to problems with both the r-g-b system and the x-y-z system of color description.

A major difficulty in the literature is nomenclature. Nearly all languages have a limited to very limited vocabulary associated with the parameters of vision. The limitation is a particular problem with regard to color. This has led to many attempts by scientists to use the same word in many different contexts, usually without specific definition, in their papers. The result has been considerable confusion. A specific example has arisen in the literature during the 1990's with regard to a 2-dimensional representation of a represented by and saturation and a 3- dimensional color space represented by either (or brightness) and hue and saturation. Whereas the bulk of the literature defines color separately from lightness, several authors discussing a 3-dimensional representation, that has traditionally been called a , have chosen to use a contraction and also call the 3-dimensional representation a color space. In this way, they implicitly define color as a perceived sensation resulting from a visual excitation that is defined in terms of lightness, hue and saturation,. Whereas the 2-dimensional color space is usually described as containing a few thousand discriminatable colors, the authors calling the 3-dimensional color representation a color space usually describe it as containing a few million discriminatable colors.

The bottom line is that inadequate theoretical investigation, limited previously by the state of the art in the requisite technical disciplines, has resulted in a lack of adequate experimental design discipline. This lack of an adequate framework and adequate experimental discipline has resulted in slower than desired advances in knowledge of the processes in vision. The lack of semantic flexibility has also contributed to this problem. The result has been unnecessary controversy among investigators. The problem exists today.

17.1.1.2 Baseline

The currently available descriptors of the human visual process do not form an adequate foundation for research. They are limited in two major respects. They are not based on a clear set of definitions relating to the illumination environment. They are not based on a detailed understanding of the mechanisms and operation of the visual system.

The human visual system, like that of all higher primates and virtually all mammals operates as described in the earlier chapters. It consists of:

< a multi-channel signaling system, channelized differently in different regions 4 Processes in Biological Vision

C the initial part of the system employs two eyes in order to achieve a stereoscopic capability. C each eye contains photoreceptors having four different spectral responses (ultra-, short, medium and long wavelengths) with the ultraviolet photoreceptors ineffectively used in humans because of the thickness of the lens system. C each spectral set of photoreceptors operate in a output-stabilizing feedback loop of variable gain that establishes the characteristics of the system under photopic conditions. C the higher density of the M-channel photoreceptors in the retina leads to a higher apparent sensitivity of this channel prior to the onset of output-stabilization by the feedback loop. C the output of each photoreceptor cells is logarithmically converted from a current driver within its axon to a voltage source at its pedicle. C the spectral outputs of the photoreceptor sets in humans and other mamals are converted into a set of difference signals within the neural circuitry of the retina. C each eye delivers three major signaling channels (brightness, geometric, & chrominance) from the entire retina to the midbrain, particularly the thalamus C The of each eye delivers un formated signals from a group of about 38,000 photoreceptors directly to the perigeniciulate nucleus of the thalamus without any signal encoding. C Two-way signaling paths project to and from the occipital lobe to support auxiliary signal processing. C The thalamus is responsible for both information extraction from the signals provided and signal switching between portions of the cerebral cortex. This switching involves at least six definable signaling channels. C The signals delivered to the saliency map of the parietal lobe, for cognition by the frontal lobe, are in abstract form that can not currently be decoded by man. C Within the cerebral cortex, signals are passed back and forth using a star-mesh interconnection architecture. < A precision optical servo system (POS). Part of this system was previously known as the auxiliary optical system. C This system is used to control the version (pointing) and (con) of the two eyes. C This system integrates sensory signals from the awareness, analytical and alarm modes under the direction of the thalamic reticular nucleus of the thalamus. C This system integrates signals from the vestibular and skeletal nervous systems. C This system prepares both volition and alarm mode commands for transmission to the musculo-skeletal and glandular systems. < Analytical and awareness operating modes that accept the signals from the brightness channel and differential signals from the chrominance signals received via independent subchannels. It processes these signals orthogonally resulting in the two-dimensional perceptual chromaticity diagram and the three-dimensional color space defined in this work. C The resulting perceptual chromaticity diagram and three-dimensional color space are compatible with, and more precisely define, the Munsell color space. < An analytical operating mode, with operations centered on the perigeniculate nucleus, and the pulvinar of the thalamus (with support from the POS and the cerebellum) that is responsible for pattern extraction and perception leading to cognition. C This pattern perception capability is the key to the analysis of fine detail and the reading capability of humans.

17.1.1.2.1 Regions of the radiometric and illumination environment

Section 2.1.1 discussed the radiation environment of the visual system in general terms, particularly its ability to operate over a dynamic range of at least 15 orders of magnitude. The available estimates of the transition points between the distinctly different operating environments has not been quantified to a significant extent. This appears to be due to the considerable number of parameters and mechanisms involved. There is a problem in differentiating Performance Descriptors 17- 5

between the historical, and largely clinical, descriptions of the visual operating regions and the more detailed and research oriented regions. It is difficult to define the transition between these regions precisely because each transition involves more than one hallmark. This work will adopt a framework similar to that used in the study of the medical syndrome of (with the suffix, -psia). This syndrome includes a more specific disease of achromatopia (with a suffix, -pia) Unfortunately, the analogy will need to be reversed to match the historical terminology. The clinically defined regions are the hyperopic, photopic, mesopic and scotopic regions.

The definition of the mesopic region is particularly difficult to define precisely because it abuts two other regions of major interest and it involves many observable changes in mechanisms and conditions. These include the physically observable changes in the iris subsystem, the perceptual changes in the color fidelity of the system (including the loss of color rendition entirely), the clinically observable changes in the threshold sensitivity of the system as a function of wavelength, and the electrophysiological changes in signal characteristics within the system.

For purposes of this work, the mesopic region will be defined as the radiometric region encompassing all of the above changes (as encountered in the clinical setting). The more narrowly (and precisely) defined mesotopic region will be defined as involving only that portion of the radiometric region involving electrophysiologically identifiable changes in the visual system (See Section 17.2.1.2.2). As an example, the operation of the physiological iris is included in the mesopic region but not in the mesotopic region. Unfortunately, these definitions do not define distinctly separate regions, only distinct mechanisms and thresholds. The illumination levels found in Section 2.1.1 and Figure 2.4.3-1 provide only a rough estimate of the transition points between the mesopic and mesotopic regions and the neighboring regions.

17.1.1.2.2 The baseline schematic of the visual system

The only detailed baseline of vision available is the Top Level Schematic of the visual process presented in this work and repeated in the following sections (Section 17.1.1.4).

17.1.1.2.3 The baseline for operations leading to perception and cognition

Very little work has been done in the interpretation of the spatial signal processing of the visual system beyond the experiments related to bipartite edges and concentric fields. Lacking a comprehensive model, these experiments have been limited to the exploratory regime. Going beyond these simple configurations into actual patterns has generally resulted in the documentation of interesting special situations but little scientific formalism. This chapter and Chapter 19 will provide many new insights into the interpretation, perception and cognition of external images within the human field of view, with particular emphasis on the foveola.

17.1.1.2.4 Past difficulties in performing experiments

With the availability of the model used in this work, the difficulty of separating the functional capability of the human, and animal, eye into discrete and orthogonal characteristics related to luminance, chrominance and temporal characteristics can be appreciated. The visual system is based fundamentally on a simple change detector. It appears that this change detector has been exploited to the maximum in the chordate eye. As exploited, it includes:

+ a single highly elliptical optical system that does not have an axis intersecting the fovea,

+ multiple independent input channels (exhibiting considerable chromatic overlap in their spectral sensitivities),

+ a dispersion and interdigitation of chromatically sensitive photoreceptors over the retina with almost completely unknown parameters, 6 Processes in Biological Vision

+ each input channel is supported by an asymmetric, state-variable based, adaptation amplifier,

+ logarithmic conversion of all photoreceptor cell output signals prior to further signal manipulation,

+ sum and difference amplifiers processing the state variable signals into multiple parallel and orthogonal signaling channels,

+ multiple signal projection channels with different characteristics,

+ a luminance signal projection channel containing species specific combinations of pre-emphasis and thresholding features,

+ multiple independent asymmetric chrominance/polarization signal projection channels,

+ signal recovery and interpretation circuits in the brain that have been mapped topographically, and to a lesser extent topologically, but have not been analyzed from a signal handling and interpretation perspective.

The presence of so many adjectives, particularly “asymmetric” and “state-variable” in reference to individual mechanisms, in the above paragraph leads to great difficulty. It becomes absolutely mandatory in describing a visual system that great care be taken in specifying the conditions under which an experiment is conducted. Lacking this level of precision, any individual work is subject to criticism and the correlation of multiple experiments becomes difficult. It also becomes obvious that using broadband radiation as a test input is usually a sign of poor test procedure design.

The asymmetries of the visual signal processing circuits account for many of the difficulties in repeating many experiments. A change in a parameter must be explicitly reproduced in any corroborating experiment. This means the change must begin from the same initial level, probably to better than +/-10%, and proceed in the same direction.

The state-variable aspect of many parameters requires that the initial and any corroborating experiments must be prepared to discuss the condition of the system for a period of at least three time constants longer than the relevant time constants. This interval is usually over 30 minutes.

The above conditions imposed by the asymmetries and state-variables account for the few repeatable experiments, to even +/-20%, in the literature other than those related to a fully dark adapted eye. Generally, to achieve even +/- 20%, the irradiation must refer to the retina, or the external aperture and a fixed artificial iris. This latter situation is the foundation for the use of Trolands as a unit of measure. The Troland does not apply to the actual illumination on the retina. The Troland is defined for the on-axis (thin lens) model of the eye. It does not account for the great variation in effective size of the eye for the off-axis condition (Section 17.1.1.2.4).

The logarithmic processing of all signals emanating from the photoreceptor cells makes it absolutely necessary to specify whether the changes in irradiance being applied to the eye are of the large signal, typically greater than 2:1, or small signal type. For a symmetrical change about an average value, the 2:1 factor is represented by a modulation of about +/- 33% of the mean.

In human, no substantial literature exists describing any pre-emphasis type signal processing within the eye. The predominant performance limitations at low levels are related to noise thresholds. At low flux levels, quantum processes are inherently noisy. There is a standard deviation associated with the mean intrinsic flux. At higher flux levels, the discrimination capability of the eye is controlled by the noise performance of the signal recovery circuits Performance Descriptors 17- 7 at the termination of the signal projection circuits in the brain. Both minimum perceptible luminance and minimum chrominance changes are based on the signal to noise ratio at the output of the terminal neuron of the signal projection system.

In the chrominance channels of human, there is an additional complication due to the form of encoding used in the projection system. The hue and saturation in each channel are not independent. Furthermore, a single noise component impacts them both. As the saturation of a chromatic input is reduced, it becomes more difficult to discriminate in either (or both) hue and saturation.

To aid in the development of the various performance descriptors of vision, approximately eight distinct definitions of the basic term color will be employed. Because of the paucity of synonyms in colloquial English for color, use will be made of precisely defined two-word expressions closely aligned to the situation being discussed.

This Chapter will present the performance descriptors of the eye using a format consistent with the historical literature. It will discuss the luminous, chrominance, temporal, and spatial descriptors of the visual system separately. This is the only rational way to avoid serious intanglements. However, the interdependence of many of these parameters cannot be avoided. With these individual groups of descriptors presented, it is then possible to discuss more complex phenomena resulting from interactions between or second order effects of the processes used to support vision.

A fundamental separation will be maintained between the characteristics of perceived color, represented by hue and saturation, and the characteristics of perceived brightness. Justification for this choice is based on the nearly complete independence of the signaling paths related to these perceived characteristics in the visual system. As a result of this decision, color will be discussed in the context of a 2-dimensional color space that is planar and rectilinear. Brightness will be discussed in terms of a 1-dimensional intensity space that is linear. Later, a 3- dimensional sensation space will be developed that is fundamentally different from any 3-dimensional space in the current literature related to vision. It will be shown how this space relates to, and includes, similar 3- dimensional representations of the perception of vision. This new space will be formally called a sensation space and informally called a color solid. When combined with other visual and non-visual sensory data, it will be referred to as a saliency space.

The discussion will make it perfectly clear that it is not appropriate to speak of the sensation space of vision in terms of a spherical coordinate system or to speak of specific differential volumes within this space as representing a “color.” The more appropriate volume is a cylinder that will describe a perceived sensation represented by a brightness and a color. This notation is conceptually compatible with the more comprehensive vector notation used in the cortex. It is also compatible with the potentially infinite extent of the luminous intensity of the scene and simultaneously with the finite extent of the 2-dimensional color space.

It will become clear that the same signaling channel is involved in the perception of both the temporal and spatial frequency aspects of a scene. In addition, the impact of tremor is significant in this complex arena when high precision is sought. In agreement with this work, Kelly has shown that the performance of the system in spatial frequency space can be defined as the same as the performance in temporal space times a conversion constant with units of angular velocity6. This conversion can be accomplished by introducing an external motion or by relying upon the normal tremor of the eyes.

17.1.1.2.4 Separation of the CIE functions from the threshold functions of this work

6Kelly, D. (1979) Motion and Vision. I. Stabilized images of stationary gratings. J. Opt. Soc. Am. vol. 69, pp 1266-1273 8 Processes in Biological Vision

Because of the many conceptual problems with the definition of the CIE luminous efficiency functions, V(λ), this work will define a separate pair of luminance and chrominance threshold functions, T(λ, F) and C(λ,F) respectively. These descriptors are defined as functions of both wavelength and stimulus intensity when using a 7053 nm body source as shown. At this , the photon flux density is nominally uniform with respect to wavelength across the visual spectrum at a specific intensity, F. Specified in their individual test protocols are both the spectral width of the sampling mechanism and the angular diameter of the stimulus. The spectral width shall be not greater than 10 nm. The stimulus diameters are specified as two degrees for a quasi photopic descriptor, T without an accent mark, and ten degrees for a quasi scotopic descriptor, T’. Other subscripted versions of these descriptors can be calculated for other conditions. Of particular interest would be a 0.6 degree field for defining the difference in chromaticity threshold with spatial field due to the finite diameter of the foveola (See Figure 17.3.2-8, color shift with field size). Over a considerable range of stimulus, known as the photopic region, the two degree luminosity threshold function will be relatively constant as a function of stimulus intensity. By spectrally smoothing the luminance threshold function within this range, a numerical equivalent to the CIE photopic luminous efficiency function, V(λ), can be obtained. Achieving an equivalent to the CIE scotopic luminous efficiency function is also possible. However, the luminance threshold function changes significantly as a function of stimulus intensity in the mesopic region. This variation is confirmed in the data of Hurvich & Jameson7.

The shape of C(λ,F) is considerably different from T(λ, F) as will be shown below.

17.1.1.3 Goal

The development of meaningful descriptors of the overall performance of a visual system is difficult because of the physical complexity associated with the situation described above. It is made more difficult by the inability of the human to discriminate clearly and distinctly between changes in luminance and chrominance. This Chapter is designed to present a set of descriptors that are as clearly defined as possible. Human frailty being what it is, it may be necessary for the reader to rely on the discussion accompanying a given descriptor as well as the explicit annotations. The following paragraphs can not be made to stand completely independently because of the above discussion. They are therefore presented in an arbitrary order, are primarily based on work in previous Chapters but may sometimes rely on references that are forward looking.

The individual spectral absorption characteristics of the four of vision have been presented in earlier Chapters. They will not be repeated here.

The fact that the luminance and chrominance signaling channels of vision are orthogonal to each other have thwarted the development of a meaningful “three dimensional color space.” Section 17.4 will address this subject.

The effects of aging on the visual system are primarily in two areas. The hardening of the lens which makes the muscles associated with less effective with age is the most obvious. The increased attenuation in the short wavelength portion of the spectrum due to increased Rayleigh scattering in the physiological optics is the second area. The accommodation problem will not be explored in this Chapter. Comments on the increase scattering will be addressed briefly.

17.1.1.4 Perspective

The sequence in which the above mechanisms are invoked in the visual system can be seen with the aid of the Top Level Schematic shown in Figure 17.1.1-2 as applied to human. The primary modifications to the global Top Level

7Hurvich, L. & Jameson, D. (1953) Spectral sensitivity of the fovea. I. Neutral adaptation J. Opt Soc Am vol. 43, no. 6, pp 485– , fig 3 Performance Descriptors 17- 9

Schematic are few. The secondary (nictating) eyelid marked (E) is omitted. The lens marked (B) shows a highly asymmetric absorption spectrum that greatly attenuates the ultraviolet reaching the photoreceptor cells labeled (UV). While this filtering leaves the photoreceptors (and probably one of the chrominance signaling paths), non- functional with regard to signaling, they remain functional at the circuit level. This circuit level functionality can be demonstrated in aphakic eyes (eyes with the lens malformed or removed through surgery).

Figure 17.1.1-2 Top level schematic of the visual system of Chordata. See text for details.

All of the other elements in the figure are important to the functioning of the visual system in human. In this figure, the first lateral processing matrix is primarily associated with forming the chrominance channels of human vision. The second lateral processing matrix is associated with forming any spatial processing channels, appearance channels, within the retina of human vision. It appears that this function is rudimentary in humans.

17.1.1.4.1 Closed loop feedback in the motor-neural circuits of vision

There are three main closed loop feedback circuits in the human visual system ( HVS). The first is that associated with the analysis and perception of fine detail by the circuits related to the foveola. This figure shows the distinct difference in signaling paths associated with the foveola, the very central portion of the fovea, and the remainder of the retina. The signals from the photoreceptors of the foveola are believed to connect directly to the Pretectum, a portion of or closely related to the Superior Colliculus. These signals are used in the exquisite analytical function of the brain that is associated with the foveola. They are believed to control the small saccadic movements of the eye via the eye muscles ((C) that are first seen in the work of Yarbus. This control of the position of the eye based on the data collected by the foveola of the retina is the most important example of closed loop feedback in the visual process. It is a major function of the so-called Auxiliary Optical System (OSA).The signals originating from outside the foveola are transmitted to the magnocellular portion of the brain.

The second most important example of closed loop feedback involves control of the aperture/iris (A) of the eye. How the signals from the retina are extracted and sent to the Superior Colliculus for this purpose is unknown.

The third and equally important closed loop operation is that of the eyelid (D). It appears to be under neural control 10 Processes in Biological Vision

but not to rely heavily on simple signals from the retina. This loop is controlled by a more complex signal processing block within the cortex. The eyelid appears to be controlled as a result of a complex computation involving both simple brightness information, perceived threat to the animal and housekeeping functions related to the maintenance of the surface of the cornea. The command to close the eyelid is also closely coordinated with the commands to redirect the point of fixation of the eye. Through this coordination, the short term memory of the visual system is not corrupted by information collected by the retina during the large saccadic motions.

17.1.1.4.2 Other feedback within the signal processing circuits of vision

It should be noted that the diagram does not show any closed loop (external) feedback among the signaling circuits of the retina or the projection neurons connecting to the cortex of the brain. The analyses presented in this work have not uncovered any external feedback within the vision system outside of the cortex. The term external is used to differentiate feedback involving a distinct signal path antidromic to the normal signal paths from the internal, and orthodromic, negative feedback found within individual signal processing and signal projection neurons. Such feedback is normally associated with an impedance in the poditic signal lead of an Activa within a neuron. This internal and orthodromic feedback is key to the operation of all signal inverting neurons and all encoding neurons of the projection system.

A similar orthodromic feedback mechanism is also associated with the support of the signal processing system by the vascular system of the eye. There are two main contributions, one global and one photoreceptor specific. First, the vascular bed of the retina provides a common impedance associated with the collector supply terminals of all of the photoreceptors in a specific region of the retina. This common impedance tends to stabilize the operating point of all of the photoreceptors in that region. A more photoreceptor cell specific impedance is also associated with the vascular system. This impedance effectively controls the gain characteristic of the adaptation amplifier within the photoreceptor cell. It is critical to the adaptation of the eye to various conditions of irradiation.

17.1.1.4.3 Application of various mechanisms

The mechanisms outlined above do not all operate in synchronism. Nor do they operate in sequence. There is considerable overlap in their operation. Some of these idiosyncracies of the visual system in human can be illustrated by Figure 17.1.1-3. The horizontal scale is logarithmic and has been given in a variety of units as indicated in Chapter 2. The vertical scale is linear and represents the brightness attribute of vision. The curved dotted line represents the instantaneous transfer function between the illuminance of the scene and the perceived brightness of that scene. This curve can slide horizontally as a function of the adaptation process. This process is designed to keep the dynamic range of the brightness channel matched to the dynamic range of the information content associated with the scene.

The maximum value of the brightness attribute within the signal processing circuits (the bipolar and lateral cells) is approximately +130 mV relative to the nominal –154 mV membrane potential of the neuron at cutoff. Thus, this maximum voltage corresponds to approximately -20 mV. relative to the inter-neural matrix. This level corresponds to saturation in the output signal of the photoreceptor cells (corresponding again to about –20 mV. relative to the INM). The four principle regions of visual operation are shown above the figure and are defined in the following glossary. Performance Descriptors 17- 11

The central rectangle of this figure illustrates the remarkably wide stable region of operation for the human visual system (HVS). It covers nearly 5 orders of magnitude of illumination. Within this region, all of the signal processing circuitry operates in a “constant amplitude” regime, insuring stability in all of the luminance and chrominance channels. This constancy of amplitude accounts for the remarkable stability in the perception of both color and luminance contrasts over this region. This region of stable operation is due primarily to the adaptation amplifiers of the photoreceptor cells augmented by the operation of the aperture control, Figure 17.1.1-3 An overall descriptor of the illumination the iris. It should be noted that the dynamic range range of the eye. Luminance values as measured with a associated with the iris is only a factor of 16:1 in the conventional photometer. Color temperature of source nominal eye. The dynamic range of the adaptation (integrated sky) was not documented.. amplifier is a much greater, 3500:1.

Above and below the region described by the rectangle, the eye continues to perform in a more limited mode. In the next higher illumination region, the hypertopic region, the performance is degraded by the saturation initially in the M-channel due to the adaptation amplifier gain falling to a constant value of one. This causes saturation in the M- channel input to the luminance and chrominance channels, probably due to cutoff in the distribution amplifier of the photoreceptor cells. The result is an initial perceived shift in scene color toward the , related to the Q chrominance channel, followed by a shift toward the as the P chrominance channel is also affected by the saturation. As illumination levels, and hence signal levels, increase further, a region of considerable perceived pain is encountered. In this region all of the distribution amplifiers of the photoreceptor cells, at least in the fovea, go into cutoff.

At illumination levels below the photopic region, there are two distinct regions of operation, the well known scotopic region and the lesser appreciated mesotopic region. The mesotopic region is characterized by two phenomena. The adaptation amplifiers are now operating at full amplification and the iris is open to maximum. The underlying square law characteristic of the photodetection process in the L-channel now introduces a more rapid loss of signal level in this channel relative to the other photodetection channels. This loss also exhibits two specific phenomena. First, the overall spectral absorption characteristic perceived by the system is gradually degraded to that associated with scotopic vision. Second, the characteristic report of the scene changing to a bluish caste just before loss of all color perception is common. As the response of the L-channel becomes insignificant relative to the other two channels, the region of scotopic vision is reached. In this region, the signal to noise ratio in the chrominance channels has become so low that there is no reliable perception of color even though there may be significant perception of shape information via the luminance channel. As the illumination continues to fall, even the signal to noise ratio in the channel labeled “luminance” becomes so low that perception of shape is also lost although some rudimentary detection of differences in brightness may be perceived. This is the area where detection of signals by the brain frequently leads to inaccurate perceptions of dangers.

Hurvich noted the above phenomena with respect to the mesotopic and scotopic regions but did not appreciate the impact of the adaptation amplifiers in limiting the rate of rise of the signal associated with the L-channel within the photopic region8. His analysis was in terms of Opponent (Hering) Theory.

8Hurvich, L. (1997) Essays concerning color constancy. Chap 7 In Readings on Color; vol. 2: The Science of Color, Byrne, A. & Hilbert, D. ed. Cambridge, MA: The MIT Press. pp 177-198 12 Processes in Biological Vision

At illumination levels above the photopic region, the hypertopic region is encountered. It is defined primarily by the fact that color constancy is not maintained in this region due to saturation in the signal at the output of the sensory neurons. Burns & Elsner have provided the clearest demarcation between the photopic and hypertopic regions9,10. Figure 1 of the first paper shows the distinct loss in color fidelity beginning at 10,000 Trolands for any test field size from one to eight degrees.

9Burns, S. & Elsner, A. (1985) Color matching at high illuminances: the color-match-area effect and photopigment bleaching J Opt Soc Am A vol 2(5), pp 698-704 10Burns. S. & Elsner. A. (1993) Color matching at high illuminances: photopigment optical density and pupil entry J Opt Soc Am A vol 10(2 ), pp 221-230 Performance Descriptors 17- 13

17.1.2 Terminology

17.1.2.1 Photometric units are archaic in research

The visual science community has traditionally used photometric units. Unfortunately, these units were designed originally for application engineering purposes in society. They are grossly inadequate for research purposes. More specifically, the commercial instrumentation available does not emulate an actual visual system. They are frequently photoconductive based and record energy, not photon flux. They do not report in units of photon flux density and still would not recognize the unique parameters related to the luminance channel if they did. Distl11 has documented the deviation between the typical photometer and the C.I.E. (1924) luminous efficiency function. The deviations are large in both the and the . At the current time, the instruments are not available with auxiliary filters to match the spectral absorption of the individual chromophoric absorbers. With the slightest degree of chromatic adaptation of a test subject, the instrumentation becomes grossly inappropriate for research.

A similar situation exists with respect to illumination sources. The use of various low temperature quasi-blackbody sources for research purposes is quaint and archaic. As noted earlier, even the C.I.E has failed to define a source for the defined Illuminant C. Illuminant C is very deficient in the short wavelength spectrum. Any illuminant with a black body temperature of less than 7053° Kelvin is deficient in the short wavelength spectrum and should not be used for research without careful notation of that fact.

The practice of recording the intensity of a source using a photometer and then passing the light through a filter, (defined at best by a catalog number) before being applied to the retina of a subject leaves the researcher with the monumental task of determining what the effect of that irradiance was on the performance of the eye of that subject.

Although seldom noted, use of a sodium glass envelope for a light source also restricts the short wavelength radiation from that source. Only quartz envelope sources should be used in research involving the short wavelength region of vision.

In summary, serious research requires more serious attention to the source of radiation applied to a visual system and the intensity recording instrumentation. A source with a very controlled blackbody temperature, not merely a recording of the current through a filament, is required. The spectral adequacy of the source should be confirmed through calibration. Similarly, any filters used should be calibrated. The intensity recording instrumentation should be photoemissive in character in order to record photon flux and should employ filters matched to the actual chromophores of vision. By using a three channel device with appropriate signal summation, an instrument can be obtained that closely matches the performance of the human eye under any state of adaptation.

The community has long suffered problems of maintaining technical specificity in the presence of semantic convenience. The suffixes of terms are frequently changed to make sentences appear more grammatically correct. It is important that precise terms be used in research. Jones has provided the most lucid discussion of the agreed terms to be used in photometry12. Although dated, it is still largely relevant.

The international standards community is progressing. In 1979, they defined a new Candela that is independent of the CIE luminous efficiency function. See Section 17.1.3 or the Glossary. However, the NBS program in optical radiometry continues to be based on energy detection, not photon detection. However, their detector of choice is now a “high quality silicon photodiode.” These are photoelectric (quantum) detectors that exhibit an output current

11Distl, R. (2000) Measure what you see. Photonics Spectra, May, pp. 176-180 12Jones, L. (1937) Colorimetry: Preliminary draft of a report on nomenclature and definitions J. Opt. Soc. Am. vol. 27, pp 207-213 14 Processes in Biological Vision proportional to the input wattage. However, the current output is a function of wavelength. It decreases at shorter wavelength because there are fewer photons in one watt. These photodiodes are quantum detectors just like the eye.

17.1.2.1.1 Limitation on the Troland, an archaic unit of photometry

During the 1960's, the Troland was defined as the equivalent of the earlier term Photon in honor of Dr. L. T. Troland who had been an early experimenter in the field of photometry. The term is used to define the irradiance, in photometric units, at the pupil of the eye prior to any absorption by the tissue of the eye. Although it is frequently used to describe the retinal illuminance, this is misleading. The actual irradiance of the retina is a function of the spectral absorption and scattering of the tissue prior to the photoreceptors and the focal length of the eye. It is also a function of the F/# of the optical system of the eye. The focal length is a function of field angle relative to the optical axis. The effective pupil size is also highly dependent on field angle. The actual irradiance is therefore a strong function of retinal position. Wyszecki & Stiles13 discuss this situation in some detail and recommend use of the expression “Troland value” as opposed to “retinal illuminance” to describe the illumination at the pupil. The actual retinal illuminance is considerably less than 10% of the Troland value. Just the difference in the index of refraction between air and the vitreal fluid introduces a factor of 1.76:1 between the pupil irradiance and the retinal irradiance. Following contemporary practice, Wyszecki & Stiles differentiated between photopic and scotopic Troland values, reflecting the different luminosity functions of the eye in these two regimes. They did not recognize the fact that the luminous efficiency function varies continuously throughout the mesotopic region. As a result, either Troland misrepresents the excitation applied to the eye in the mesotopic region.

Although not defined explicitly in the definition of the Troland, the value of the parameter is a function of the spectral intensity, or color temperature, of the source. For the basic definition, based on the Candela, the assumed color temperature is only 2042 Kelvin (confirmed in W & S (1982, pg 253) by the Conference Generale des Poids et Mesures (CGPM) in 1967). A large correction factor must be introduced for other color temperatures (2.464:1 for

D65) based on energy rather than flux. The correction factors calculated by Wyszecki & Stiles ignore any variation in luminous efficiency associated with the mesotopic region.

The Troland value is only equal to the product of the luminance of the source times the aperture (real or artificial) of the eye along the optical axis of the eye. Even for the point of fixation, a minor correction is required (although generally ignored) in this value. When discussing off-axis conditions, both the effective pupil size and the thick-lens model of the eye must be used in Troland related investigations.

17.1.2.1.2 Available commercial photometers lack precision

Commercial photometers have traditionally been simple radiometers modified to include a fixed filter. The combination of the filter and the spectral response of the photodetector were matched to provide an overall spectral response matching as close as practical the smoothed C.I.E. luminous efficiency function. Sometimes the photodetectors were photoconductive (energy sensitive) units. Sometimes they were photoelectric units. In recent times, dual range units have become available that also provide a filter combination matching the smoothed C.I.E. scotopic luminous efficiency function. Such units suffer from the archaic nature of the C.I.E. standards and can only emulate the performance of the eye that is not chromatically adapted and is not operating in the mesopic or lower photopic regions. To emulate the visual system in these regions, a more sophisticated instrument would be required. This instrument would sense the individual spectral ranges of each photoreceptor channel, introduce a squareing mechanism in the long wavelength channel and sum the resultant signals logarithmically in accordance with the luminance equation.

13Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons pp. 100-105 Performance Descriptors 17- 15

An early design of a typical multichannel photometer was described by Sziklai14. He accepts the imaginary aspects of the CIE tristimulus functions and compensates for the artificial hump in the x-bar channel. He was apparently unaware of the square-law nature of the L–channel. Thus, his design is more properly labeled a tristimulus photometer for the photopic region only. Thornton has more recently defined a similar photopic regime only multi- band photometer.

17.1.2.1.3 Precision requires photon-flux based radiometric units

Although photometric units have been used throughout the exploratory phase of vision research, the precision required in future precision research demands the use of more precise spectroradiometric units. This will be demonstrated throughout the remainder of this chapter. The photometric system of units is only adequate for the design of general and photographic systems. The majority of the instruments sold as photometers are single channel devices that measure an integrated response over a given spectral region weighted to match the CIE photopic luminosity function by a transmissive filter. In some cases, the filter can be changed to emulate a scotopic luminosity function. However, the luminosity function varies continuously in the transition from the photopic to scotopic region. Most of these units employ energy sensitive rather than photon-flux sensitive detectors. These weight the spectral content of the sensed image improperly and are not capable of emulating the HVS. More seriously, these units are not able to emulate the adaptation characteristics of the visual system or the logarithmic signal summation mechanism employed in vision. These are serious handicaps when performing research.

By using a modern spectroradiometer with computer interface, the researcher can enter the actual spectral absorption of the individual chromophores and logarithmically calculate the actual luminosity function of the visual system for any illumination level.

17.1.2.2 The precise definition of “color”

Defining color with precision has been a problem for centuries15. Fehrman & Fehrman even go so far as to define color as an illusion16. However, as any magician will tell you, something is an illusion only to those that do not understand the trick. Relying on logic and their assertion that color is an illusion, Fehrman & Fehrman continue and define color as an intangible, “a vast interactive process.” This section will show that color is not an illusion, is not intangible and is not interactive with the sensor. It is a rigorously defined phenomena. If as they state, the color experience only exists within the observer’s brain, it would be impossible for a television system to create the common A-scope and C-scope presentations. These presentations are created at the studio using non-color cathode ray tubes, to monitor the quality of the “color” sensed by the electronic circuitry. It would also be a waste of time for the (currently very large) robotics community to attempt to create robotic eyes.

It is also necessary to address some recent comments by Goldsmith17. He attempts to separate the perception of color by certain animals from the wavelength dependent behaviors of other animals. Naturally, being homocentric, he initially limits the perception of color to humans. He then broadens this capability to other primates and then broadens it further to include his life long subjects, bees. This distinction is not supported here. It can be shown that the same differential chromatic signals are transmitted to the brains of any number of animals crossing all phylogenic lines. Whether one wishes to say one animal appreciates the color of an object more than another is probably

14Sziklai, G. (1951) A tristimulus photometer J. Opt. Soc. Am. vol. 41, no. 5, pp 321-323 15Crone, R. (1999) A History of color. Boston, MA: Kluwer Academic Publishers, pg. 247 16Fehrman, K. & Fehrman, C. (2000) Color; the secret influence. Upper Saddle River, NJ: Prentice-Hall, pp. 1-2 17Goldsmith, T. (1994) Ultraviolet receptors and color vision: Evolutionary implications and a dissonance of paradigms. Vision Res. vol. 34, no. 11, pp 1479-1487 16 Processes in Biological Vision

permissible. However, all animals use these signals to make wavelength dependent behavioral decisions. I personally do not eat Rhubarb because of the color. I know it is virtually identical to celery. So what! Whether this is behavioral or intellectual will be left to the reader.

A specific solution to the definition of color and individual colors will be presented in Section 17.3.4.

17.1.2.2.1 Expanding the definition of colorimetry

Colorimetry has been defined by Wyszecki & Stiles (p. 117) as “The branch of color science concerned in the first instance, with specifying numerically the color of a physically defined visual stimulus.” They then continued by appending to the definition a series of conditions allowing the human eye to be used as a null detector in colorimetry experiments. In essence, the conditions required an illumination level in the photopic regime (in order to insure color constancy) and a numerical framework that uses continuous functions. To complete the framework, Wyszecki & Stiles invoke what is generally described as the trichromatic generalization:

“Over a wide range of conditions of observation, many color stimuli can be matched in color completely by additive mixtures of three fixed primary stimuli whose radiant powers have been suitably adjusted. Other color stimuli have to be mixed with one of the primary stimuli before a complete color match with a mixture of the other two primary stimuli can be obtained.”

Within the above framework, many simple concepts, such as Grassman’s Laws have been adopted without detailed justification. However, the above context does not allow for any variation in the performance of the visual system with retinal position, or under non-photopic conditions, or under transient conditions. Under these conditions, a broader framework is required.

To provide a broader framework, it is useful to define that part of colorimetry defined within the laws of linearity as object-space colorimetry. Within this framework, the visual system is used as a null detector in steady-state laboratory measurements. Flicker experiments and experiments using a rotating wheel are not included in the field of object-space colorimetry. Most commercially available instrumentation is limited to this operating regime. The broader framework encompassing all visual conditions can then be defined as perceptual colorimetry. The intensity nonlinearity, spatial irregularity, and transient performance of the visual system are accommodated within this regime. Most commercial instrumentation designed for photometry and colorimetry is inadequate in this extended colorimetric framework.

17.1.2.3 Metameres, initial conceptual definitions

A major problem in previous discussions of color has been the problem of . Many sources in object space with different spectral distributions can appear chromatically identical to the human eye. These scenes are called metameres.

Wyszecki & Stiles introduce metameres in their chapter 3 at primarily a conceptual level. The material quickly degenerates into requiring an “imaginary color stimulus” because of their underlying trichromatic generalization (pg 117). They provide two definitions of metamers on page 184;

Metamere color stimuli are color stimuli with the same tristimulus values but different spectral radian power distributions.

An equivalent definition states that metameric color stimuli are color stimuli that have different spectral Performance Descriptors 17- 17

radiant power distribution but match in color for a given observer.

These definitions require the control of many parameters that are not described further here. These parameters are discussed more fully in Section 17.3.4.3.1.

Two additional definitions are important in discussing metameres, that of metameres of course and also of color.

Color– (a. k. a. perceived color) that aspect of by which an observer may distinguish differences between two structure-free fields of view of the same size and shape, such as may be caused by differences in the spectral composition of the radiant energy concerned in the observations (W & S, p. 487).

The above can be considered the formal definition of color. It is based on perception. An alternate definition is frequently useful that describes the color of a structure-free field of view in object space that generates the above perception. This definition of color is frequently described as psychophysical color.

Psychophysical color– that aspect of a structure-free field of view in object space specified by the tristimulus values of the radiant power (color stimulus) entering the eye.

Both of the above definitions of color play a role in current colorimetry. However, it will be shown below that it is only the definition based on perception that is precise. Many pairs of psychophysical metameres do not in fact appear to be metameres to the human eye. The differences are frequently significant.

Metameres have traditionally been defined in the psychophysical context and is the only context discussed in the colorimetry chapter of Wyszecki & Stiles. However, the fact that two different structure-free fields of view with different tristimulus values frequently appear to be perceptual metameres is troubling18. As a result, this work differentiates between the two definitions of Wyszecki & Stiles that they considered equivalent.

Metameres– (a. k. a. perceptual metameres) color stimuli that have different spectral radiant power distributions but are perceived as identical for a given observer.

Psychophysical metameres– color stimuli that have the same tristimulus values but different spectral radiant power distributions.

Wyszecki & Stiles explored the subject of psychophysical metameres in great detail (38 pages)19. Whereas the data they summarized is useful, the mathematical analyses are less useful. They attempted to explain the phenomena using the CIE concepts of color space and tristimulus values (based on linearity and ). The result is a definition of metameric color stimuli unrelated to biological vision. This definition required that two metameres must exhibit equality in three equations, one related to the tristimulus value r-bar, one related to g-bar and one for b- bar. Thornton has shown that colors defined in this way are not in fact perceptual metameres (Section 17.2.8).

Adopting the actual model of biological color vision, the situation is simpler and more precise. Instead of using the tristimulus values of an imaginary “Standard Observer,” the actual absorption characteristic of each chromophore of biological vision is used. Omitting any discussion of the O-channel in human vision, three equations are required to demonstrate a complete metameric match between two color stimuli. However, they are not the three equations found in psychophysical colorimetry. Equation One equates the P-channel values for the two metameres. Equation Two equates the Q-channel value for the two metameres. Equation Three equates the R-channel values for the two

18Thornton, W. (1992) Toward a more accurate and extensible colorimetry. Part 1. Introduction Color Res Appl vol 17(2), pp 79-122 19Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. John Wiley & Sons pp 183-221 18 Processes in Biological Vision

metameres. These equations allow for a much larger set of metameres and a much more precise match than does the tristimulus formulation. This range of matches can be subdivided into three distinct classes, the first requiring a precise match in each of the P, Q & R values of the color stimuli, the second requiring a complete match of two ensembles of P, Q & R values and the third requiring a chromatic match of only the individual P and Q values.

While precise metameric matches can be calculated, it is not possible to confirm the uniqueness of such precise matches perceptually at this time. As far as is known, the brain only asserts a complete match based on the somewhat more tolerant ensemble values of P, Q & R. Figure 17.1.2-1 shows the experimental environment associated with chromatic and complete metameric matches. The simpler chromatic match shown in frame (A), typically uses the light reflected by two color samples from a single source of illumination. Because of the interplay of the radiation spectra of the source and the reflectance spectra of the samples, such chromatic matches are a function of the source characteristics. Besides the spectral distribution of the samples in chromatic matches, the match also depends on the average reflectance of the samples used. As a result, the chromatic match equating the P and the Q values may not result in equal R values. Experiments are currently under way to resolve the differences in average reflectance between the currently distributed Munsell Color Atlas and the recently developed comparable Japanese atlas. Frame (B) shows the test configuration for achieving a complete metameric match. By using two separate illumination sources of variable intensity, a match may be obtained that equates the individual P, Q & R values. When obtained, the match is based on the radiant spectral characteristics of the sources and the average reflectance of the samples as well as the reflectance spectra of the samples.

Figure 17.1.2-1 Test configuration for metameric matching. A; configuration for making chromatic matches using a single common light source. B; configuration for making complete matches using independent light sources. Lower row; set of relevant performance parameters. See text.

The functions shown in the lower set of frames suggest the parameters that can vary and that must be controlled in these two types of experiments. If two sources are employed, both their intensities and radiant spectra must be controlled or known. The reflectance of the two samples can be significantly different. Scattered light must be minimized for accurate comparisons. The absorption spectra of the actual photoreceptors must be used, and not some arbitrarily transformed set of spectra. While the resulting signal levels at the axons of the spectrally diverse photoreceptors may be of interest, it is the signals resulting from signal processing within the neural section of the Performance Descriptors 17- 19

retina that are critical to the metameric experiment. It is these signals that are evaluated by the brain in determining a match.

Several second order caveats apply to performing successful metameric matches. Because of the change in the spectral sensitivity of the visual system with intensity of the color stimuli, the experiments should be carried out within the photopic regime, and more precisely the regime of color constancy. To avoid inaccurate results, it is also necessary to carefully define the test protocol used. The most successful tests require a bipartite field with the match determined by concentrating the point of fixation of vision on the midpoint of the bisecting line of the bipartite field. To avoid introducing ambiguities due to Maxwell’s Spot (Section 17.3.1.7.2), it is advisable that the bipartite field have a diameter of less than 1.2 degrees, or much larger than three degrees. Large fields of ten degrees are commonly used. The area surrounding the test samples will affect the state of adaptation, and therefore the color constancy, of the eyes of the evaluator. This area is best made a neutral color not significantly different in illuminance from that of the samples. The details related to matching experiments are described in greater detail in Section 17.1.9.1 and more fully discussed in Section 17.3.1.3.1.

The task of integrating the spectral distribution of a broadband source to establish a P– or Q– value requires determining what the appropriate wavelengths delimiting the range of integration are. This subject needs additional study as of 2016.

17.1.2.4 The “expanded exponential sinusoid” SCREWED UP ART

The fact that the simple exponential curve does not represent either of the two commonly studied branches of the dark adaptation characteristic has been recognized for a long time. The reason is simple. The underlying processes are not described by an exponential equation and the expression of these underlying processes is not through a linear relationship. The underlying process is a higher order physical one describable by a nominally second order (sometimes third) differential equation. The solution of such an equation can take three forms depending on the damping factor in the equation. The most common form is the product of an exponential term and a sinusoidal term. It is frequently labeled an exponential sinusoid. This solution specifies the voltage on the collector of an amplifier circuit in the absence of coupling to other amplifiers via the vascular supply. The variation in this voltage significantly impacts the gain of this amplifier. This variation is normally expressed in the form of:

“The Expanded Exponential Sinusoid” Eq. 17.1.1-a

For appropriate values, such an expression still looks similar to an exponential sinusoid but clearly is not. It appears stretched in amplitude because of both the exponent and the difference in the denominator.. Therefore, it will be labeled a “expanded exponential sinusoid” for semantic convenience.

If the coupling between amplifiers via the vascular system is assumed, the solution takes a different form that allows the amplitude of the sinusoid term to vary independently of the amplitude of the expnential. This solution can be written as:

1 “Alternate Expanded Expon.Sinusoid” Eq. 17.1.1-b y = n 11−⋅+[]eAxx ( sin(ω ⋅ ) 20 Processes in Biological Vision

In this form, the waveform may or may not exhibit a shoulder depending on the magnitude of the coupling represented by A. In the case of a distinct shoulder, the termination of the plateau is frequently labeled the α-break or, because of reliance on the duplex theory, the rod-cone transition. This putative relationship is illusory.

In a second solution of the above second order differential equation, the sine function disappears and the expression found in the dark adaptation characteristic is of the form:

1 “Extended Exponential” Eq. 17.1.1-c y = n 11−⋅+⋅[]exx ( ω

This solution also looks similar to an exponential but clearly is not. For appropriate values, it appears to be changing more slowly than expected with time. Therefore, it is labeled an “extended exponential” for semantic convenience. It does not exhibit a shoulder. Wachtmeister uses the term “kohlrausch kink” to describe the abrupt change in slope associated with this waveform.

17.1.2.5 Nomenclature associated with the composite ERG and LERG

The ERG and LERG are discussed widely in the literature. Interpreting this information requires a careful determination of whether the data was acquired in response to a change in illumination characterized as a long pulse relative to the time constants of the eye or in response to a short pulse, mathematically an impulse. For the intermediated condition, pulses of 0.1 seconds to five seconds, the interpretation becomes considerably more complex.

The literature contains an impressive list of labels for various features associated with the ERG waveform that reflect the observational history of the ERG. The original names date from Jolly (1908) and were assigned in time sequence to markers for responses due to unknown mechanisms. It is now possible to associate most of the names with the underlying source of the features. However, it is necessary to reject any chemical bias and adopt the fundamental electrolytic nature of the neuron system to do this. The ERG is basically a global summation of the individual voltage waveforms from;

+ the photoreceptor cells, both Class C and D waveforms,

+ from a combination of the lateral and bipolar cells of the signal manipulation stage, Class E waveforms, and

+ under appropriate conditions voltage waveforms from the ganglion cells of the signal projection stage, Class F waveforms.

Because the summation may contain signals from the lateral cells, it has an inherent variability based on the spectral content of the illumination used in the experiments. When present, the signals from the ganglion cells introduce a variability based on the amplitude of the test signals as they exist within the signal manipulation stage. To obtain repeatable results between laboratories, it is absolutely necessary to specify the spectral characteristics of any illumination (both test, background and preadaptation) explicitly and to define the adaptation state of the subject completely. If Class F waveforms are present, the amplitude of the illumination must also be carefully documented–especially with regard to signal changes relative to any background. Under these conditions, the observational based labels become unique characteristics of the source waveforms. Performance Descriptors 17- 21

A group of authors writing in Heckenlively & Arden20 have provided the most comprehensive, consistent and up-to- date discussion of these ERG features, using about half of the letters of the alphabet in the process. Their perspective is primarily from the medical clinic. Because of this focus, they do not address the a-wave and b-wave in detail. To save space below, these authors will be addressed by name followed by the expression “in H & A–pg xx.” A tabulation of all of these features (waves) appears in Section 11.1.3. As pointed out on H & A–pg 91, some of these waves are only observable with direct current electroretinography (dc-ERG) or electro-oculaography (EOG), both external forms of retinography. The a-wave and b-wave are frequently not resolvable in clinical ERG apparatus. They require more intensive instrumentation or the use of LERG techniques to resolve them because of the signal levels and impedances involved. The basic ERG sums the individual signals from millions of individual detectors, through the use of Ganzfeld illumination, in order to achieve adequate signal levels for recording purposes. Frequently, this summing is not adequate and additional data reduction procedures are necessary. Much of the literature includes waveforms resulting from the averaging of a large number of individual experiments to eliminate random noise and asynchronous signals from the final result. One of the remarkable features of the retina is the uniformity of its signaling channel topology and topography. Without this uniformity, it would be impossible to perform the amount of averaging found in most ERG figures.

Granit provided an early attempt to describe some of these features using his potential waves, PI, PII, and PIII. They were named based on their sequence of disappearance under anesthesia. His instrumentation was pre-transistor and less capable than used today. Page 7 of Heckenlively & Arden provides a description of Granit’s waveforms prepared by Riggs and a conversion between Granit’s notation and some of the more modern notation. The old nomenclature will not be discussed here.

The various features of the ERG are usually discussed based on a recording where a positive voltage on the cornea relative to a second return electrode is drawn as up. The location of the return electrode is frequently a matter of discussion. As shown earlier in this work, this is because of the fact that the ERG is essentially recording the currents in various “ground loops” of a complex and relatively poorly designed (from this particular perspective) electronic system. The voltage recorded is due primarily to these currents passing through impedances associated with ground bridges between various ground planes. See Section 11.1.1.3. Thus, the recorded signals are a function of where the signal and return leads are positioned relative to this multiple ground plane visual system. This fact is explicitly illustrated in figure 9-2 by Griff in Heckenlively & Arden. He shows three waveforms recorded by three probes in response to the same event. The signals are quite different and even have inverted features relative to each other. The caption to his figure 9-4 illustrates the problem further. He pointed out that the transretinal potential was inverted and superimposed on the transepithelial recording, and then states that it was coincidental that both recordings had equal amplitude. In the context of this work, they should have the same amplitude if they were due to the same event, the probes were both located quite near to the source of that event and the test equipment was not impacting the measurements.

There is reason to believe that some of the data recorded by the ERG may emanate from the initial circuits of the cortex, particularly when the earlobe is used as a signal return or as a ground lead.

The literature of the LERG and its variants is briefer and considerably more recent. As probability might suggest, the experimenters in electrophysiology involving probes have frequently chosen the opposite polarity for their graphic presentations compared to the ERG community. For consistency in this section, the a-wave will be taken as negative going regardless of the potentials sensed by a given probe configuration. (See Section 17.6.2)

Until quite recently, with development of the suction pipette technique, virtually all ERG and

20Heckenlively, J. & Arden, G. (1991) Principles and practice of clinical electrophysiology of vision. St. Louis, MO: Mosby Year Book 22 Processes in Biological Vision

LERG measurements represented voltages. This has now changed. Excellent current data (more fundamental) is becoming available.

Because most of these waveform definitions are based on one of two approaches; external observation followed by probing and/or external observation followed by pharmaceutical experiments, it is natural for different authors to attempt to subdivide individual waveforms into component waveforms based on the their proclivities and approach. Lacking a specific and generally accepted top level schematic of the visual system, this generally leads to an assortment of putative origins for these waveforms. This appears to be a particular problem with the b-wave. It has been subdivided into an early and late b-wave, putatively defined in terms of the ever convenient rods and cones. It has also been subdivided into both AC and DC waves. In general, a simpler cause of these two waveforms measured by the same probe under different, and sometimes simultaneous conditions, is the different response of chromatically distinct photoreceptor types to different levels of excitation. This will cause a different delay and slope in each of their Class D waveforms. Their summary waveform will satisfy the observed phenomena. These waveforms are frequently discussed in some texts as components of the early receptor potential. However, the early receptor potential is related to the Class C waveforms emanating from the dendrites of the photoreceptors located in the Outer Segments.

17.1.2.6 Concepts relating to optics

For research purposes, the physiological optical system is much more complex than the commonly used Gaussian approach to optics can support. The optics is fundamentally an elliptical (non-spherical) thick (not thin) lens system employing gradient (not fixed) index materials in a variable (not fixed) focal length system with a highly curved (not flat) Petzval surface. The retina is shaped to match this Petzval surface. However, the point of fixation, commonly taken as determining the visual axis along with the center of the pupil, is not coincident with the optical axis of this system. These facts have not usually been recognized by the publications from the more practically aligned schools of optometry. The difference significantly impacts discussions of the actual spatial performance of the combined physiological optics and the retina.

17.1.2.6.1 Spatial characteristics of the physiological optics and retina

Although the common wisdom is that the variation in size and lattice geometry of the retina causes the variation in spatial resolution of the eye, this is not supported by the documentation or theory. The lattice spacing varies by little more than a factor of two while the spatial resolution varies by significantly more than a factor of ten with field angle. The variation is due primarily to the physiological optics. The performance of the optics is described fundamentally by the photon flux density profile at the Petzval surface. Although actually a density profile, the projection of this profile on the Petzval surface is known as the Airy disk (and the disk exhibits concentric rings around it in high quality optical systems). The profile and disk are both two dimensional and the two elliptical axes of these features grow rapidly with field angle. The profile is generally not symmetrical. Therefore, the spatial resolution associated with these profiles is determined by the complete two dimensional Fourier transform, not just the Fourier cosine transform or the Laplace transform. Although difficult to determine, Daugman (discussed below) provides an excellent data set of the spatial resolution of the physiological system in the human eye. Only in special cases is the one dimensional Fourier transform adequate to describe a test configuration in visual optics.

To discuss the spatial resolution of the retina, it is important to know more than just the lattice spacing and photoreceptor size. It is necessary to make estimates about the lattice constants of each individual chromatic type of photoreceptor and/or how the signals from these photoreceptors are used in perception. Currently, there is virtually no precise data about the lattice constants of the various chromatic photosensing channels. Based on behavioral data, it appears that the luminance channel is used to evaluate the spatial resolution capability of the system. The chrominance channels can be used for such evaluations only after careful coaching of the subject in what appears to Performance Descriptors 17- 23

be an un-natural situation. If the luminance channel is used, the dominant signaling component in this channel is the M-channel.

17.1.2.6.2 Computing the limiting optical performance of the visual system

Figure 17.1.2-2 illustrates the true purpose of the iris in the human eye. Without it, the system could not be optimized as effectively over a broad range of illumination. With it, the system operates at reduced aberration during high luminance by using a higher f /# (smaller pupil). As the available light level decreases, the pupil opens. The resulting f /3 lens provides more light to the retina but the quality of the image actually decreases due to the aberrations associated with an elliptical lens system optimized for a very wide field of view. This is contrary to the operation of a modern well corrected but narrower angle lens-film system wherein a lower f /# actually gives higher resolution imagery. The graphical technique combines the scene and luminance parameters with the spatial frequency performance of the lens system in the upper but falling curves and combines the threshold noise of the cortex referred to the retina and spatial resolution of the retina on the lower rising curves. The Aerial Image Modulation (A.I.M.) point defines the operating point of the system under a given set of conditions.

17.1.2.7 Concepts involving resolution and bandwidth

The concepts of spatial and temporal resolution, and spatial and temporal bandwidth have been treated very awkwardly over the years in the vision literature. There have been many reasons. First, the psychophysical community have necessarily been performing end to end experiments without significant knowledge of the actual detailed mechanisms Figure 17.1.2-2 Concept of optimizing the performance employed within the visual system. In many cases, the of an imaging system using a variable iris with a badly aberrated lens system.. At f/8, the lens-retina system Duplex Theory, the Univariance Principle and the operates at maximum performance (spatial frequency) but assumption of Linearity in the system have led them to requires a lot of light. At lower light levels, an f/3 is design experiments that can now be shown to be required but performance is still lost because of the inappropriate. Second, the mathematics required in aberrations of the elliptical optical system. describing these concepts properly and completely is beyond the scope of algebra and simple calculus. Third, the difference between the available channel bandwidth and the bandwidth of the signal occupying that channel has not always been appreciated. Fourth, in the absence of an adequate top level schematic of the visual system, it is impossible to design an adequately controlled experiment to describe these aspects of the system precisely.

A particular problem has been the description of the temporal bandwidth of a signal produced using two different (poorly specified) colors to excite the visual system. The assumption has been made universally that the visual system is in some sense linear and that the perceived responses are representative of the temporal or spatial bandwidth of the system. Unfortunately, the system is neither linear nor additive. This fact is demonstrated by the wide range of results obtained by different investigators using similar experimental protocols.

The relationship between the spatial resolution of the physiological optics and the temporal bandwidth of the neural signals is a complex one. It involves very subtle and complex signal encoding that is well beyond the scope of simple illuminated bar charts, mondrians and checkerboards. 24 Processes in Biological Vision

An additional problem involves the fundamentally different operating mode of the signaling system with respect to the foveola versus the remainder of the retina. The majority of the retina is used in a staring mode for purposes of alarm against danger. It is fundamentally a change detector with a wide field of view. The foveola, on the other hand, operates in an imaging mode through the introduction of a tremor developed by a specialized servo system. This part of the system is fundamentally an interrogator of a small portion of the scene.

17.1.2.7.1 Temporal bandwidth of the signal generated by the P/D process

The literature has not generally recognized that the signal generated by the photoexcitation/de-excitation process exhibits a variable upper frequency pole in its temporal frequency spectrum. The frequency of this pole is a function of the irradiance absorbed by the chromophores associated with each specific photoreceptor cell. Therefore, the temporal bandwidth of a composite luminance signal resulting from a broad band radiation source may exhibit separate maximum frequencies for each chromatic component. This can cause minor variations in the signal amplitude as a function of temporal frequency. However, this would only be recognized in highly structured and carefully designed laboratory experiments. The description of the signal observed in the chrominance channel is more dramatic and is discussed below.

17.1.2.7.2 Temporal bandwidth of the generator waveform

The temporal bandwidth of the generator waveform recorded at the pedicel of the photoreceptor cells can be quite complex due to several factors. First, the adaptation amplifier introduces a low frequency pole at about 0.1 Hz. When combined with the high frequency poles of the P/D process, the result is a bandpass characteristic. If the signal current passed to the pedicel is high, the logarithmic conversion to a voltage occurring at the pedicel is a non- linear process resulting in changes to the spectrum of the signal. If the signal current from the P/D process is very large, it may also cause saturation in the adaptation amplifier. This also introduces a non-linear process that can distort the spectrum further. The nature of the changes in the signal spectrum are complex functions of many parameters. These last two conditions are of limited interest in this work and will not be explored further.

17.1.2.7.3 Temporal bandwidth of signal resulting from signal summation

If two broadband signals that are in phase but of different bandwidth are added together, the resulting signal envelope in amplitude versus frequency space will be additive also. The result is a spectrum that is the sum of the two spectrums at each frequency along the frequency axis. Such summation will not result in any nulls in the spectrum that were not in both of the initial spectrums.

17.1.2.7.4 Temporal bandwidth of signal due to signal differencing

The minimum and maximum frequencies associated with a signal resulting from the difference between two signals does not vary from the lowest minimum frequency and the highest maximum frequency of the pair unless non- linearities are introduced into the processing.

There are two distinctly different methods of signal differencing in vision. The first occurs in the image plane of the optics and is due to the coherent nature of light itself or of the patterns created in the light. The second occurs in the signal manipulation stage of the retina and is purely electrical in character. These methods can introduce nulls into the resulting temporal frequency spectrum.

Many experiments have been performed demonstrating notches in the spatial frequency response of the eye due to interference effects. These are classic physics demonstrations applicable to any optical system employing Performance Descriptors 17- 25

electromagnetic radiation. Similarly, experiments have been performed using harmonic waves in spatial coordinates to create null patterns in the image formed on the Petzval surface of the optics. These demonstrations do not relate directly to the performance of the visual system. They relate to the unique conditions under which the radiation is presented to the eye. The fact that the resultant electronic signals in the temporal frequency domain exhibit these same effects is incidental.

Within the chrominance and appearance channels of human vision (and the polarization channels of other animals), signal differencing occurs. In the human, most of this differencing occurs in the chrominance channels receiving signals from the output of the photoreceptor cells. It is the nature of differencing that if the two signals are of equal amplitude, the net response will be zero, a null condition. If the two signals are the result of a single signal of variable spectral wavelength being applied to both of the channels being differenced, it is possible, although unlikely in vision, to measure a spectral response with any number of nulls in it. Normally there is one null spectral frequency associated with each chrominance channel. Under dark adapted conditions, or in response to equal flux illumination in object space, these nulls occur at 494 nm in the P-channel and at 572 nm in the Q-channel. The presence of these nulls is critical to the operational architecture of the visual system. A simultaneous null in both of these channels results in the perception of an achromatic or scene. In the presence of non-equal-flux illumination, the adaptation amplifiers of the two photodetection channels will change gain. Because of this change in gain, the spectral wavelength of the null(s) in object space will change. This is the mechanism that causes the eye to compensate for unusual lighting conditions after a period of time and still perceive a white table cloth when illuminated by a distinctly colored light.

The above discussion relates to the spectral content of the signal and not the channel through which it travels. In no case is the resultant signal spectrum to be considered a description of the visual channel temporal bandwidth. This work has not encountered any situation that suggests that the temporal bandwidth of the channel employed in signal detection or signal manipulation is a limiting factor in the visual process. Within the signal projection stage, there are clear limitations on the signalling channel which will be discussed later.

17.1.2.7.5 Temporal bandwidth of the spatial signal from the foveola

Because of the limited spatial resolution of the physiological optics outside the fovea, operation of the eye in this domain relies primarily on temporal changes in illumination to signal an alarm. The alarm causes the line of fixation of the eye to be brought to coincide with the line of sight to the change. It is only in the area of the foveola that the spatial performance of the optics is converted into a temporal signal for careful analysis in the cortex. This is done by introducing a tremor into the line of fixation. As a result, the fine spatial detail in the scene is converted into fine temporal detail in the signaling channel. Speaking in the frequency domain, this is done by multiplying the spatial resolution in cycles/angular degree, by the velocity of the tremor in angular degrees/second, to obtain the spectral resolution in cycles/second. The calculation is easier if the tremor is of constant velocity. However, this is impossible over any extended interval. The tremor can emulate this condition however if the muscles introduce an impulse into the rotational state of the ocular globe. There is little data on the angular characteristics of tremor. It is difficult to measure. However, it is defined by a wideband signal with a fundamental frequency near 30 Hz and extending to 90 or 150 Hz. If the harmonics and phase of the angular rotation are appropriate, the tremor would be represented by a sawtooth waveform approximating a constant angular rotation for over 80% of its period. This waveform would result in a nearly linear transform of spatial resolution of the image into temporal resolution in the signaling channel(s). Note that this process results in the spatial information being encoded in sidebands of a carrier frequency, equal to the nominal tremor frequency of 30 Hz, within the signal frequency spectrum. There are suggestions in the data base that the tremor consists of two orthogonal components supporting encoding that exhibits a nominally vertical and horizontal component. If present, these components could be easily orthogonally decoded in the Auxiliary Optical System (AOS) of the neural system.

The presence of orthogonal encoding of the spatial data around a carrier frequency of 30 Hz strongly suggests that 26 Processes in Biological Vision

the decoding of this information occurs separately from any chromatic information since this same temporal frequency regime is used for chrominance signal encoding. The conclusion can be drawn that interrogation of fine scene detail, by the closed loop servo mechanism that includes the foveola and AOS, is accomplished using only the direct signal pathwasy leading from the foveola to the Pretectum. This is accomplished irregardless of the chromatic sensitivity of individual photoreceptors in the fovea.

17.1.2.7.6 Temporal bandwidth of the channel supporting signaling

Electrophysiological experiments generally support a maximum temporal frequency of action potentials within the signal projection stage of 100 Hz or possibly up to 150 Hz. This value is found in both the luminance and chrominance channels. This maximum channel bandwidth appears adequate to support the signal encoding used in both the luminance and chrominance channels. Within the signal manipulation stage, the upper limit of the channel bandwidth is very difficult to measure. However, the nature of the electrical circuit elements present and the architecture of the circuits would suggest it is at least 100 Hz. wide. Risetime measurements of the generator potentials, Class D, as they pass through the signal manipulation stage could provide new and precise information in this regard. The available replicas of the Class D waveform found within the retina suggest that no degradation due to channel bandwidth has occurred.

The low pass limit of the signal manipulation stage is controlled by the adaptation amplifier in its operation to remove the wide average illumination range of the incident radiation. The half amplitude low frequency pole is at 0.1 Hz.

The signal projection stage of vision does introduce limitations on and distortions to the signals passed from the retina. These limitations and distortions are of minimal importance in normal vision, especially in society prior to the 20th Century. During the 20th Century, everything from the Kinetoscope to the switched laser has contributed to effects that are distorted when passed through the signal projection stage. The results range from the trivial (after- effects), to the practical (movies and television) to the mysterious (magic).

17.1.2.8 Cartography requires conformality

Lacking significant theoretical input, the vision community has adopted various coordinate systems based more on conceptual analyses than any formal rigor. As found in cartography, the proper display of data requires compliance with certain rules. These rules insure that the graphical presentation of the data can be used to draw meaningful conclusions. The rules are grouped under the mathematical title of conformality.

A map maker usually encounters two conflicting choices21. When given a set of datapoints, he must choose whether to make distances proportional to the actual case or to make the shapes of objects correspond to the actual case. He seldom has the option of achieving both. Conformality relates to the level to which these two criteria are met. It involves two conditions, the orthogonality of the presentation and the equiangularity of the presentation.

Conceptual attempts to describe color perceptions in terms of an equilateral triangle has formed an awkward legacy in vision. The tendency has been to define degrees of color in this space using scales perpendicular to each of the three sides. Such scales are clearly not orthogonal. Attempts to project this triangular space onto an orthogonal coordinate system (such as the C.I.E. XYZ color space) result in a new coordinate space wherein the angles related to features in the old space are greatly distorted. This is caused by the lack of proportionality between the unit vectors associated with the axes of the new space compared to the old space. This is illustrated by:

21Robinson, A. Morrison, J. Muehrcke, P. Kimerling, A. & Guptill, S. (1978) Elements of Cartography, 6th ed. NY: John Wiley & Sons Gt() j PerformanceGt( ) Descriptors 17- 27 ⋅ R(t) = F(t).i + G(t). j where Θ = arctan Ft() i and θ = arctan Ft()

“Vector form of R(t) and constructs” Eq. 17.1.2-1

Θ is the apparent angle in the new graph and θ is the intrinsic angle associated with the underlying data or graph. In this case, the angles in the new graph only equal those in the original if the ratio of the two unit vectors is equal to 1.000.

17.1.2.9 Conceptual loading of the signaling channels

Figure 17.1.2-3 provides a cartoon of the utilization of the signaling channels in human vision. The upper frame describes the luminance channels of vision. The lower frame describes the chrominance channels. In both frames, the solid lines represent the bandwidth capacity of the channels. The dashed lines represent the bandwidth of the signal content. Although clearly different and supporting different requirements, the similarity of the visual system to the systems developed by man to provide color television service are striking. Two subcarriers are shown at the nominal frequencies used throughout this work. In the upper frame, only one tremor carrier and one set of sidebands are shown supporting the foveola. There may be two separate sets of sidebands associated with the foveola and transmitted in morphologically separate orthogonal channels. These separate channels would support separate vertically and horizontally oriented sections of the AOS. There is probably no signal related to the tremor carrier in most of the peripheral luminance channels of the signal projection stage. The peripheral signals appear to be transmitted at baseband.

In the lower frame, the two chrominance channels are shown superimposed for convenience. They would actually be transmitted over morphologically separate channels within the chrominance channels of vision. Although not demonstrated, the literature appears to support the genetic choice of the wider, and faster responding, upper sideband for the signals related to the M-photoreceptor channels. The S- and L-channel signals appear to occupy the narrower, and slower responding, lower sideband.

The subcarriers associated with the chrominance channels and the foveola are created by distinctly different mechanisms. One mechanism involves physical motion (tremor), the other a free running electronic oscillator.

Figure 17.1.2-3 Concept of the temporal spectrum utilization in the human visual system. Upper frame shows the luminance channel for both the peripheral channels and the channels supporting the foveola. Lower frame shows the two chrominance channels superimposed for convenience. See text. 28 Processes in Biological Vision

17.1.3 Glossary

Discrete regions of radiant intensity based on the mechanisms of vision

Hypertopic region –The very highest level of radiant intensity tolerated by the visual system in the absence of pain. The region is characterized by hard signal saturation in one or more of the spectral channels (usually the M-channel). Hard signal saturation implies no change in current through the channel as a function of input intensity. The subject typically perceives a yellowing of any object in the field of vision.

Photopic region –The operating region of the visual system where all of the adaptation amplifiers of the individual spectral channels are all operating at amplification factors greater than 1.0 but none have reached their maximum gain.

Mesopia– A clinical syndrome describing the limited performance of the visual system under certain conditions. See mesotopia and Section 17.3.3.6.1.

Mesotopic region – 1. The operating region wherein one or more of the spectral channels of vision is operating with its adaptation amplifiers at maximum gain. Color constancy is lost under this condition.

2.The operating region below the photopic region characterized by the L- channel adaptation amplifier operating at full gain but the L-channel signal falling more rapidly than in the M- and S-channel signals with falling illumination levels. Signal to threshold performance is typically limited by quantum noise fluctuations in the illumination. A region of decreasing saturation in the perceived colors of objects due to a decreasing signal level in the P & Q chrominance channels relative to the threshold level. See mesopia and Section 17.3.3.6.1.

Scotopic region –The lowest operating region of vision characterized by all adaptation amplifiers operating at full gain but a complete absence of L-channel sensitivity in the spectral response of the eye. A region of achromatic vision due to the signal level in the P & Q chrominance channels falling below the threshold level.

Theoretical Photopic Luminous Efficiency Function

Defined as the threshold performance of the dark adapted eye as a function of wavelength measured with a photopic intensity probe (typically of 2 degree diameter and a flicker frequency between 1 and 20 Hz.) in the absence of any background illumination.

Not indicative of operation under actual photopic conditions (unless illumination is at a color temperature near 7053 Kelvin & scene at low contrast--typically below 2:1)

Performance is defined in terms of the perceptual recognition of the test probe in the presence of the natural thresholds present in the visual system without any determination of whether the probe exhibited a chromatic aspect (hue or saturation). The threshold is normally probabilistic under Performance Descriptors 17- 29

dark adapted conditions. However, it may be deterministic under other states of adaptation and in the presence of background illumination.

Theoretical Scotopic Luminous Efficiency Function

Defined as the threshold performance of the dark adapted eye as a function of wavelength measured with a scotopic intensity probe (typically of 10 degree diameter and a flicker frequency between 1 and 5 Hz.) in the absence of any background illumination.

Fairly indicative of operation under actual scotopic conditions due to natural lighting. Not indicative of operation based on low color temperature artificial illumination.

Performance is defined in terms of the perceptual recognition of the test probe in the presence of the natural thresholds present in the visual system without any determination of whether the probe exhibited a chromatic aspect (hue or saturation).

Visual Threshold

A term used in a variety of visual situations including both deterministic and probabilistic, absolute and differential, and monocular and binocular. Because the threshold model of the visual system has not been well defined, most uses of the visual threshold have involved the probability of perceiving a given stimulus or change in stimulus. In that case, the threshold is specified at a given probability value, p. Under more clearly understood conditions, the alternate approach is to assign a given signal to internal threshold ratio to the observed external visual threshold, where the internal threshold may be deterministic or probabilistic. In this scenario, the external visual threshold may be a function of the state of the adaptation of the visual system (and therefore a transient), a function of the degree of signal integration occurring before perception (and therefore a function of the signal integration capability of the visual system that is in turn a function of the size and duration of the applied scene), and a function of the background surrounding the scene.

Metameres–Two color samples that appear identical under identical illumination and surround conditions within the photopic range because they exhibit identical values of P and Q in the chrominance channels.

Trans-metameres--Two color samples that exhibit identical values of P and Q in the chrominance channels under different illumination and/or surround conditions and that therefore appear identical.

Brightness– The psychophysical perception of the intensity of an image in object space. This characteristic is a function of the intensity of the irradiance reaching the cornea of the eye and the state of the visual system. The brightness can be described in terms of a source of irradiance or as the result of reflectance of a source by an object in object space. The brightness is a function of the irradiance, the reflectance of the object, the transmission of the lens group and the state of adaptation of the eye, all as a function of wavelength.

Candela– The standard of luminous flux. (Current narrow band definition, 1979) The candela is the luminous intensity, in a given direction, of a source which is emitting monochromatic radiant energy of frequency 540"1012 Hertz (555.016 nm in standard air) and whose radiant intensity in that direction is 1/683 Watt (4.092"1017 photons) per steradian. An isotropic radiator of one Candela produces 0.0184 watts of light at 540"1012 Hertz. (Previous broad band definition) The candela was the luminous intensity, in the perpendicular direction, of a surface of 1/600,000 square meter of a blackbody at the temperature of freezing platinum under a pressure of 10,325 newtons per square meter (near 2042 Kelvin).

Irradiance, (E)– The absolute intensity of the radiation incident on the cornea of the eye and within the capture 30 Processes in Biological Vision

angle of the pupil of the optical system and the spectral passband of the visual system. The units are watts.

Irradiant spectral intensity, E(λ)– The absolute intensity of the radiation incident on the cornea of the eye and within the capture angle of the pupil of the optical system as a function of wavelength. The units are watts per unit wavelength.

Irradiant flux intensity F( λ)– The absolute intensity of the photon flux incident on the cornea of the eye and within the capture angle of the pupil of the optical system as a function of wavelength. The units are photons per unit wavelength.

Lightness– The perceived relative brightness of an element in a scene relative to a reference element. Generally described using a range from light to dark.

Lumen– (Current definition) The luminous flux of monochromatic radiant energy whose radian flux is 1/683 W (4.092"1017 photons) and whose frequency is 540"1012 Hertz (555.016 nm in standard air).

Modulation– The variation in the lightness of a scene element compared to a reference scene element (that may describe the background of object space).

17.1.4 The simplified block diagrams used to define the descriptors of vision

When discussing different aspects of the visual system, it is frequently possible to use a simplified block diagram. Such diagrams are presented in this section. While extremely useful, it must be remembered that some of the parameters associated with these diagrams are functions of the state of adaptation of the system. It is therefore necessary to specify whether the models are being used in the scotopic, mesotopic, photopic or hypertopic performance ranges.

The following Sections will examine the performance of the eye in each of the above performance ranges. Each of these major sections will use simplified graphical variants of the Top Level Schematic developed in Chapter 11. Sections 17.2, 17.3 and 17.4 will rely upon the block diagram shown in Section 17.1.4.2. Sections 17.5 through 17.7 will rely heavily upon the simplified oculomotor servomechanism diagram of Section 7.3.5 and the detailed circuit diagrams of Section 11.7.

17.1.4.1 The key role of adaptation in the visual process

The phenomenon of adaptation plays a key role in the luminance, chrominance and temporal performance of the visual system. It, along with color differencing, can be considered keystones in the architecture of the entire visual system. The phenomena is associated with three distinct mechanisms within the eye;

• the dynamics of the iris (pupil) of the stage 0 eye, • the dynamics associated with the bleaching of the available chromophores of the stage 1 sensory neurons and • the variable gain characteristics of the adaptation amplifieres associated with each stage 1 sensory neuron.

The remainder of the neural system orthodromic to stage 1 operates in a nominally constant amplification state.

The dynamics of the iris have been presented in detail in Section 2.4.3 of this work. Performance Descriptors 17- 31

Many textbooks have referred to the conceptual work of Cornsweet22 when describing the effect of bleaching on the performance of the human eye. Unfortunately, his description was more speculation than the result of research and is inadequate for describing the actual phenomenon involved. He relied upon the duplicity theory of distinct rods and cones which is shown to be faulty in this work. As an example, his figure 7-11 presents straight lines on a semi logarithmic graph lacking any data points and calculated from an earlier conceptual equation offered by Rushton. It does not differentiate between an external quantum noise limited threshold versus an internal noise limited threshold. A more realistic graph would use a logarithmic abscissa to describe the level of bleaching.. Where he has provided data, it is largely archaic relative to the more recent literature.

The variable gain intrinsic in the design of the individual adaptation amplifiers found within each photoreceptor cell is also an important feature in dark adaptation.. This portion of the adaptation phenomenon is the result of a unique circuit configuration that has been identified in the sensory neurons of virtually all sensory modalities. It is a fundamental phenomenon contributing to the extreme operating intensity range of the visual system in object (stimuli) space. When the adaptation amplifiers of all spectral channels change their gain in unison, adaptation to different levels of object luminous intensity, without change in spectral content, within a reasonable length of time is achieved (lightness constancy). When the amplifiers change their gain individually over a reasonable length of time to compensate for changes in the spectral content of the objects luminous intensity, a major degree of color constancy is achieved. Whenever, these amplifiers are operating at less than full amplification, they exhibit a transient response in returning to their fully dark adapted operating condition. This response is conventionally labeled the dark adaptation characteristic of the system. There is also a light adaptation characteristic associated with the change in the gain of these amplifiers but it is much more rapid, of less practical importance and less well studied.

The pervasive aspects of adaptation cause it to be discussed throughout the vision literature. Wuerger recently discussed its impact on color changes following chromatic adaptation23. Using her paper, one can trace the early first order proposals of von Kries, through the more advanced proposals of Walraven, el. al. to those of Shevell & Wesner. Each group proposes a better empirical explanation of the observed performance. It can be seen that these proposals, especially those of Shevell & Wesner24, are converging on the model proposed in this work. They propose a variable gain mechanism prior to a subtractive process occurring in a later stage. Unfortunately, most of the literature continues to use photometric units where radiometric units are clearly required and many authors are using tricolor display monitors with phosphors that are not well related to the chromophores of vision. Adaptation from the overall performance perspective is developed in Section 17.6 of this work.

17.1.4.2 The signaling matrix applicable to luminance and chrominance descriptors

[Figure 11.6.4-2] presented a simplified block diagram applicable to discussions concerning the luminance and chrominance channels of biological vision. The analysis accompanying that figure showed the first order performance of the visual system (avoiding flicker effects, aftereffects, stereo-optic considerations and certain nonlinearities) can be described by the analog electrical signals found at the S-plane of the individual . Except for certain specialized encoding techniques (spatial and diversity encoding to minimize the physical size of the ), this location corresponds to the output of Stage 2, the signal processing stage.

Figure 17.1.4-1 develops the signaling matrix embodied in the Matrix Theory of Color Vision embodied in this

22Cornsweet, T. (1970) Visual Perception. NY: Academic Press 23Wuerger, S. (1996) Color appearance changes resulting from iso-luminant chromatic adaptation. Vision Res. vol. 36, pp. 3107-3118 24Shevell, S. & Wesner, M. (1989) Color appearance under conditions of chromatic adaptation and contrast. Color Research and applications. vol 14, pp. 309-317 32 Processes in Biological Vision

work. This Matrix Theory was initially introduced in Sections 1.5.1 & 1.7.5 as a replacement for earlier Zone Theories. The matrix shows the analog signals at the output of Stage 2 and their characteristics as a function of spectral wavelength. This figure will be discussed in detail in Section 17.2-17.4.

Figure 17.1.4-1 The luminance, chrominance and appearance channels of the eye of tetrachromats and aphakic humans. The spectral response in the O-, P- and Q- channels are shown as sinusoidal for illustration. The UV photoreceptor cells are known to be functional in humans of all ages. Research is ongoing to determine if the signal in the O-channel of the aphakic human is typical of tetrachromats. If it is, an aphakic human will be able to tell us what “color” other animals perceive in the ultraviolet.

17.1.4.3 The block diagram applicable to temporal descriptors

The temporal descriptors of vision include both simple delays associated with transmission of signals over finite distances and much more complex processes that are functions of multiple parameters. To discuss the temporal properties of vision, it is necessary to expand the Top Level Schematic down to the circuit level. Particularly with regard to the photoreceptor cells. They are the site of the fundamental transduction mechanism as well as the adaptation mechanism.

Figure 17.1.4-2 illustrates the various signal paths from the photoreceptor cells to the stellate cells at the entrance to the brain. The multiple Nodes of Ranvier along each signal path within the area defining the optic nerve are not shown in this figure. However, these circuits contribute significant time delay to the overall operation of the visual Performance Descriptors 17- 33 system.

The simplicity of the signaling circuits shown is startling in relation to their capability. 34 Processes in Biological Vision

Figure 17.1.4-2 The large signal circuit diagram of the fundamental signal paths of a highly evolved animal eye. (A) Generic photodetection module, (B) Generic luminance channel-- R, (C) One of three generic chrominance channels--O, P & Q. (D) Generic appearance channel--Zn. Performance Descriptors 17- 35

17.1.4.4 The block diagram applicable to oculomotor performance descriptors

The detailed discussion of the servomechanisms of vision are presented in Sections 7.3-7.5. Figure 17.1.4-3 reprints the Overall Servo System of human vision found in those sections. It is required to support the discussions in Sections 17.7. It is also important in understanding the ability to read and interpret fine detail as developed in Section 17.7.5. This figure labels the major signal path associated with both voluntary (cognitive) and involuntary eye motions. The involuntary functions are focused on the stereo, alarm and interpretive paths. The interpretive path includes the inner servo loop consisting of the foveola, POS and oculomotor plant. The major role played by time delay (related primarily to the signal projection tasks) is highlighted. To minimize the total delay in critical processes, the inner servo loop (foveola, POS, oculomotor plant) does not include the cortex. Not shown in this figure is the cerebellum, a crucial element in the inner servo loop called upon extensively by the pretectum.

Figure 17.1.4-3 Overall Servomechanism of the human visual system. Similar systems are found among the chordates. The significance of the delay associated with signal projection is highlighted throughout the figure. 36 Processes in Biological Vision

17.1.5 Problems with “black,” univariance, “silent substitution” and arbitrary normalization

Two time-honored concepts of psychophysics are in need of re-conceptualization based on this work. Even the question of whether black is a perceptual phenomenon remains open to discussion. The Univariance Principle was originally conceived at the beginning of the 20th Century. It was promulgated more broadly by Rushton beginning in 1959. He subsequently redefined it in 1971. The silent substitution method of exploring the performance of the visual system has its roots in the same time periods. Both of these concepts rely upon the putative linearity of the visual system originally proposed by Grassman in the 1860's. Estevez & Spekreijse reviewed these developments in 198225. They also presented a comprehensive treatise on their silent substitution methodology based on the rules of conventional colorimetry. Chapter 12, the equations of Chapter 16 and the above models highlight a series of problems with these concepts. The problems become worse as higher precision is sought and narrower spectral band stimuli are used. These problems will be discussed briefly below with additional details provided in Appendix T.

17.1.5.1 The phenomenology of “black”

Volbrecht & Kliegl have recently revisited the debate concerning the validity of black as a “real” perception26. The problem with these discussions is they lack a fundamental model of the visual system. Volbrecht & Kliegl develop the positions of Maxwell versus Hering in the 19th Century. Their arguments are based purely on observations mostly related to their own vision. A key question in the argument is whether a human perceives black in the absence of a stimulus. However, there is no discussion of the fact that the human visual system is AC coupled. The human visual system can not deliver a constant signal value to the brain representing an absolute stimulus intensity applied to the eye (or to the retina). This fact is embodied in the difference between the perceived brightness of an image and the actual lightness of that image. The fact that the human perceives a gray (Eigengrau) in the absence of any stimulus, whether the eyelids are closed or not, merely reflects the above situation. In the language of the television engineer, the visual system does not possess a DC restoration circuit. Lack of such a circuit is why most television screens produce a neutral gray screen when the transmitting station sends a black signal. High priced television sets frequently have a DC restoration circuit and their screens go black when the station transmits black.

Based on the actual circuitry of the human visual system, black as a phenomenon is the absence of any stimulation to the photoreceptors of the eyes. The perception of black varies with the circumstances. In the absence of any stimulus to the retina, the visual system reports a neutral gray (Eigengrau). Neglect perceptions related to color for the moment. If a stimulus varying in intensity (of finite contrast) is applied to the retina, the retina will perceive the area of minimal stimulus intensity as more black than the Eigengrau. Similarly, the retina will perceive the area of maximum stimulus intensity as more white than the Eigengrau. As the contrast of the stimulus increases, the perceived difference between will increase until the signal resulting from the stimulus occupies all of the limited dynamic range associated with the luminance channel of vision. This range is typically less than 200:1.

At very low stimulus values, the impact of noise must be considered in the above discussion. This noise normally originates in the variation in the photon flux of the stimulus. The contrast-to-noise ratio of the stimulus usually exceeds the above dynamic range under photopic conditions. The perception of noise is suppressed in the luminance

25Estevez, O. & Spekreijse, H. (1982) The “silent substitution” method in visual research. Vision Res. vol. 22, pp 681-691 26Volbrecht, V. & Kliegl, R. (1998) The percepton of blackness: an historical and contemporary review. Chapter 10 in Backhaus, W. Kliegl, R. & Werner, J. Color Vision: perspectives from different disciplines. Berlin: W. de Gruyter Performance Descriptors 17- 37 signaling channel under this condition. Under mesotopic conditions, the photon noise may dominate the perception of both the black and white regions of a scene. Under scotopic conditions, the effect of photon noise associated with the more black scene elements is usually suppressed by the circuits of stage 3 and stage 4 of the visual system. The photon noise associated with the more white scene elements may still be perceived.

17.1.5.2 The Univariance Principle

This Principle was documented in its modern form by Rushton27. It has been promulgated widely within the psychophysical community and is frequently referenced in their literature. However, it is not always stated in a specific form. Based on a very simple linear and floating model of the visual system, Rushton proposed that: “Any two that are equally absorbed by will be equally seen by rods.” Wyszecki & Stiles paraphrased Rushton on page 587 that: “It follows that rhodopsin spectral absorption curve must coincide with the scotopic luminous efficiency curve, V’(λ).” The curve Rushton used to justify this relationship was not the C.I.E. V’(λ). His justification relied upon a sparse set of psychophysical data points (with no direct association with the putative rods) overlayed on a similar curve by Crawford. The original discussion promulgating the principle contained no model of the process being discussed and occupied less than one-half page.

The top level schematic of the visual system highlights a problem with the Univariance Principle. First, there is no rhodopsin in the sense that he used it and “rods” are not a functional designation in vision. Second, omitting the UV- and O-channels of vision for the moment, there are three separate and distinct spectral channels (classes of receptors) that are used to absorb photons and generate signals. Rushton recognized this and extended his Principle in 1971 to say “For each class of receptor the result of light depends upon the effective quantum catch, not upon what quanta are caught.” Estevez & Spekreijse say that Rushton repeatedly demonstrated the validity and usefulness of the Principle and built a research methodology entirely based on its validity. However, they provided no discussion of the precision of the results obtainable with this methodology. The above model of the complete photoreceptor cell has shown that further clarification of Rushton’s second Principle is needed. The words result and effective are clearly in need of clarification. To add precision to the concept, it is important to specify what the result is and where it is measured.

The result can be taken at the input to the neural signal processing, at the output of the adaptation amplifiers, at the S-plane of the retina or as the perceived response after all other second order effects have been included.

1. If the result is measured at the input to the adaptation amplifiers, it is clear that the transfer function of the L- channel exhibits a square law term that is not compatible with the linearity requirement of Grassman’s laws.

2. If the result is measured at the output of the adaptation amplifiers, the variations in adaptation among the individual spectral channels, impact the effective quantum catch of those channels. However, the square law term related to the L-channel is eliminated for signals within the photopic region.

3. If the result is measured at the pedicle of the photoreceptor cells, the exponential conversion of the signal, from a current proportional to the flux to a voltage, is not compatible with Grassman’s laws based on a linear system.

There is a further complication within the signal processing of stage 2. The luminous signal and the chrominance signal are treated differently.

4. If the result is measured at the output of the bipolar neurons of the S-plane, the logarithmic summation introduces variations in the perceived luminance signal not contemplated by Rushton or others.

27Rushton, W. (1972) Visual pigment in man, In, Handbook of Sensory Physiology, Vol. VII/1, Photochemistry of Vision Dartnall, H. Ed. NY: Springer-Verlag, pp 364-394 38 Processes in Biological Vision

5. If the result is measured at the output of the horizontal cells of the S-plane, the logarithmic subtraction process imposes a more subtle restriction on the perceived chrominance signals. This restriction negates the additivity and commutativity laws of colorimetry.

The above realities suggest the Univariance Principle requires restating. To meet current goals in the precision of visual research, it is suggested that the Univariance Principle be:

Under achromatic adaption and non-flickering small signal conditions within the photopic region of vision,

the electrical signal at the pedicles of the photoreceptor cells depend upon the effective quantum catch, not upon what quanta are caught,

the perceived luminance response at the S-plane of the retina is a function of the wavelength of the quanta caught (particularly for narrow spectral band irradiance),

the perceived chrominance response at the S-plane of the retina is determined by the difference in the quantum catch by the individual pairs of photoreceptor cells and not by the wavelength of the quanta caught.

17.1.5.3 The silent substitution method

The silent substitution method, as defined by Estevez & Spekreijse, relies upon Grassman’s Laws of linearity as encapsulated in Rushton’s Univariance Principle. However, many of the demonstrations of this method involve backgrounds that effectively limit the experiments to small signal conditions.

Estevez & Spekreijse discuss the results of Donner & Rushton on page 686. Their results appear to be in agreement with the above elaboration of the Univariance Principle. They found silent substitution is possible within the scotopic region (the L-channel signal is trivial because of its square law term), fails within the mesotopic region, but was observed again within the photopic region (the L-channel signal is linear again due to the action of the adaptation amplifier). They also note their puzzlement over the fact that “near the dark adapted state, changes in the sensitivity functions could occur without disturbing silent substitutions.” The adaptation amplifiers within the photoreceptor cells were performing their function.

Estevez & Spekreijse note that the origin of the term “silent substitution” was a result of the instrumentation used to observe the firing rate of the ganglion cells of frog. By using an audio amplifier and speaker, they were able to listen to the firing rate of the cells. If they could substitute a stimulus without hearing a change in frequency, it was deemed a “silent substitution.”

As in the case of the limitations on the Univariance Principle, the silent substitution method requires much greater care in application as the desired precision is increased or the spectral bandwidth of the stimuli are reduced. The fundamental difference between the signal processing in the luminance and chrominance channels must be recognized.

There is a significant problem with the first paper of Estevez & Spekreijse28. They used the human corneal spectral data of Wald (1964). These spectra were derived using the difference spectra technique. These spectra are grossly

28Estevez, O. & Spekreijse, H. (1974) A spectral compensation method for determining the flicker characteristics of the human color mechanisms. Vision Res. vol. 14, pp 823-830 Performance Descriptors 17- 39

different from the electrophysiologically measured spectra of biological vision (both at the S-plane and at the plane of the ganglion cells). This calls into question whether their data was obtained under optimal conditions.

17.1.5.4 Problems leading to expansion of the CIE functions, V(λ) and V’(λ)

The CIE has struggled with the name for the function described by V(λ). In their vocabulary, it is associated with the inadequately defined Standard Observer dating from the 1920's. While originally designating it a visibility function, adopted the name efficiency function in 1951 in the absence of any physical or mathematical model showing it was related to the efficiency of the visual system. It is important to note that because of the above difficulties, there are several problems with the the CIE photopic and scotopic luminous efficiency functions (previously visibility functions) of 1951. First, V(λ) is not actually a description of efficiency. It is a relative sensitivity measurements under poorly specified test conditions. Second, V(λ) is not defined in terms of specific stimulus intensity levels. V(λ) is a relative sensitivity function defined in terms of the diameter of the test image projected onto the fovea of the eye. The photopic function is defined without reference to a specific stimulus intensity level based on the assumption that the mechanism providing brightness constancy over the photopic region is operating.

The scotopic variant of V(λ) is defined in the absence of any defined stimulus intensity level. Finally, the nominal scotopic function is defined at a position not less than five degrees from the line of fixation (Wyszecki & Stiles, pg 258) while the photopic function is defined at a location centered on the line of fixation.

With the adoption of the Visibility Function in 1924, it became under attack immediately. Judd, a member of the committee refused to accept the new function as realistic (Section 17.1.9.2). In 1931, Purdy reviewed the shortcomings of the function again (17.2.6.5.1).

In the 1951 time period, the Visibility function, V(λ), was recognized as a relative function that could be converted to an absolute function, the Luminous Efficiency Function by introduction of a constant labeled the

“Maximum luminous Efficiency,” Km = 680 lumens/watt. This value was subsequently changed to 683 lumens/watt. Since the maximum luminous efficiency was a function of the visibility function, the reasoning and analysis were clear examples of circular reasoning.

Marriott, writing in Davson (Don of the visual sciences in his day), noted and discussed the inadequacies of the C.I.E. visual and color spaces as far back as 196229. “At the time of this writing,, the data of colorimetry are undergoing re-examination. The results that have been accepted as standards since the C.I.E. adopted the

visibility function V l in 1924 and the “Standard observer” color matching system in 1931 have recently been questioned. In all probability, new standard functions for colour-matching will be laid down in the next few years; meanwhile, it is difficult to decide what results should be used.” He went on, “The C.I.E. functions have been officially accepted since 1931 and are adequate for most practical purposes; for theoretical studies of colour vision, however, they must be regarded as capable of improvement.” The C.I.E. Chromaticity Diagram of 1931 was largely replaced by the new “Uniform Color Spaces of 1976." These remain empirical in character and attempt to maintain the now obsolete, but widely used, C.I.E. Chromaticity Diagram. Marriot provided additional details in this area.

Marriott went on, “The C.I.E. V(λ) function is a compromise solution to the problem based on an average of results of the flicker method, the step-by-step method, and the direct comparison method.” The theoretical weakness of such a combination of inconsistent results is obvious, but is much outweighed by the practical value of a single visibility function, which ca be used without large discrepancies, for all photopic brightness. In fundamental color research, however, the imperfections of the function must be realized.”

29Davson, H. (1962) The Eye, Volume 2. NY Academic Press p 241 40 Processes in Biological Vision

In 1969, Wright, one of the original laboratory investigators, made a parody of the above assertion of Marriott, when he suggested the accuracy of the values at a given wavelength for the visibility function were probably in error by a factor of 10 and in fact no measurements were incorporated into the standard for wavelengths less than 400 nm (Section 17.2.1.6.5).

Finally, all of the above discussions were based on matching energy levels at a given wavelength on the assumption that the sensory neurons were energy-sensitive. It is now totally clear, based on their physical chemistry and quantum physics that they are quantum-sensitive. This difference introduces another factor into the calculations and generally indicates all research quality measurements should be made in a radiometric environment rather than a photometric environment.

- - - -

There is another major concern related to the visibility function unknown to previous investigators. The stage 5 cognition process evaluates the signals received from the O–, P–, Q– and R–channels in an unknown manner (Sections 11.1.4.2.1 and 11.6.4.4). This unknown function is concatenated with the initial signals, UV–, S–, M– and L–, generated by the stage 1 sensory receptors and the summing and differencing performed by stage 2 signal processing. It appears the stage 5 cognition process is not a linear summation because the sensation of “vivid yellow,” usually associated with a wavelength of 583 nm is not associated with a peak in the R– signal, and no obvious feature of the Q–signal (Section 17.3.9.3). The vivid yellow perception can also be enhanced by the creation of the Purkinje effect generally reported to peak at 580 nm (Section 17.2.6).

The clearest way to evaluate the visibility function non-invasively is to evaluate subjects with stage 2 , those unable to generate the O–, P– and Q–channel color signals. Such a subject will perceive only the R–channel signal associated with the summation of the stage 1 signals. It is proposed that this perception will be the closest possible psychophysical perception of the visibility function, V(λ). Invasively, the simplest method is to locate a neuron projecting an R–channel signal from a stage 2 signal processing engine or a stage 3 signal projection neuron.

- - - -

Definition: The shorthand notation, V(λ), is more completely, and properly, expressed as Vt(λ, F, area, location, adaptation state) where the F indicates the intensity of the test signal (in quanta per pulse) while the eye is uniformly adapted with respect to wavelength. As long as it is associated with a Standard Observer, it does not represent the spectral response of a real subject under actual photopic operating conditions.

A new photopic visibility function, Vo(λ), is needed to reflect the actual spectral performance of the visual system under photopic operating conditions. The expanded form of this expression would be as above except the background level must be specified as well, Vo(λ, F, area, location, background) . The data to support this description is widely available now, although it was not in the first half of the 20th Century. Figure 17.1.5-1, from Sperling & Harwerth, provides a good example of an actual photopic operating visibility function for the young Rhesus monkey obtained psychophysically30. Note, the measurements were made in quantal units, not with respect to energy or power.

30Sperling, H. & Harwerth, R. (1971) Red-green cone interactions in the increment-threshold spectral sensitivities of primates Science vol 172, pp 180-184 Performance Descriptors 17- 41

As noted by Sperling & Harwerth, “Clearly, the narrow peak at 610 nm cannot be accounted for by any additive combination of the sensitivities inferred from these pigment functions (referring to the widely accepted sensitivity functions with peaks near 435, 555 & 575).” On the other hand, the peaks at 435, 555 and 575 are easily obtained from the peaks of the actual photoreceptors near 435, 535 & 610 nm. Sperling & Harwerth demonstrated this in their differential adaptation experiments. Curves fitting the data in the above figure better will be presented later in this chapter.

Thornton has provided similar Vo(λ) data for the human, except the experiments have a few caveats attached to them. See Section 17.2.8. Figure 17.1.5-1 A photopic operating visibility function, [xxx rewrite To account for bleaching ] Vo(λ), for the rhesus monkey. Background was 3000 While the quantum efficiency of photodetection in Trolands from a 5500Kelvin source, labeled W. The lines represent nominal absorption spectra, in the original each of the spectral channels of vision remains figure, at 445, 535 & 610 based on the Dartnall essentially constant below the hyperopic region, the monograph. From Sperling & Harwerth, 1971. overall system efficiency is reduced, inversely with respect to illumination, within the photopic region to maintain brightness constancy. Within the mesotopic and scotopic regions, the quantum and system efficiencies actually remain constant but the signal to noise ratio of the system degrades. The use by the CIE of a ten degree (scotopic) test field, instead of the two degree (photopic) test field in the CIE protocols is a method of spatially compensating for this loss in intrinsic signal to noise ratio. Note that the association of a two degree test field with the photopic standard of 1951 does not imply all of the data used to determine the standard (in the interval of 1915- 1931) was collected using a two degree field.

Definition: The shorthand notation, V’(λ), is more completely, and properly, expressed as Vt’(λ, F, area, location) where the F indicates the intensity of the test signal (in quanta per pulse) while the eye is dark adapted. The function

Vt’(λ) is more properly named the Scotopic Threshold Visibility Function. The equivalent operating function,

Vo’(λ), exhibits the same spectral characteristic since the feedback mechanism remains non-operational in this regime. The resulting spectrum does represent the actual spectral performance of the visual system under scotopic conditions.

Ikeda & Shimozono have provided both the operational photopic visibility function and the operational scotopic function for a human in one graph31. Figure 17.1.5-2 shows their results on a continuous vertical axis. The CIE threshold photopic visibility function, Vt(λ), and threshold scotopic visibility function, Vt’(λ), have been added for comparison. These functions were adopted based on data that had been smoothed to the equivalent of a 30 nm wide sliding window filter. It should be noted that the CIE photopic threshold visibility function does not have the same peak wavelength (555 nm) as the M-channel component of the photopic operational visibility function (532 mm), as assumed since 1931. Similarly, the CIE scotopic threshold visibility function does not have the same peak wavelength (505 nm) as the M-channel component of the scotopic operational visibililty function (532 nm) as assumed since 1961.

31Ikeda, M & Shimozono, H. (1981) Mesopic luminous efficiency functions J Opt Soc Am vol 71(3), pp 280-284 42 Processes in Biological Vision

17.1.5.5 Problems associated with arbitrary renormalization

The common practice of plotting a normallized photopic threshold function on the same coordinates as the normallized scotopic threshold function (Fig 1(4.3.2) in Wyszecki & Stiles) obscures three significant facts. First, the two curves are not obtained under similar conditions. The photopic response is normally obtained on-axis using a two degree diameter probe. The scotopic response is normally obtained at five degrees off-axis using a 10 degree diameter probe. Second, the two curves do not exhibit the fact that the intrinsic sensitivity of the S– and M– channels do not change with stimulus level. Third, the two waveforms are dimensionless in the resultant figure.

As noted in a NBS discussion of the process of normalization, each of the above functions has been peak normalized32. Each of the functions has associated with it a normalizing factor that is not expressed. Several authors have chosen to renormalize such a composite peak normalized graph. A common technique is to renormalize the two waveforms at 555 nm based on the adoption of this number for the peak of the CIE photopic luminous efficiency function (Fig 2(4.3.2) in Wyszecki & Stiles). This process introduces another pair of normalization functions that are also not expressed. As a result, investigators have drawn the inappropriate conclusion that the absolute scotopic luminous efficiency has a higher peak than Figure 17.1.5-2 Operational visibility functions shown on the photopic function by a factor of about 2.5:1. They the same graph for HS. Top curve; –2-log photopic have gone farther and concluded that the scotopic Trolands. Bottom curve; +2-log photopic Trolands. The luminous efficiency function is associated in some way CIE threshold visibility functions have been added for with a factor described as 1700 lumens/watt. This comparison (dashed lines). Solid lines from Ikeda & Shimozono, 1981. factor is frequently indicated as associated with the peak of the scotopic luminosity function, at 507 nm, on this renormallized graph. No explanation has been provided for the physical meaning of the factor, 1700 lumens/watt. Without describing, and accounting for the individual normalization factors used, this result is totally misleading. A more correct expression would be 1700"(x/y) lumens/watt where x and y are the normalization factors used in the scoptopic and photopic data collection and presentation process. One of the NBS staff has presented a detailed monograph on the arcane subject of normalization33.

32Nicodemus, F. ed (1976-85) published in parts Self-Study Manual on Optical Radiation Measurements. Wash. DC: National Bureau of Standards Tech Notes 910-1 through 910-8 33Nicodemus, FE. (1973) "Normalization in Radiometry", Appl. Opt. vol. 12, No. 12, pp 2960-2973 Performance Descriptors 17- 43

This is clearly shown in the data of Kokoschka34. In his plot, the “luminous efficiency,” as plotted at a given wavelength below 532 nm, actually goes down as the intensity of stimulation increases. His plot is interesting in that he plotted the scotopic luminosity function along with photopic luminosity data for a ten degree field. A more appropriate plot would show the two curves normalized to 100% at a wavelength of 532 nm, the peak in the intrinsic M–channel response under both conditions. In this case, the peak in the photopic luminosity function would be approximately 0.5 log units higher than the scotopic luminosity function. This difference would reflect the larger area under the smoothed luminosity functions due to the logarithmic signal processing discussed in this work. This is the method used in the figures of Section 17.2. This method also highlights the fact that the threshold response is dominated by properties other than the relative efficiencies of the individual spectral absorbers. It is dominated by other computational mechanisms. Specifically, the relative importance of the individual spectral components is controlled by EITHER the relative density of the individual spectral absorbers or the signal transfer efficiency at the synapses leading to the bilateral cells of the retina OR both. The Purkinje Peak in the threshold response is also a function of the logarithmic signal processing and the color temperature of the stimulus.

The original goal of these normalization procedures was to accommodate the fact that neither of the two functions had been measured in absolute terms, or under the same conditions. The areas of the test stimuli was grossly different and the scotopic function was measured eccentrically with respect to the line of fixation. This work has demonstrated that the intrinsic sensitivity of the photoreceptors of the S– and M–channels have not changed within the mesotopic region. The appropriate technique would be to renormalize the two functions at a wavelength where either the S– or M–channel photoreceptors are dominant. Using this procedure, the two normalized sensitivity functions overlay each other at wavelengths shorter than 532 nm and only diverge due to the operational factors related to the L–channel.

Renormalization at a shorter wavelength is also consistent with the data of Kokoschka. In his plot, the “luminous efficiency,” as plotted at a given wavelength below 532 nm, actually goes down as the intensity of stimulation increases. His plot is interesting in that he plotted both the scotopic luminosity function and the photopic luminosity data for the same ten degree stimulus field. A more appropriate plot would show the two curves normalized to 100% at a wavelength of 532 nm, the peak in the intrinsic M–channel response under both conditions. In this case, the peak in the photopic luminosity function would be approximately 0.5 log units higher than the scotopic luminosity function. This difference would reflect the larger area under the smoothed luminosity functions due to the logarithmic signal processing discussed in this work.

17.1.6 Problems with center-surround experiments

While easy to perform, center-surround experiments have produced conflicting and controversial results over a long period of time. This has been due to the lack of a comprehensive model of the underlying processes. This has resulted in analyses based on a long series of inadequate assumptions. The underlying problem came to prominence in 1980 when Shevell wrote a “letter to the editor.”35 The protagonists all assumed a linear visual system, including a linear detection process, but differed in how to envision the subsequent signal processing. The paper includes mention of many, but not all, of the factors involved in center-surround experiments. It notes the unusual impact of the intensity level of long wavelength irradiance (although it does not recognize a square law relationship). It also discusses a largely conceptual “‘two-process’ theory in which the adapting field both causes a gain change (as proposed by Walraven) and also contributes directly to the color signal (this contribution is called the “additive effect” since it affects the color signal in the test area by a fixed amount rather than a fixed proportion).”

34Kokoschka, S. (1972) in German Die Farbe vol. 21, pp39-112. Figure reproduced in Wyszecki, G. & Stiles, W. (1982) Op. Cit. pg 409 35Shevell, S. (1980) Unambiguous evidence for the additive effect in chromatic adaptation Vision Res. vol. 20, pp. 637-639 44 Processes in Biological Vision

The above quotation provides a direct insight into the problem of center-surround experiments. The visual system is not linear and the signal processing is fundamentally logarithmic. Depending on the absolute values of the intensity of signals applied to the three spectral channels of vision, the perceived color of the chromatic signals can appear to add linearly or proportionately. The experimental problem is complicated further by the contribution of the spectral channels to the luminance signal. The perceived color is a composite of both the chrominance and luminance channel signals. As a result, the perceived result of center-surround experiments is highly variable, paticularly at light levels in the low photopic and mesotopic regions. Figure 2 of Shevell highlights the problem. He compares his curved representation and the straight line representation of Walraven to a set of data points that can be equally well fit by a line of opposite curvature. The caveat to Figure 2 presented by Shevell highlights the limited applicability of both of their models. The logarithmic signal processing model combined with the square-law detection mechanism related to the long wavelength spectral channel of this work provides a better theoretical fit than either of their simpler models. It is also applicable over a wider intensity and contrast range than they address.

It is suggested that all center-surround experiments be reviewed in the light of the above discussion before any of their associated analyses are accepted.

A recent paper by Dacey, et. al. has broadened the subject of center-surround experiments36. They employed more reasonable light sources for the chromatic aspects of their research work. These were narrow spectral band LED’s at 460, 525 & 652 nm. It is not entirely clear whether their dimensions for their test spots were with respect to the retina or an equivalent retina based on paraxial optics in air. They propose the location of chrominance signal generation is prior to the ganglion layer of the retina. They describe it as probably occurring in the circuitry of the outer retina. At different points they refer to bipolar cells and amercine cells. Both references appear conceptual in character. In section 3.1, they define cells with branching dendritic trees and multiple cone contacts as diffuse bipolar cells. Recall that the morphological designation bipolar cells refers to the shape of the cells and not the nature of their output signals. They have traditionally been documented as exhibiting monopolar output signals. Dacey, et. al. note their cells exhibited hyperpolarizing or depolarizing light responses. Cells with the above characteristics are defined as horizontal cells in this work. Unfortunately, they still use the term inhibition for a process that involves simple subtraction. They also employ a linear model of the summation process (their equation 2) that only provides a precise solution over a very limited range of signal intensities. Their summary is broad ranging. They are correct in their summary where they say, “these initial results suggest that the basic spatial structure of the ganglion cell receptive field ( in macaque) is established at the level of the bipolar cell.” They note that Taylor has taken a position similar to theirs based on “spiking” amercine cells37. This work suggests the basic spatial structure of the ganglion cell receptive field is established by the horizontal cells located at this level. Conceptually, the amercine cells of Taylor are the same as the horizontal cells of this work. Spiking amercine cells are seldom reported. Amercine cells are typically electrotonic unless loaded electrically by a test set. The spikes reported by Taylor are probably related to his test set.

17.1.7 Historical composite descriptors of vision

Hart has described the competition in the 19th Century between the early trichromatic theory based on the physics of the day and the later opponent theory based on the psychophysics of that day. He summarized in 199238: “However, over the past several decades, it has become apparent that human and nonhuman primate color vision is indeed mediated by an essentially trichromatic process at the receptor level, but is encoded for neural transmission in a

36Dacey, D. et. al. (2000) Center surround receptive field structure of cone bipolar cells in primate retina Vision Res. vol. 40, pp 1801-1811 37Taylor, W. (1999) TTX attenuates surround inhibition in rabbit retinal ganglion cells Visual Neurosci. vol. 16, pp 285-290 38Hart, W. ed. (1992) Adler’s Physiology of the eye. St. Louis, MO: Mosby Year Book. pg. 710 Performance Descriptors 17- 45 physiologic paradigm of the color opponent process.” This work shows that his description was on track but too narrow.

While the vision of the large chordates is indeed mediated by a degenerate tetrachromatic mechanism that is essentially a trichromatic process at the output of the receptor cells, neural transmission involves separate encoding and signal projection for the luminance information and the chrominance information. Only encoding of the chrominance information can be described as involving an opponent process. Luminance channel encoding is a purely additive (albeit logarithmic) process. Besides encoding, signal transmission also includes the actual signal projection from the eye to the brain. The asymmetry of the signal projection channels plays a major role in the transient chromatic performance of the eye. Therefore, four fundamental situations must be recognized to understand the operational and performance limits of the human eye:

+ The signal detection stage of the human eye involves four parallel channels that operate independently and perform all signal detection and amplification functions in vision.

+ The physiological optics of the human eye are nearly opaque to ultraviolet light. This causes the net performance of the signal detection stage to appear to be trichromatic.

+ The signal manipulation stage of the human eye involves two distinctly separate and parallel signaling venues that all operate under fixed amplitude conditions. There is a fundamental difference in operation between the single luminance channel and the two chrominance channels of human vision.

+ The signal projection stage of the human eye transmits the luminance and chrominance information to the cortex over distinctly different types of data channels and the data channels associated with the chrominance information are distinctly asymmetrical.

Uttal has presented a valid question in his 1981 book. “Can valid psychophysical laws be formulated?39” Man invariably attempts to derive “laws” to describe processes and the results of processes. In the visual science, this has invariably involved;

+ the adaptation of laws from other fields according to one analogy or another and

+ the proclamation of a simple law supposedly covering a wide range of a given parameter.

This process has surfaced three significant difficulties. First, the chosen analogy has frequently been inappropriate at a detailed scientific level. Second, the operation of the visual system employs multiple stages, and multiple mechanisms within those stages, that operate according to different algorithms as a function of the exciting stimuli. Third, most of the observed results related to vision are functions of more variables than the investigator explicitly controlled. As a result, all of the laws developed in the literature must be qualified as to their range of applicability. This qualification must account for both implicitly and explicitly recognized variables. This requires very careful definition of the test instrumentation and protocols used, more careful than that generally found in the literature. As an example, it is completely inadequate to give the wattage of an illumination source when it is the spectral output as a function of wavelength (or at a minimum the color temperature) of the source that is the relevant unstated variable.

The unidimensional laws such as those of Fechner, Beer, Grassman, etc. cannot generally be applied to vision without considerable qualification. As will appear below, a similar statement can be made concerning the simple multidimensional hypotheses concerning chromatic theory proposed by Young-Maxwell versus Hering. Finally, one must be cautious when proposing an equality between two processes of grossly different underlying complexity

39Uttal, W. (1981) A taxonomy of visual processes. Hillsdale, NJ: Lawrence Erlbaum Associates, pg. 42 46 Processes in Biological Vision

such as the simple isotropic absorption spectrum of a retinoid in dilute solution versus the complex and highly structured absorption spectrum represented by the scotopic luminous efficiency function of the actual human eye (as opposed to the highly smoothed response of the eye of the Standard Observer).

17.1.7.1 The CIE Standard Observer and other (largely archaic) descriptors

This work will show that the standards adopted beginning in the 1920's, and not fundamentally overhauled since at least the mid 1930's, are archaic. Their original formulation was so convoluted that it was necessary to define a “Standard Observer” that was neither a real person or the average of data from real persons. The averaging of data sets by the CIE was based on broad spectral smoothing to the extent that all information below the level of about a 30 nm smoothing window was lost. The fundamental problem was the assumption of linearity in the visual system. The secondary problem was the failure to preserve conformality in the expression of the data available. The C.I.E. began publically recognizing some of these shortcomings beginning in 1976. As they stated in 1986 with specific reference to the XYZ system, “Pending the development of an improved coordinate system, the use of one of the following coordinate systems is recommended whenever a three-dimensional spacing perceptually more nearly uniform than that provided by the XYZ system is desired40.” [Underline added] Those suggested were the C.I.E. 1976 uniform color space, the CIELAB and the CIELUV color spaces. Stiles & Wyszecki stress the lack of uniformity in the proposed uniform color spaces (UCS)41. Gouras lists and discusses a broad range of studies and cross-comparisons performed in a search for a better system42. Fry reviewed the arguments for and against the CIE and Judd representations but retained the underlying linear assumption and the equal-energy stimuli of the 1924 CIE standard43. Neither of these efforts have produced a new product. This work presents such a replacement coordinate system that is theoretically defendable and satisfies the needs of the research community.

Following presentation of the New threshold luminousity function (aka Luminous Efficiency Function), a discussion of the differences with the old standards will be presented. See Section 17.2.3 for the luminosity function and Section 17.3.1.3 for the color performance. Following the presentation of a New Chromaticity Diagram for Research, a specific discussion of the shortcomings of the C.I.E. Standards will be presented. See Section 17.3.5 in Part 1b.

17.1.7.2 The use of empirically based standards and templates

Many researchers have used the C.I.E. synthetic tristimulus functions and the templates of Dartnall in the past as an aid. These aids are obsolete for research purposes, particularly when used as a reference in spectral difference experiments based on the linearity laws. These difference experiments have consistently computed an absorption peak in the human visual spectrum near 565-575 nm that has never been confirmed by electrophysiological data or micro-spectro-radiometry. Partridge & De Grip review a number of templates previously used in vision prior to presenting data on transverse microspectrography of single photoreceptors44. While Dartnall was able to establish the slope of the long wavelength side of the photopic spectrum, if not merely the slope of the L-channel absorption spectrum, as the same as predicted by Fermi-Dirac statistics, he was not able to similarly quantify the slope of the short wavelength side of these spectra. He generally defined a lesser slope.

The problem with the short wavelength side of the Dartnall templates is that they incorporate an absorption due to

40C.I.E. (1986) Colorimetry, CIE Publication #15.2, Vienna: Central Bureau of the CIE 41Wyszecki, G. & Stiles, W. (1982) Op. Cit. pp 310 and 164-169 42Gouras, P. (1991) The perception of colour. Boca Raton, FL: CRC Press, Inc. pp 224-248 43Fry, G. (1987) Judd’s 1951 color-mixture diagram Color Res. Appl. vol. 12, no. 2, pp 88-93 44Partridge, J. & De Grip, W. (1991) A new template for rhodopsin (vitamin A1 based) visual pigments. Vision Res. vol. 31, no. 4, pp. 619-630 Performance Descriptors 17- 47

the β−peak in the ultraviolet. The shape of the cumulative absorption between these two peaks, and the distance between these two peaks, in the absorption spectrum does not scale when the principle absorption is used as a template and moved along the wavelength axis. Wolbarsht discusses the derivation of Dartnall’s templates and explores sliding the composite absorption along the horizontal axis while holding the distance between the two peaks constant in terms of wavenumber45. The results are not compelling. He plots Dartnall nomographs in the same paper that do not contain any β-peak.

In the case of the overall spectrum and the S-channel spectrum, the psychophysical slope is actually steeper than that predicted by Fermi-dirac statistics at the shortest wavelengths due to the additional absorption of the physical optics.

These aids (standards and templates) do not present the effect of the logarithmic summation in the luminance channel. Any difference experiments that ignore these additional features and employ linear algebra cannot be taken seriously in research.

17.1.8 “Rod intrusion” as a concept

The literature of luminous efficiency measurements frequently describe the steps taken to prevent “rod intrusion” in their data. However they fail to describe the properties of the rods doing the intrusion or the mechanism of intrusion except in the most conceptual way. The CIE has had a special committee, TC 1-43 attempting to formalize the subject of “rod intrusion” for more than a decade.

CIE TC 1-43, Task Title: “Rod Intrusion in Metameric Colour Matches”

Mission– To write a report giving a step by step procedure for calculating the effect of rod intrusion on a trichromatic colour match. To use the procedure to calculate the effect of rod intrusion on typical industrial metameric colour matches. It is interesting that this charter does not identify any earlier relevant work.

Unfortunately, being a volunteer organization that requires consensus, deadlines are not set within CIE committees and it is impossible to say whether TC 1-43 will ever issue a report.

Most discussions of rod intrusion rely in some way upon the interpretation of the dark adaptation characteristic of Hecht as involving separate “rod component.” The expressions cone plateau and rod plateau (level) are based on this interpretation. This assumption is mathematically unsupportable and has been shown to be untrue in Section 16.4.2. Another frequent reason for rod intrusion is the change in color rendition caused either by a broadband achromatic intrusion by a rod in the overall spectrum or the loss of the L-channel response at low levels as predicted by this work and readily identified in visual spectra as a function of light level (Section 17.2.2.2).

Ebrey & Koutalis, in 2001, presented a great mass of data from a genetics perspective that lacks any organizing structure46. They closed with the following. “Finally, the kinetics of the gecko rod receptor potential appears rod-like, despite the rod being filled with an M/LWS pigment. Ebry introduces a wide-ranging analysis of various enzymes associated with the visual process by the pharmacological community. This discussion is largely unrelated to the visual (specifically transduction) process. They introduce a section on visual photoreceptors with, “A continuing theme in this paper is an attempt to define what is a rod and what is a cone. We have seen that using the type of pigment in the photoreceptor is inadequate and that so far not enough is known about the other components of the transduction cascade to use them as definers, although they may be the reason for the underlying physiological differences between different kinds of photoreceptors.” They go on, “Some cones, like the human parafoveal cones,

45Wolbarsht, M. (1976) The function of intraocular color filters. Fed. Proc. vol. 35, no. 1, pp 44-50 46Ebrey, T, & Koutalos, Y (2001) Vertebrate Photoreceptors Prog Ret Eye Res vol. 20(1), pp 49-94 48 Processes in Biological Vision closely resemble rods in a light microscope. In addition, cones from the periphery of the retina often have different morphologies from those in the central retina. Moreover, there is good reason from the visual pigment work presented above to think one might want to not lump all cones together but rather distinguish them at least by which one of the five classes of visual pigments they have. Some efforts in this latter category are starting to appear and investigators are trying to delineate the properties of cones more precisely.” One useful distinction they made in their Table 1 was the spectral sensitivity of the dark adapted scotopic eye ranged out to ~500 nm for weak stimulants and extended to the red for the photopic eye for weak stimulants. Based on this theory, the statement can be restated as extending to ~570 nm for the scotopic eye at 50% response (due to the loss of the L-channel sensitivity) and to 660 nm for the photopic eye at 50% response with the S–, M– & L–channels active [Figure 17.2.2-3 ].

Ebry & Koutalos made another observation on an unrelated subject. “There is a second important morphological distinction between the outer segments of rods and cones. In cells which are morphologically rods at the light microscopic level, electron microscopy studies have found that most of the membrane area in the outer segment is modified plasma membrane which has pinched off from the plasma membrane to form disks (see Cohen, 1972). The plasma membrane, not the disk membrane, acts as the ion selective permeability barrier between the inside and outside of the cell. Rods can have up to a couple of thousand of these disk membranes. In contrast, all of the membrane area of the outer segments of cones is in contact with the extra-cellular medium. The surface area to volume ratios are quite different for rods and cones. Thus, in spite of the reservations just stated, the morphological distinction between rods and cones is probably useful. What is most important is to explain and refine the distinctions between different kinds of photoreceptor cells.” [xxx move this paragraph and reference to the photoreceptor chapter and interpret]

In section 4.7, they state, “So far, all mammal retinas that have been studied contain no more than three members of the five visual pigment families.” This statement does not leave room for any “rod” pigment if the three are assumed to subserve the S-, M- and L- channels.

Their section 5 provides a broad discussion of the electronic performance of the photoreceptors. However, the graphics do not provide a definitive difference between rods and cones. Their figures 5, 6 & 7 are indistinguishable although figure 5 is described as involving rods. [xxx move this paragraph and reference to the photoreceptor chapter and interpret]

They conclude, “With regard to phototransduction in particular, information on cones is quite sparse compared to what is known about rods. Part of the reason for this disparity is the lack of adequate amounts of cones themselves.” This statement is incompatible with the common assertion that the fovea is “rod free” and therefore must consist only of cones.

In 2002, Stabell & Stabell47 have presented work building on the work of Hunt during the early 1950's. They also presented a relevant paper in 1977 that focused on rod intrusion48. The term rod intrusion does not appear in the 2002 paper.

Quoting Stabell & Stabell (2002), Hunt found “The most striking finding obtained was a marked decrease in saturation of the test colors when the adapting light intensity was lowered. As one of several possible explanations of this change, Hunt suggested that the color response of the cones was increasingly desaturated by the addition of a ‘‘whitish’’ response from the rods. However, when they compared the results of a test field confined within the

47Stabell, B. & Stabell, U. (2002) Effects of rod activity on color perception with light adaptation J. Opt. Soc. Am. A vol 19(7), pp 1249-1258 48Stabell, U. and Stabell, B. (1977) Wavelength discrimination of peripheral cones and its change with rod intrusion Vision Res vol 17, 423–426. Performance Descriptors 17- 49

rod-free fovea with the results obtained with a foveally fixated semicircular test field of 20 deg, the reduction in saturation as light adaptation was lowered was found to be very similar—if anything, slightly more pronounced—when the rod-free fovea was test stimulated. On this evidence the rod desaturation hypothesis was rejected, and they concluded that the rods could play only a minor role in producing the desaturation effect obtained.” They conclude no systematic study had occurred since Hunt. Therefore, “In the present study an attempt is made to examine anew the contribution of rod activity to chromaticity changes with light adaptation.” They explored the visual field 17 degree nasal of the point of fixation. They used the three primaries, 460, 530, & 650 nm of the Wright colorimeter.

Their primary conclusion was interesting, “The present results are in opposition to the conclusion of Hunt that rods may play only a minor role in producing the desaturation effect obtained when the adapting light intensity is lowered.” They did describe what they called “the absolute dark-adapted cone threshold of the background light. This threshold was found at 20.7 log photopic Trolands.” See Section 17.1.2.1.1.

While focused on 650 nm light (page 1256), they did establish several “absolute visual levels” based on the Wright colorimeter. “Hence, as the background intensity is gradually increased from – 4 log ph td, the sensitivity of the rod system to the test light decreases until eventually at 0 log ph td the rod system is light adapted to such an extent that the test intensity of 15 ph td is below rod threshold. At this background intensity level, then, only cones are effectively excited by the test light.” In their interpretation, and words, higher light levels do not cause saturation in the rods but causes “the test intensity at 15 ph td is below rod threshold.” More appropriately, this observation, if valid, can be stated as at 15 ph tr, saturation within the rods has caused their AC sensitivity to fall to a negligible value.

They go on, “However, the analysis is not readily applicable to the results obtained with short-wavelength tests. Thus it will be seen that the chromaticity measurements during the cone-plateau period and following complete dark adaptation are closely similar at 0 log ph td also for the 450-nm test light, despite the fact that the rod receptors are strongly activated under the dark-adapted condition by the 450-nm test light at this background intensity level.”

They conclude, “Apparently, the desaturation effect of rods depends on the test wavelength used, that is, on the relative response of the different types of receptor triggered by the test light.” Their concluding paragraph is worthy of reading because of the ambiguities left unresolved.

- - - - -

Fotios, an architect, has gotten into the discussion in his recent paper which drew considerable criticism49. Berman’s response appears to be far from the main stream, talking about contribution from a broad spectrum photoreceptor physically on the ganglion neurons and not in the focal plane (Petzval surface) of the optical system. Such a photoreceptor could not participate in resolving shapes in the far field.

Recent attempts to treat rod intrusion have focused on Yaguchi’s laboratory. A 2004 paper50 describes the three color opponent channels of color vision using the descriptions, L–2M, L + M – S and L + M. His 2005 paper merely inserts a presumed rod element into his equation for the perceived response associated with these three arbitrarily defined luminance and chrominance channels51.

49Fotios, S. (2006) Chromatic adaptation and the relationship between lamp spectrum and brightness Lighting Res Technol vol 38(1) pp. 3-17 (including critique) 50Shin, J-C. Matsuki, N. Yaguchi, H. & Shioiri S. (2004) A applicable in mesopic vision Optic Rev vol 11(4) pp 272–278 51Yaguchi, H. (2005) Mesopic color reproduction In Zhao, D. Luo, M. & Yaguchi, H. eds. Illumination, Radiation, and Color Technologies 50 Processes in Biological Vision

17.1.9 Particularizing the photometry and colorimetry of vision

The discussions in the literature of the photometry and colorimetry of the visual system are complex and contradictory. Many techniques have been devised to evaluate the photometric and colorimetric performance of the visual system. However, they are predominantly based on a simple two terminal model of the system as described by the expression “psychophysical,” the psychological response of the total system to a physical stimulation. The physical stimulation is necessarily described in object space (external to the eye). The psychological response frequently involve the motor neuron system (pushing a button or providing a verbal response) which involves elements of the neural system beyond the visual system. Interestingly, the sampled-data character of the visual system, as required by the employment of action potentials in the signaling channels, has not been addressed substantively in the vision literature.

The discussions of the photometry and colorimetry of the visual system have also been based on an archaic premise dating from the 1800's, that the visual system is linear with respect to intensity of stimulation across the visual spectrum and a white light is perceived when the eye is presented with equal portions of a red, green and blue light. This premise has led to the consistent failure of the constellation of photometry and colorimetry techniques to give consistent results. It has also led to the inability of the vision community to explain in detail what constitute metameres.

[xxx combine with the above two paragraphs ] Historically, the visual system has been assumed to be linear and only involve a single signaling channel between the retina and the cognitive neural system. It is now clear that the system involves multiple parallel signaling channels, within both the optic nerve and in higher order elements of the central nervous system. The stage 3 signaling paths all involve sampled-data signaling. These multiple paths make the design of proper experimental protocols much more demanding. It is also clear the system is not linear. It is fundamentally a logarithmic system with the addition of an additional adaptation mechanism that is also nonlinear. Fortunately, a logarithmic system can be approximated by a linear system under small signal conditions. However, the visual system operates over an extended stimulus intensity range on the order of ten or twelve orders of magnitude. Care must be taken to differentiate between large signal and small signal conditions in the experimental arena.

Wyszecki & Stiles have provided the most comprehensive material on photometry and colorimetry to date52. The material is now quite old although it is still widely used as a reference. It includes three chapters that appear in the reverse of the natural order in the view of this author, Chapter 3 Colorimetry, Chapter 4 Photometry and Chapter 5 Visual Equivalence and Visual Matching. In Chapter 5, they present a wide variety of experimental configurations for determining the performance of the human visual system and make the important observation on page 392,

“The results obtained by the different measurement procedures, each with its own particular criterion, usually differ systematically from one another. These differences offer clues toward a better understanding of the functioning of the visual mechanism, but they are also disturbing as they put constraints on the validity of the basic principle of photometry.”

Because of the difficulty in controlling the operating state of the visual system and even different regions of the

52Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd Ed. NY: John Wiley & Sons Performance Descriptors 17- 51

retina, it is normally necessary to employ the system as a null detector in intensity differencing experiments. Even using the system as a null detector does not avoid the temporal response characteristics or the sampled-data character of the system.

“The matching of brightness is the fundamental operation in visual photometry” according to Wyszecki & Stiles (page 249). They describe three principle photometric methods.

C Broad-band photometry– “The most widely used method. It involves either a thermal detector or more commonly a photon detector whose relative spectral responsivity has been modified, often referred to as ‘corrected,’ to approximate the V( l) function.” It should be noted that a thermal detector is inconsistent with the quantum nature of the visual system.

C Spectroradiometric photometry– The preferred method if a realistic result is required. It involves measuring the spectral concentration of the appropriate radiometric quantity and then calculating the desired photometric quantity (luminance) in accordance with the appropriate equation of the visual response at that radiometric level.

C Visual photometry– The comparison of two stimuli of similar relative spectral radiant power using symmetrical fields juxtaposed to one another, where the intensity of one stimulus can be varied. The eye is used fundamentally as a brightness matching device.

They go on to say, “Visual photometry is rarely used in routine photometric measurements. It suffers from low precision, and the visual judgements made by individual observers differ somewhat from one observer to the next and from the (hypothetical) standard photometric observer, characterized by V(λ) and V’(λ).”

17.1.9.1 Stimulus matching methods

Figure 17.1.9-1 shows conceptually the four major matching methods of photometry and colorimetry. The three methods on the left are static. The subject is usually asked to adjust the intensity of one or more of the components shown in order to achieve a “best match.” As a result, the duration of any given observation is usually longer than 150 msec. In the technique on the right, the situation is dynamic. The subject is also asked to adjust the intensity of one or more of the components while the two fields are being alternated at a fixed rate. The flicker frequency becomes a significant factor in the results.

Figure 17.1.9-1 Three major matching geometries of photometry & colorimetry. In the sequential method, the experimental components shown on the right using bipartite fields are presented sequentially using the total field at a specified flicker frequency.. Modified from Wyszecki & Stiles, 1982.

The “photometric” method on the left is primarily associated with luminance matching between two stimuli of similar spectral content. If the spectral content is not similar, the matching procedure frequently results in multiple match points and introduces the previously complex problem of identifying and defining metameres. 52 Processes in Biological Vision

As discussed in Sections 17.1.2.3, 17.2.1 (work of Thornton) & 17.3.4.3, the understanding of metameres is critically dependent on an adequate understanding of the visual system. Metameres do not exist in object space, they are perceptual phenomenon resulting from the signal sensing and manipulation mechanisms within stages 1 and 2 of the system. They exist in two forms, chromatic metameres and complete metameres. Two stimuli are chromatic metameres only when both their P channel voltages are equal and their Q channel voltages (technically their O, P and Q channel voltages) are equal. Two chromatic metameres are complete metameres if their R-channel voltages are also equal.

The “colorimetric” methods illustrated in the two central frames attempt to match two fields of different spectral content by adjusting the intensity of one or more of the components to achieve a precise match. Historically, these matches have assumed the visual system follows the law of color addition in object space given as R(λ)R-bar + G(λ) G-bar + B(λ) B-bar = WAW-bar. The intensity values given as a function of wavelength are narrowband. The barred values are primary stimuli of fixed wavelengths chosen arbitrarily, λR, λG, λB, except for L-bar and W-bar. L-bar is a test stimulus of variable wavelength and W-bar is a fixed stimulus defined as white. The values of R(λ), G(λ) &

B(λ) are the tristimulus values obtained for the set of reference wavelengths, λR, λG & λB. Any test wavelength L- bar, can be used in the maximum saturation method. In the Maxwell method, the test source is specified as a white.

There are major problems with the maximum saturation and Maxwell methods.

C The dominant problem is that the visual system does not employ the law of color addition applicable to object space.

C The use of three wavelengths in the maximum saturation method does not produce a match if L-bar is a wavelength shorter than the peak of B( λ). This failure is due to the tetrachromatic capability of the human eye in the region between 400 and 437 nm.

C The use of R(λ)R-bar plus G(λ)G-bar in the upper half of the maximum saturation bipartite field cannot match an arbitrary L(λ)L-bar plus B(λ)B-bar. It is typically necessary to remove the B(λ)B-bar term from the lower bipartite field and add it to the upper bipartite field to obtain a match. The result is a set of color matching functions that require a negative intensity for the expression, B(λ) (illustrated in W & S, page383). This requirement shows the inadequacy of the underlying hypothesis of linear summation. It is widely noted to be unrealizable. This failure of the conventional matching protocol is due to the use of a linear law of within the visual system.

C The color matches obtained using either method fail with major changes in retinal illuminance (W & s, pp 376- 378).

The criteria for a complete match under the Maxwell method is not that the x & y chromaticity values of the two fields match. The criteria is that the P and Q values of the two fields match to give a chromatic match and that the R values also match to give a complete match (Section 17.3.4.3).

Use of the sequential method shown on the right introduces another complication discussed in Section 17.2.1.5. The stage 3 chrominance channels of vision are modulated asymmetrically and involve a low pass filter in the decoding circuits used to recover the information. The result is a significant impact on the measured results as a function of the flicker rate. The rolloff flicker frequency is near 3 Hz.

The diameter of the bipartite or sequential fields have a significant impact on the results of the experiments. The retinas exhibit a significant change in color performance at the edge of the foveola (1.2 degree diameter) as recognized by Maxwell’s Spot (Section 17.3.1.7.2). Investigators have used a wide variety of bipartite and sequential field shapes. Wyszecki & Stiles describe about ten on pages 288-293. They provide a list of protocols Performance Descriptors 17- 53

using these field configurations in matching experiments on pages 392-394. Many of these require revision to meet the demands of a multiple parallel channel signaling visual system.

Section 17.3.4.3 develops the subjects of metameres and compliments et al. in greater detail.

17.1.9.2 Problems with luminance descriptors

Lacking a model of the signal processing occurring within the visual system and with only limited knowledge of the necessary physics and chemistry at the time, the early investigators of the luminance characteristics of the human eye relied primarily on psychophysical tests to provide the luminance transfer function of the eye. To obtain comparable results in different laboratories, test conditions were standardized to the maximum amount possible at the time. This standardization did not generally include the filter bandwidth on the various spectrometers used because many of these were locally constructed. Similarly, the spectral characteristics of the illumination was not well standardized among laboratories (see background in Section 17.1.5.4).

Lacking a sophisticated model of the eye, the available luminance response information was collected and basically averaged for each spectral wavelength. This was the genesis of the C.I.E. Luminance Response of 1924 (2 degree Standard Observer). The technical shortcomings of this standard were reported in the literature almost immediately by Judd, the Chairman of the Committee responsible for its creation. This standard only applied to the “photopic” or high light level response of the human eye. It was only in 1951 that the C.I.E. expanded its standard to recognize the two extreme conditions. The 1924 Standard was renamed, the CIE Photopic Observer Curve of 1924 (2 degree Standard Observer), and the new Standard was named, the CIE Scotopic Observer curve of 1951 (2 degree Standard Observer). These standards still did not specify the light level at which they were applicable for they did not recognize the continuous transition occurring with illumination level. Palmer53 made an effort to define this transition. However, his effort was basically an attempt to define a linear interpolation of these two Standards as a function of illumination level. His efforts provided several insights but used so many different parameters than used for the C.I.E. Standards that the works are not comparable. In addition, the Standards were prepared without specifying the color temperature of the source used to collect the data. Wyszecki & Stiles review the experimental evidence of why Palmer’s linear summation hypothesis is not acceptable54.

17.1.9.3 Problems with chrominance descriptors

Investigations of the chrominance response of the eye have been hampered by two problems; lack of a detailed understanding of the operation of the eye and the assumption that the luminance and chrominance functions were closely related. Without a model based on a significant amount of electrophysical evidence, many of the early hypotheses can only be described as conjectures. After these two basic problems, there were two more significant problems; the assumption that the eye was fundamentally a linear device and that the sum of the responses from the individual chrominance channels represented the luminance response (at least under photopic conditions). Embedded in the linearity assumption is the related assumption that the signal levels in the various chromatic channels track each other regardless of illumination levels. Following the above axioms, the basic hypothesis enshrined by the C.I.E., has been that color vision involved a trilateral process and the process was stable over a significant range of illumination levels. The first corollary is the color performance of the human eye can be represented on a trilateral diagram with the corners approximated by the generally accepted and semantically defined primary perceived colors of red, blue and green.

The above rational has resulted in the C.I.E. Chromaticity Diagram of 1931 and its progeny. These diagrams are

53Palmer, D. (1967) The definition of a standard observer for mesotopic photometry. Vision Res. vol. 7, pp 619-628 54Wyszecki, G. & Stiles, W. (1982) Op. Cit. pg 406 54 Processes in Biological Vision

known to be poor representations of the performance of the eye for scientific purposes. However, they have gained wide commercial use and are destined to be used for a very long time in that regime. For scientific purposes, a more accurate and precise diagram is needed. The C.I.E. has struggled to provide more useful chromaticity diagrams based on empirical factors.

This work looks at the complete model of vision and defines a different set of fundamental conditions. The fundamental conditions are two; the chrominance signaling system is fundamentally separate from the luminance signaling system, and the chromatic signal processing of vision involves mathematical differences between pairs of chromatic signals.

Although the chrominance and luminance signaling channel share the same photon detection channels, they are completely separated within the analog signal processing regime of the retina. Their perception within the brain is indicative of this fact. The perceived color of an image is separate from its perceived brightness. Unfortunately, the experimental procedures to demonstrate this situation are difficult. Suggested procedures will be highlighted below.

The chromatic difference signals are independent of each other and are therefore best represented as orthogonal components on a composite graph. This postulate applies to tetrachromatic vision as well as trichromatic vision.

There are two complications that arise within the above context. First, each chromatic detection channel involves a highly non-linear electronic gain mechanism, dependent on the signal level received from the transduction function and incorporated into the dendritic structure of each photoreceptor cell. The transduction process itself, as defined herein, for the L-channel is fundamentally and significantly different than that of the other channels. It involves different parameters and mechanisms.

Because of these two complications, the resultant amplitude transfer functions associated with the various photoreceptors do not track each other when the illumination level is changed. The individual channels respond differently with regard to signal intensity delivered to both the chrominance differencing circuits and the luminance summation circuits.

A satisfactory theory of human, as well as animal, vision must utilize a model that can account for the fundamental chromatic perceptions reported by the subject and also account for the long list of special effects noted by various investigators. Previous theories of vision have not reached that stage of sophistication. This work appears able to explain these effects. Because of time and page limitations, only a few of them can be discussed in detail.

17.1.9.4 Threshold performance descriptors

Many investigators have sought to describe the threshold performance of the human eye. This has been extremely difficult without a clear understanding of the photodetection process and the signal manipulation within the visual system. As a result, most experiments to date have relied upon psychophysical perceptions. A significant result of this work has been the recognition that the threshold performance of the system in the photopic and hypertopic regions is primarily determined by the dynamic range capability of the signaling channel. The threshold in these regions can be considered a “hard” or deterministic level. It is only in the mesotopic and the scotopic regions that random noise becomes significant. In this region, the threshold level can be considered “soft” or statistical in character. The noise threshold in the scotopic region is significantly different than the noise threshold in the mesotopic region.

There has been a common attempt to consider the photoreceptors of the eye as thermal noise limited devices such as photo-conductors. However, a clear understanding of the photoexcitation process would show that photodetection in Performance Descriptors 17- 55 vision is a quantum statistical process similar to that of photo-emission rather than photo-conduction. As in a photomultiplier tube where a photon above a certain energy will cause the ejection of an electron into free space, a photon must be above a certain energy in order to excite a visual chromophore. Also as in a photomultiplier tube, the quantum mechanical process of exciting an electron into a higher energy state is a thermal noise free process. For typical photomultiplier tubes, photographic films and visual sensors in animals, the thermal noise energy associated with the detection process is at least an order of magnitude lower than the energy required of the photons. The result is an essentially thermal noise free detection process. The important question with regard to vision is when does noise, other than quantum statistical noise, become a factor in vision. As will be shown below, the performance of the visual system is determined differently in the photopic, mesotopic and scotopic regimes. The performance is also slightly different in the L-channel compared to the M- and S-channels.

In the photopic regime, the performance of the visual system is not noise limited. Instead, it is limited by the dynamic range of the signaling channels. In both the mesotopic and scotopic regimes, the visual system in animals is stochastic noise limited. In the mesotopic regime the predominant noise is that associated with the quantum noise of the input illumination. In the scotopic regime, the noise is primarily of cortical origin. This stochastic noise limited performance in a two dimensional array of detectors can cause a problem when the data is processed in the brain. The result is perception of various shadowy hazards in the field of view, which need not actually exist, under very low light conditions.

17.1.9.5 Internal calibration of the human visual system

At least two internal calibration procedures can be identified based on the author’s experience. Upon awakening in a a dimly or reasonably lighted room, but before the eyes are opened, two distinct conditions are regularly observed.

C A uniform field of pale blue dots is observed across the entire perceived field of view. The dots appear to be at or near the size and density of the S–channel photoreceptors. The typical duration of this event is a few to ten seconds

C A field of short, –red (almost neon like) lines is observed where the orientation of the lines appears to be predominantly vertical and horizontal relative to the normal axes of the eyes. The lines have a minimal width (similar to the diameter of the pale blue dots) and to have an aspect ratio of about 10:1. The lines have a moving, as if boiling) appearance. The lines are not uniformly distributed. There is clearly a greater density of lines (probably by 3:1) in the region defined by the 1.2 degree diameter foveola. There does not appear to be any delineation of the larger fovea. This pattern is also observed for a period of 10-20 seconds unless the eyes are opened.

Upon opening the eyes, both of these calibration routines are obscured by the higher contrast information in the exterior scene.

17.1.10 Other individual descriptors

Foster and Snelgar have discussed the separation of the descriptors of vision in order to relate to the chromatic- opponent and achromatic (luminosity) mechanisms55,56. Such a separation is key to the understanding of vision. It

55Foster, D. & Snelgar, R. (1983) Test and field spectral sensitivities of colour mechanisms obtained on small white backgrounds: action of unitary opponent-colour processes: Vision Res vol 23, pp 787-797 56Snelgar, R. Foster, D. & Scase, M. (1987) Isolation of opponent-colour mechanisms at increment threshold Vision Res vol 27, pp 1017-1027 56 Processes in Biological Vision

is totally supported by this work. It bridges the chasm between spectral sensitivity curves of human vision and the π parameters of Stiles. Sharanjeet-Kaur et al. have also explored the spectral responses of vision at slow (1 Hz) and 25 Hz flicker rates57. Their work shows additional subtleties of the visual process and bridges the chasm between the “fundamental spectra” of the Stockman school and the “spectral sensitivity curves” of Foster and Snelgar (and Stiles) and this work. See Section 17.2.1.5 for further discussion of the Stockman material.

17.1.10.1 Frequency Domain Descriptors

In vision, the frequency domain is unusual in that includes both the temporal frequency domain and the spatial frequency domain. While this has not caused difficulty for the majority of investigators working in only one of these domains, it requires careful definition if the properties of both domains are to be correlated. It is also important to note that the performance associated with each of these domains is a function of the location within the field of view of the retina. Even more significantly, the laboratory results are strongly influenced by the spectral character of the stimuli used.

Traditionally, it has been easier to perform psychophysical experiments related to the contrast performance of the system versus frequency than it has been to explain the results. The number of variables involved in the explanation is quite large. It requires a detailed knowledge of the system to annotate these variables and describe their interrelationships.

Frequently, investigators have used a graphic to present their threshold sensitivity functions with respect to frequency that has resulted in loss of perspective on exactly what was being presented. It frequently appears that the functions are crossing the horizontal axis at a very high angle. In fact, the horizontal axis is an absolute limit corresponding to 100% contrast, i. e., a black and white test target of the highest possible contrast. The distance from this asymptote is actually a measure of the threshold level within the signaling channel relative to a 100% contrast situation at the specified excitation level.

17.1.10.1.1 Specific definitions related to contrast functions versus frequency

As a starting point, the term contrast sensitivity function, CSF, frequently has different meanings in different papers. To solve this problem, the term will be modified to the Contrast Spatial Frequency, CSF, and the Contrast Temporal Frequency, CTF, functions. Beyond these two terms, the additional relevant parameters will be indicated either by a subscript or parentheses. The temporal frequency response is usually given in terms of Hertz. The spatial frequency response is frequently given in angular measure, cycles per degree in object space. Care must be observed when the data is referred to the retina or to image space in terrestrial eyes. The frequency in cycles per degree is not the same in these two spaces due to the difference in the index of refraction between air and the vitreous humor of the eye, and Snell’s Law.

It will become apparent below that, at least in the HVS, most of the mechanisms affecting the spatial frequency contrast are in fact temporally based mechanisms. Only the spatial performance of the lens group of the eye is based on a purely spatial mechanism. As a result, the CTF and CSF show a familial resemblance. This has been documented in Kelly58. In that paper, Kelly declares: “retinal image motion is the sine qua non of vision.” However, They did not factor this fact into the low frequency portions of some of his figures. The interface between these two domains is closely related to the seldom studied tremor of the visual system. This aspect will be addressed

57Sharanjeet-Kaur, (no initial). Kulikowski, J. & Walsh, V. (1997) The detection and discrimination of categorical yellow Ophtha Physiol Opt vol 17(1), pp 32-37 58Kelly, D. (1979) Motion and vision. II. Stabilized spatio-temporal threshold surface. J. Opt. Soc. Am. vol. 69, pp 1340-1349 Performance Descriptors 17- 57

in Section 17.1.2.3.2. The actual performance related to the CTF and CSF will be presented in Sections 17.6 and 17.7 respectively.

17.1.10.1.2 Attempts to differentiate between temporal and spatial contrast

Kelly introduced his study of the spatio-temporal performance of vision by modeling the spatial and temporal performance of the eye as orthogonal functions (his equation 1). He then insisted that approach did not work and proceeded to introduce alternate formulations that all included a cross product between the performance in the two dimensions (his equation 2). He then reverted to a template approach not supported here. His figures 13 & 15 provide a reasonable description of the modulation of the signal presented to the cortex by the luminance channel but it lacks mathematical precision. His graphical work focuses on a conversion factor of 2 degrees/second between the temporal and spatial domain (his figure 15) that will be compared to other sources in Section 17.6.3. It must be noted that his test set had an angular RMS sensitivity of “about one minute of arc” and was unable to sense the amplitude of the tremor of the eye. His statements concerning a stabilized image must be interpreted in terms of a residual motion being present for which he did not fully account (his figure 6). In the context of this work, his data related to an image moving at a constant velocity relates to the tracking mode of Section 15.2.5. For his data related to an image moving at zero velocity, the actual motion is that associated with tremor and represented by the analytical mode of Section 15.2.5.

Experiments have also been performed to quantify the spectral contrast performance of the visual system59. To avoid confusion with the above acronyms, the term Chromatic Contrast Frequency (CCF) function will be used when discussing these experiments. The same function has been described using the term chromatic flicker in Wyszecki & Stiles. (1982). These experiments have been performed in both the temporal and spatial frequency domains. If the test samples are carefully chosen to minimize the luminance difference between the samples, the luminance channel, R, does not participate in the signaling process and only the P and Q chrominance channels are involved. This results in a more complicated situation than recognized by Kelly & van Norren. Since these are orthogonal difference channels with asymmetric temporal frequency characteristics, there are a multiplicity of different test protocols that can be implemented. In general, each of these protocols will generate a different form of chromatic contrast performance.

Most conceptual models of the mechanism underlying the contrast performance of the system versus frequency have generally relied upon a series of quasi-independent band pass filters60. Kelly generally follows this approach. No morphological or electrophysiological signs of such filters have ever been found and no such conceptual model has been reduced to practice. The following material will demonstrate that only low-pass filters are used in the visual system.

Kelly has attempted to fit a single equation to his data using a function in the frequency domain that Hodgkin applied to a related visual model in the temporal domain. In both cases, the generic equation only applied to a specific data set. It did not describe the general situation. Both authors relied upon auxiliary equations to manipulate the original equation to apply over a wider range. This work has shown that all of the frequency selective filters of the system are low pass filters. There are no bandpass filters within the visual system. However, in two cases, individual low pass filter stages are employed in feedback circuits. As a result, these overall circuits exhibit a high pass characteristic. By serially combining the low pass and high pass filter elements of the various Stages of vision, an equation can be derived that does describes the correct contrast performance of the system over a wide range of conditions.

59Kelly, D. & van Norren, D. (1977) Two-band model of hereochromatic flicker. J. Opt. Soc. Am. vol 67, pp 1081-1091 60Miller, N. & Newman, N. (1998) Walsh and Hoyt’s Clinical Neuro-Ophthalmology, 5th ed. vol. one. Baltimore, MD: Williams & Wilkins pg 165 58 Processes in Biological Vision

The models discussed in this chapter will be limited to first order models. Several mechanisms in vision require more sophisticated models for their complete description. The operation of the iris is particularly complex but of relatively little experimental interest. It can be described in detail using a hysteresis loop of nearly parallelepiped proportions and two opposite sides exhibiting different time constants. The method of encoding employed in the chromatic signal projection paths of stage 3 are asymmetric with respect to signal level where the signal level is a chromatic difference. This feature complicates the detailed discussion of the performance of the chromatic contrast performance of the system.

Kelly, et. al. have provided the results from an extensive set of carefully (but not adequately) planned experiments. The range included the temporal, spatial and chromatic contrast performance versus frequency. His use of an equal- energy light source, instead of the prefered equal-photon-flux source, in some experiments without careful control of the color temperature leads to some uncertainties in the interpretation of his data. However, he did define the change in operating regime between the scotopic/mesotopic and the photopic as well as the change between the photopic and the hypertopic. His work has clearly demonstrated the similarity of the spatial frequency and spatial frequency characteristics suggested by the theoretical model of this work61.

Kelly & van Norren summarized the conflicts in the literature in their 1977 paper. This literature is generally based on the use of photometric units. They said: “Unfortunately, no two of these techniques yielded the same results, so it is not certain than any of them succeeded in measuring the characteristics of independent cone classes.” In that paper, they deviated from their earlier use of an equal energy source in the use of a mixture of red and green designed to produce a broadband yellow. The red and green was derived from a 3400 Kelvin tungsten halide light source (neither equal energy or equal photon flux) using filters. They continued to use a 1.8 degree field in object space (roughly the size of the foveola) and a 2.3 mm artificial pupil. This effort produced a low frequency portion of the CTF at an illumination of 860 Trolands that did not exhibit a horizontal component. It would be useful to repeat this experiment using a narrowband yellow at 572 nm (see next section). There is a null in the chromatic contrast characteristic at this wavelength. Use of this wavelength would insure there was no component of chromatic contrast introduced into the experiment as a function of illumination level.

In all of the located experiments, the experimenters did not compensate for the loss in absorption associated with the long wavelength spectral channel in the scotopic and mesotopic ranges. As a result, the test contrast generated by the test set was not the same as the test contrast sensed by the visual system, particularly at levels below about seven Trolands.. This fact led Kelly & van Norren into a series of experiments exploring the “Silent-Green” and Silent- Red flicker effects. It is suggested that these effects were largely spurious and due to the use of a stimulus that did not correlate with the actual sensitivity of the chromatic channels. Their proposition that the visual channel exhibited both an opponent color response and a achromatic response is supported by this work but on entirely different grounds. They presented eight corollaries based on their proposed dichotomy. This work will present a more general continuum. Portions of this continuum can be correlated with some of their corollaries. Future low level tests should differentiate between the test contrast based on the absorption of the chromophores of vision and the incident test contrast calculated using an arbitrary spectral band.

17.1.10.1.3 Lack of attempts to differentiate between chromatic and temporal or spatial contrast

In reviewing the literature, it is abundantly clear that the psychophysical community has paid little attention to the spectral quality of the illumination used in spatial and temporal contrast threshold measurements. The unstated assumption being that their test protocol only excited the subject’s luminance channel of vision. This has led to much of the difficulty and confusion in correlating various investigators data that was noted by Kelly & van Norren.

61Kelly, D. (1979) Op. Cit. Performance Descriptors 17- 59

Lacking an adequate model of the visual system, these investigators have made minimal efforts to excite only a single signaling and/or perception channel of the visual system. As a result, it has been impossible to separate and control the relevant variables during the experiments. Lacking this control, it has been impossible to de-convolve the data and obtain explicit insights into the operation of the system.

It is critically important that future experiments not rely upon photometry in the representation of their stimuli. It is perfectly clear from the Overall Block Diagram, the spectral characteristics of each chromophore and the New Chromaticity Diagram for Research presented in this work that more precise radiometric and temporal conditions must be met in future experiments:

+ The experiments must seek to excite either the temporal, the spatial or the chromatic channels of the visual system individually. The design of such experiments is not a trivial problem. There is considerable crosstalk between these different domains as noted by Kelly.

+ The experiments must recognize that the performance of the system depends on the mean flux level absorbed by the spectral channel associated with each individual type of chromophore. This includes the irradiation of the channel before each test as well as during each test. Adaptation is a spectral channel specific function.

+ The experiments must recognize that the signal and data processing capabilities of the visual system are different for the foveola and the rest of the retina (as clearly defined by Maxwell’s spot (Section 17.3.1.7.2) and the nature of a large selection of after images).

The New Chromaticity Diagram for Research, especially when drawn with the auxiliary axes defining the discrimination capability of the P– and Q–channels is particularly valuable in designing well controlled experiments. [Figure 17.3.3-12 in Section 17.3.3.6]. By comparing the new diagram with the spectral content of the P–, Q– & R– channels, it is clear how the spectral content of the stimuli must be controlled. It is also clear that there are two fundamentally independent chromatic difference channels and that each exhibit an independent chromatic contrast function.

As an example, to determine the chromatic contrast function of the Q channel, the intensity of the stimulus must always be high enough to cause operation of each chromatic channel in the photopic region. Maximum differentiation in the data requires that the mid wavelength stimulus not contain any spectral content at wavelengths longer than 572 nm and the long wavelength stimulus not contain any spectral content at less than 572 nm. When making threshold experiments, best results will be obtained when the mean of the mid wavelength stimulus spectrum is as close to 532 nm and the long wavelength stimulus spectrum is as close to 640 nm as practical.

As explored in Chapter 11and as to be discussed below in Section 17.6, the temporal frequency characteristics of the P– and Q–channels are quite different from those of the R–channel. Furthermore they are temporally asymmetrical. This makes determination of the chromatic contrast functions between red and blue and between green and magenta particularly demanding.

Failure to recognize these temporal frequency differences in the past has contributed to the pollution of experiments designed to measure only the temporal or spatial contrast frequency functions. This fact is highlighted in a comparison of figure 1 of Kelly & van Norren in 1977 and figure 4 of Kelly in 1961. The 850 Troland curve in the 1961 paper is essentially the sum of the two distinct curves in the 1977 paper measured at 860 Trolands but using spectral filters matching the absorption spectrums of the chromophores of vision. The use of these filters seriously impacts the integrity of the photometric intensity measurements.

17.1.10.1.4 Temporal Frequency Domain Descriptors 60 Processes in Biological Vision

The temporal description of the human eye has suffered from neglect compared to the static and quasi-static luminance and chrominance descriptions. First, because of instrumentation difficulties, there have been almost no characterizations of the transient response of the human eye to the onset of illumination. Second, the characterization of the transient response of the human eye following cessation of illumination have not been comprehensive in terms of original illumination levels or spatial location within the field of view.

During the early scientific characterization of the temporal response following cessation of illumination, usually described as the adaptation curve, two relatively distinct zones were frequently observed in graphs of the luminance sensitivity versus time. Lacking any other confirmation, these two levels were assigned relationships to the contemporary relationships being discussed verbally in the morphology arena, e.g. there appeared to be two general classes of photoreceptors, rod shaped and cone shaped ones. Although this morphological difference has suffered with time and has not been correlated with the visual performance of the eye to this day, the “adaptation curve” portion of the complete temporal response is still shackled with the “rod & cone” terminology, even though many adaptation curves fail to present two distinctly different sensitivity plateaus. As will be seen below, the transient response following illumination onset has never exhibited two plateaus. No correlation between the onset transient and any morphological feature of the eye could be found in the literature.

With the development of the field of electronics and the field of the Response of Physical Systems behind them, the early experimenters might have come to a different conclusion concerning the “adaptation curve.” In this era, anyone trained in the above fields and looking at this curve would quickly recognize it as the performance of a single 2nd order physical system. The mathematical description of a 2nd order system involves two arguments and several initial conditions. The arguments are a time constant and a natural frequency. By varying these arguments, the experimenter can describe the adaptation curve as a function of the spatial position in the field of view. It is true that the observed response is not precisely that of a 2nd order system. However, this is due to the non-linear gain characteristic of neuron incorporated in the photoreceptor cells, specifically the adaption amplifier Activas associated with the dendritic structure. When this characteristic is factored into the equation, the result predicts the characteristics of the signal at the pedicels of the photoreceptors with excellent precision.

Using the model developed herein, the complete transient response of the eye to illumination can be defined for any illumination level or change in level. The dominant feature in the response is the performance of the adaption amplifier Activas of the Photoreceptor cell and the diffusion parameters associated with the bioenergetic material providing power to those Activas.

17.1.10.1.5 Spatial Frequency Domain Descriptors

Many investigators have measured the spatial performance of the HVS, usually allowing the eyes to fixate on the stimulus. As a result, most of the data refers to the performance of the analytical channel associated with the foveola. Most past attempts to model the spatial frequency response of the visual system have sought to locate lumped constant filters or in some cases sampled-data networks that can account for the variations in the spatial frequency response of the system without recourse to the temporal domain. These attempts have not gone beyond the conceptual stage. This work will introduce an alternate approach wherein the spatial performance of the eye is a result of a conversion of spatial position and motion into a temporal signal related to relative phase and to frequency. This alternative is implemented differently in different areas of the retina. Within the foveola, the approach is based on the mechanism called tremor and its ability to modulate the spatial information into a temporal data stream.

As a result of this change in approach, it is proposed that Kelly’s quote in Section 17.1.2.3 be modified to include two additional words: “retinal image motion is the sine qua non of imaging in vision.” The visual system operates Performance Descriptors 17- 61

perfectly well as a change detector in the time domain without any retinal image motion. It is also able to sense motion intrinsic to local elements of a scene. However, to form an image, the image projected by the lens must move relative to the retina. This requirement explains why the blood vessels on the surface of the retina are essentially invisible. Their shadows do not move relative to the retina.

Kelly has presented significant data in his 1979 paper. No model is associated with the data in that paper. Only a template solution. More recently, a multi-institutional team have been collecting spatial contrast performance as a function of spatial frequency under the designation MODELFEST. All of this data will be reviewed in Section 17.6.3.

17.1.10.1.6 Chromatic Frequency Domain Descriptors

Some interesting but complex experiments have been performed in the spatial chromatic frequency domain. Only a few noteworthy experiments have been performed in the temporal frequency domain of vision. There is a larger array of data available with respect to the transient chromatic domain as it appears in flicker experiments. This data is addressed in Section 17.6.1 & 17.6.2. Kelly & van Norren provided additional data on the chromatic response versus frequency in their 1977 paper. They did not associate a model with their experimental results.

17.1.10.2 Parametric properties clarified

This Chapter brings together considerable disparate data. This action provides clarification of a number of properties related to the model that could not be defined in isolation. These include the nominal signal levels occurring in the signal processing section of the retina, the effect of various photoexcitation, vascular (hydraulic), and channel related (temporal) time constants.

One of the most important properties involves the signal levels at the pedicels of the photoreceptors. The signal manipulation subsequent to the pedicels is designed to process constant peak amplitude signals.

The chromatic channels of the visual system are designed to employ constant peak amplitude voltage signals at this location (the logarithms of the current through the axon diode). The perception of chromaticity will be seen to be critically dependent on this condition. Further, the lateral cells related to the two chrominance signaling channels are seen to provide signal differencing without any difference in amplification between the pairs of input signals.

The very strong implication from the above situation in the chromatic channels is that all photoreceptors create generator currents and generator potentials of equal size at the pedicels, within the gain capabilities of their individual adaptation amplifiers.

The luminance channel appears to involve different relative amplitudes between the various chromatic photodetection signals. It is quite easy to account for these different amplitudes within the signal processing stage. Therefore, it will be assumed, lacking adequate data to the contrary; that under steady state, non chromatically adapted conditions, the output voltage of all of the photodetection channels is nominally the same. Any difference between them suggested by the perceived luminosity function or luminance equation is due to differences in amplification within the signal manipulation stage. More specifically, the signals at all pedicels can reach the same maximum voltage. However, different amplitude voltages may be applied to the bipolar cells of the luminance channels. This is accomplished using different impedance synapses at the input to the common emitter terminal of the Activas within the bipolar cells.

The above conditions with regard to both the luminance and chrominance channels suggest that the mosaic of photoreceptors in the retina of all Chordata during genesis consists of groups of four different chromatic photoreceptors in a repetitive pattern. Some chromatic photoreceptors may be represented more than once in each 62 Processes in Biological Vision

group. In large animals, the ultraviolet photoreceptors are vestigial. In some species, the ultraviolet photoreceptors appear to disappear in early life. Douglas, et. al62. have traced this phenomena in trout Salmo trutta and roach Rutilus rutilus, both fresh water teleosts. For human, the result is that there are at least vestigial ultraviolet photoreceptors, as seen in aphakic subjects, and the density of each chromatic photoreceptor type is essentially equally distributed throughout the retina. Their figure 7(b) shows the mosaic pattern underlying the Outer Segments of trout.

The mosaic nature of the chordate retina implies that the flux density received from an 7,053 K scene, by the photoreceptors related to each chromophore, are the same or in proportion to the presence of each chromophore type in the basic group of the mosaic and in their relative cross-section within each group.

17.1.10.3 Anomalies and Effects

Based on the explanation of the luminance, chrominance and temporal characteristics of the human eye developed in this Chapter, a straightforward explanation of most of the unusual situations reported concerning the operation of the eye can be provided. Frequently it is necessary to separate effects due to external anomalies, frequently introduced by a magician, from those caused by computational anomalies within the visual system. A number of books have addressed this separation63. A technical discussion of these explanations will be grouped in a later Chapter.

17.2 The Luminance Characteristic of the human eye

This Section will address two distinct performance descriptors; one displaying the (absolute) sensitivity to illumination versus wavelength of the eye, and the second displaying the differential sensitivity to illumination versus wavelength. Both of these will be presented first in a theoretical context, second by the perceived performance in these two areas as memorialized in the current C.I.E. Standards and third in a new proposed form. The relationship between the theory and the empirically based standards will also be developed in detail. This is particularly important because of the significant difference in performance between the normal and aphakic human eye.

There is little data available on the color performance of the human eye as a function of field angle. It has only recently been shown that the human retina is tetrachromatic like the retinas of other chordates. Recognition of this fact places a different perspective on understanding the operation of the human visual system.

Because the spectral sensitivity of the retina and many other parameters related to the photoreceptor cells are variable, it is useful to address the architecture of the visual system as prior to and subsequent to the formation of the signals at the pedicles of those cells.

The signaling system subsequent to the pedicles of the photoreceptor cells operates in a fixed gain, large signal mode. With the exception of certain asymmetries in stage 3 of the chrominance channels, this portion of the signaling system is symmetrical with respect to time. This portion is also characterized by fixed gain coefficients between individual circuit elements (given labels based on the letter K).

The portion of the visual architecture prior to the pedicles of the photoreceptor cells operates in an environment characterized by variable input signal amplitudes and variable amplifier gains individualized with respect to spectral channel. While individual circuit gains within this portion of the system may be characterized by constants (and

62Douglas, R. Bowmaker, J. & Kunz, Y. (1987) Ultraviolet vision in fish. In Seeing Contour and Colour, Kulikowski, Dickinson & Murray, Ed. NY: Pergamon Press pp. 601-616 63Luckiesh, M (1922 & 1965) Visual illusions. NY: Dover Publications. [in my personal library] Performance Descriptors 17- 63

quasi-constants) labeled with the letter K, the overall performance of the complete system is better characterized by an auxiliary group of parameters using the label C.

The significantly different performance of the aphakic eye in the ultraviolet influences the fundamental interpretation of how the human visual system works. This characteristic will be discussed in Section 17.2.2. The obvious conclusion is that the human retina is tetrachromatic throughout the lifetime of the individual. However, the lens group absorbs virtually all of the light in the ultraviolet band between 315 and 400 nm. Whereas, the human retina is tetrachromatic, the complete eye is largely trichromatic, except for a potential cusp in the area of 300-315 nm.

To define the luminance performance of the eye requires considerable care in defining what is desired. One goal is to define the quantum efficiency of the photodetection process in both absolute terms and in relative terms for a given background irradiance. A second goal is to define the perception threshold of the overall visual system under a specified set of conditions. Measurements of these types are very difficult to make in practice. One of the easier measurements to make is the spectral absorption characteristic of the eye as a function of wavelength. However, there are a variety of parameters that affect the results obtained. A specific test should be labeled as belonging to one of the following test environments. 64 Processes in Biological Vision

The visual system was designed to accept low contrast signals modulating a slowly changing average irradiance level in each of the spectral channels. Most of the unusual transient effects observed in the laboratory are a result of the asymmetries in the system that were not anticipated, or accepted as a tradeoff, in the overall design. These results include those associated with the Retinex theory.

The nonlinearities and asymmetries of the visual system related to intensity and time make precise determination of its luminance parameters particularly challenging. These luminance (more properly radiance) parameters will be discussed in Section 17.2. The variation in these same parameters on a spectral channel basis makes measurements of the chrominance performance equally challenging. These chrominance parameters will be discussed in Section 17.3. The underlying temporal characteristics will be summarized in Section 17.4. The details of the spatial performance of the visual system will be discussed in Section 17.5. The spatial parameters related to the process of reading will be introduced in Chapter 19.

As discussed above, the luminosity function varies significantly with the state of adaptation of the eye, with irradiation level (Section 7.2.4), with the color temperature of the source irradiation and to a lesser extent with age. Little data is available relative to age (less than 40 subjects). However, what is available suggests the transmission of the lens group varies less with age than the dispersion in performance due to other variables64. Figure 17.2.1-1 provides an overview of the subject matter for the complete eye. Section 17.2.1.4 will provide a similar figure for the retina only. The luminous efficiency function is a continuous variable as a function of illumination, although it does exhibit two regions of reasonably constant shape, the photopic and scotopic regions. The spectral absorption characteristics of the chromophores of long wavelength trichromats are shown normalized at the bottom of the figure. The function is a direct function of these underlying spectral absorption characteristics, although this is not obvious because of the logarithmic signal processing employed. This signal processing also results in the two auxiliary peaks at 487 and 580 nm known as the Bezold-Brucke and Purkinje peaks respectively. The auxiliary peak at 580 is frequently reported as the actual peak in the absorption function of the long wavelength chromophore. It is not. The hatching on the left is indicative of the absorption introduced by the lens group of large terrestrial chordates. This absorption is a function of the thickness of the lens group. The larger the animal, the longer wavelength for the cutoff wavelength of this mechanism..

The material developed in this section is being

Figure 17.2.1-1 (Color ln) The tetrachromatic luminous efficiency function of human vision along with its components and variations. The figure highlights the importance of logarithmic signal processing in vision.

64North, A. & Fairchild, M. (1993) Measuring color-matching functions. Part II. Color Res. Appl. vol. 18, no. 3, pp. 163-170 Performance Descriptors 17- 65

accepted in the literature65, and confirmed through independent computations66, on a daily basis. See Section 17.2.2.5.1.

17.2.1 Determination of the luminosity related functions of the visual system [xxx edit entire section to consolidate ] The luminosity related functions of the eye are highly state dependent. If all three spectral channels of the human eye are not fully dark adapted, it is important to quantify the exact state of adaptation of each channel separately. As an example, the luminosity function data of Hurvich & Jameson clearly shows a distinct change in the adaptation state of the L-channel between experimental run #1 and #967. Apparently, the subject caught sight of a pilot light or the reflection of some red light source while relaxing.

Under completely dark adapted conditions, all of the adaptation amplifiers of the eye are operating at their maximum gain and are stable. All other parameters of the eye, except for the translation function in the L-channel are also stable. Under these conditions, the perceived sensitivity of the eye is a direct function of the spectral content and the intensity of the irradiation applied to the eye. Because of the unique characteristic of the L-channel translation function, the human eye exhibits four distinct luminosity functions. Two are stable with radiant intensity, the photopic and scotopic luminosity functions. The mesotopic luminosity function is a continuous variable with intensity. The hypertopic luminosity function represents an overload condition and will not be developed here. Very carefully defined experimental procedures must be used to obtain accurate graphs of these functions.

To obtain a luminosity function that is independent of the input illumination conditions, it is necessary that the input irradiance contain an equal number of photons per spectral wavelength interval. This can be done by using a source operating at a color temperature of 7053 Kelvin. For any other source temperature, the resulting luminosity function is a function of the source temperature and it should be properly labeled to reflect this fact.

Since the luminosity functions for each illumination regime are each complex functions of the input irradiance, they do not vary in a smooth manner with changes in color temperature. It is only after sufficient smoothing to remove all of the local maxima, minima and inflection points that a curve similar to the C.I.E. standard luminosity functions are obtained.

17.2.1.1 Historical determination of the luminosity function

The visual community began making significant efforts to define the luminosity function of human vision with the arrival of the early electrical age, nominally the 1850's. In that time period, the only known materials subject to photoexcitation were considered photo-conductors. This name was as much colloquial as scientific. The photo- emissive effect was unknown, and the internal energy levels associated with the various components of a molecule were also unknown until the 1920's. Today, the effect observed in different materials would be described by the more global photoelectric effect which includes both the photo-conductive and photo-emissive effect. As will be shown in the next paragraph, the chromophores associated with photodetection in vision are photo-emissive in character, employing the internal photo-emissive effect. Unfortunately, when discussing photometry and colorimetry, the visual community has continued to assume the visual system is based on photo-conductive material to this day. All data, models and theories in the literature to date are based on the use of an equal-energy per unit

65Saito, M. Adachi, N. & Kondo, H. (2007) Full-color illumination that neeeds no electric power Optics Express vol 15(4), pp 1621-1626 66Babucke, H. (2007) private communications 67Hurvich, L. & Jameson, D. (1953) Spectral sensitivity of the fovea. I. Neutral adaptation. J. Opt. Soc. Am. vol. 43, no. 6, pp 485- , fig 3. 66 Processes in Biological Vision

bandwidth illumination source.

As the field of photometry advanced into the 20th Century, the human eye was assumed to be a linear device with respect to wavelength. At the time it was frequently used as a null detector in many experiments. As developed in Wyszecki & Stiles; “The matching of brightness is the fundamental operation of photometry...The observer’s eye functions are [sic] little more than a sensitive null instrument that could be replaced by wholly physical light sensitive devices with response properties deviating widely from those of the human eye, including a different and unrelated spectral responsivity.” Unfortunately, the above characterization is much too broad. The complexity of the signal processing in the eye makes it a very poor scientific instrument, even when used as a null instrument in photometry. As noted elsewhere herein, experimenters have great difficulty in separating the response of the subjects with regard to chromatic and achromatic responses. These two responses do not correlate well. In addition, it does not operate in the same mode as photo-conductors and the Uni-variance principle only applies to individual spectral channels (not the visual spectrum as a whole).

Because of the poor understanding of the mechanisms of vision up through the present, it has been difficult for the vision community, both science and engineering, to develop well founded terminology with respect to the sensitivity of the eye to radiation. The Science of Color68 includes some information on this situation. The performance was generally couched in terms related to “visibility data.” Early investigators spoke of the visibility function of the eye when actually referring to the sensitivity of the human eye to narrow band equal energy radiation as a function of wavelength.. This term was superceded in 1939 by the term luminosity function. In 1951, this term was subdivided into two terms recognizing the difference between the photopic and scotopic levels of excitation. Up to now, these functions are defined based on empirical measurements using instrumentation of poorly (or unspecified) spectral bandwidth and light sources of unspecified color temperature (generally in the 2400 to 6000 Kelvin range. The bulk of the data was collected using temperatures near the lower value and the results were clearly deficient in the “blue” portion of the spectrum.

The so-called luminous efficiency functions embraced by the C.I.E. are actually measures of the response of the nominal eye to radiation, not illumination, as a function of wavelength. The highly smoothed data collected to describe this relationship has been arbitrarily defined as the luminosity function of the eye at an undefined radiation level thought to lie within the scotopic and the photopic operating ranges of the subjects eyes. These functions have been used to define the filter characteristic placed in front of a broadband, photoconductive detector of radiation. The combination of filter and (generally photoconductive) radiometer was thereby renamed a photometer.

Up until the present era, the most precise descriptions of the spectral sensitivity of the human eye date from 1983. Foster and Snelgar measured the spectral sensitivity under a variety of conditions and noted the peak long wavelength sensitivity moved from 570 nm to 610 nm in the presence of a white conditioning illumination spatially coincident with the test field69. In the same volume, Thornton & Pugh provided spectral sensitivities showing distinct peaks at approximately 430 nm, 530 nm and 615 nm70. Hood & Finklestein presented data showing the drastic change in spectral sensitivity with exposure interval and spatial diameter, essentially from a single peak function for small brief stimuli to tri-peaked sensitivity to larger, longer stimuli71. Krastel et al. show similar

68Science of Color, 3rd printing (1963) Jones, L. Ed. and Chairman, Committee on Colorimetry, Wash. D.C.: Optical Society of America pp. 223-232 69Foster, D. & Snelgar, R. (1983) Initial analysis of opponent-colour interactions revealed in sharpened field spectral sensitivities In Mollon, J. & Sharpe, L. eds Colour Vision NY: Academic Press pp 303-311 70Thornton, J. & Pugh, E. (1983) Hue cancellation and increment thresholds In Mollon, J. & Sharpe, L. eds Colour Vision NY: Academic Press pg 366 71Hood, D. & Finkelstein, M. (1983) A case for the revision of textbook models of color vision: the detection and appearance of small brief lights In Mollon, J. & Sharpe, L. eds Colour Vision NY: Academic Press pp 387+ Performance Descriptors 17- 67 variations with test conditions, including a peak long wavelength sensitivity near 610 nm, in the same volume72.

Wyszecki & Stiles describe more than ten methods of determining the luminosity function of the visual system, most of which are not compatible with the more precise terminology of luminous efficiency function. Some of them provide data that can be interpreted as a relative luminous efficiency functions. Most of the methods involve differential measurement techniques which are normally less precise than absolute measurement techniques. The Absolute Threshold Method is described in subheading (vi). This method can provide a true luminous efficiency function and is compatible with the derivation of both the absolute and relative theoretical luminous efficiency functions of this work. The comments of LeGrand in that paragraph are not supported by the model and equations of this work. The equations and graphs of the following sections will clearly demonstrate that multiple photoreceptors are active under threshold conditions and it is their cooperative responses that actually determine the detailed shape of the luminous efficiency function. This work provides the framework necessary to broaden and define the “envelope” of the sensitivities of the individual photoreceptor mechanisms discusses by Pirenne in that paragraph.

The next paragraph will also show the importance of separating the above methods into those associated with the threshold performance of the system and those only providing relative amplitude performance relative to an arbitrary peak response.

There has been little recent discussion of the theoretical foundation of the luminosity function. It has been assumed for decades to be a linear summation of the light absorbed by three photoreceptors. This has been formalized by the same equation used in deriving the chromatic characteristics of the eye.

C = xR + yG + zB Eq. 17.2.1-1

where C is the “total color” and x, y & z are in percent

As discussed in detail in Section 17.3.3, this equation is a complete mis-statement of the signal manipulation within the human eye. The appropriate equation is developed in the next Section.

17.2.1.2 Theoretical Background

17.2.1.2.1 Energy related matters

There are very significant theoretical and practical differences between materials with a very narrow band gap between their valence and conductance bands and materials with a wider band gap. Materials with a very narrow band gap exhibit a finite resistivity at room temperature. This resistivity is often a function of temperature, and this temperature can be raised by the irradiance of the material by light. Such materials are called photo-conductors. They are sensitive to the energy deposited on them by the radiation received. A current passing through such materials typically exhibits a noise component whether the material is irradiated or not. This noise component is normally described quite accurately using Gaussian statistics.

A wide band gap material will not exhibit a significant resistivity at room temperature and will be classified as an insulator. However, upon irradiance with photons of high enough energy, i.e. actinic irradiation, nearly all materials will exhibit a current upon the application of a voltage. This current may be between two terminals of the material, (due to the solid state photo-emissive effect) or between a terminal attached to the material and a second electrode nearby but separated from the material by a vacuum (due to the vacuum photo-emissive effect). The second case

72Krastel, H. Jaeger, W. & Braun, S. (1983) An increment-threshold evaluation of mechanisms underlying colour constancy In Mollon, J. & Sharpe, L. eds Colour Vision NY: Academic Press pp 545-552 68 Processes in Biological Vision

was the subject of the Einstein Photoelectric Effect of 1905, for which he won a Nobel Prize in 1921. This work ushered in the quantum physical era. This Effect was later shown to equate the “photoelectric work function” of the surface with the internal bandgap of the material. These materials are sensitive to the number of quanta of actinic photons deposited on them by the radiation received. Materials with a wide bandgap generally exhibit a noise component, associated with any induced current, that is quite different from that of photo-conductors. The noise is normally due to the quantum statistical characteristics of the incident radiation. At the theoretical level, this noise is described by Bose-Einstein statistics. For irradiation by photons of less than a critical energy, no current is generated by the photo-emissive effect.

Making the assumption that the visual system employed photo-conductors, early investigators began using equal energy per unit bandwidth, sometimes per unit frequency, light sources in their experiments. The assumption was that this type of energy source would excite the different photoreceptors of the eye equally. Unfortunately, the visual system does not employ photo-conductors. The chromophores of vision are wide band gap materials exhibiting the internal photo-emissive effect. In the absence of irradiation by photons of sufficiently high energy, no signal is generated, and no noise is generated. Under actinic radiation, the signal generated is related to the number of photons per unit area received times the absorption coefficient of the material at that photon energy. Single photon events are easily recorded using photo-emissive materials. The photo-emissive characteristic of the photodetectors of the toad, Bufo marinus, was beautifully demonstrated in the electrophysiological experiments of Baylor, et. al73. Although aware of the phenomena, those investigators did not appreciate completely the nature of the randomness, given by Bose-Einstein statistics, associated with their experiments.

[xxx Rewrite ] Today, a fundamental determination is made as to the type of photo-electric material or device under study before any experiments are designed to evaluate that material or device. In the case of vision, this determination is made more difficult by the “square law” operation of the visual detector associated with the L- channel. Because of this situation, the only real method of determining the “quantum efficiency” of the visual photodetectors as a group is based on signal to noise ratio calculations. These are difficult to quantify in themselves. For quantum based events, they must be based on Bose-Einstein and not Gaussian statistics.

This section will present a series of graphical descriptors capable of defining the theoretical sensitivity of the nominal human eye to radiation and to a more abstract term, illumination.

17.2.1.2.2 Noise related matters

When measuring the luminous performance of the visual system, it is important to distinguish between measurements made relative to some high level of response, generally the peak response in the 532-550 nm region, and measurements made relative to a low level, such as the noise level of the system. The latter approach results in a luminous threshold function which is an absolute descriptor of the system.. The former approach only provides a relative response of little theoretical significance. Each of the eleven approaches mentioned above needs to be examined and categorized against these criteria.

17.2.1.3 Operational considerations

The animal eye was shown in Chapter 16 to operate in four distinct illumination regions and to incorporate a number of non-additive mechanisms. The human eye operates similarly but effectively in only three illumination regions. This makes it necessary to evaluate the luminance performance of the human eye separately for each of these

73Baylor, D. Lamb, T. & Yau, K.-W. (1979) Responses of retinal rods to single photons. J. Physiol. vol. 288, pp. 613-634 Performance Descriptors 17- 69

regions. The complexity of the signal detection, signal processing, signal projection and signal interpretation circuitry makes it extremely important to understand the functional aspects of the entire system before attempting to evaluate its response to radiation.

Because of the automatic adaptation characteristics of the eye, it is difficult to discuss the absolute sensitivity of the eye except at the lowest irradiation levels, i. e. the scotopic and mesotopic regions. At higher irradiation levels, the signals presented to the circuits proximal to the photoreceptor cells are not indicative of the absolute performance of the photodetection process. This is due to the changing amplification factor of the adaptation amplifier of each photoreceptor cell. Once the radiation level becomes sufficiently high, the hypertopic region of operation is reached. There is further circuit saturation in this operating region and it is even more difficult to describe performance in simple terms.

To obtain accurate sensitivity data, it is absolutely mandatory that the color temperature of the radiation source be well characterized and the spectral bandwidth of any filters be well known.

17.2.1.3.1 The relationship between dark, light and chromatic adaptation

A one-day conference was held on March 20, 2000 devoted to the study of adaptation from a largely psychophysical aspect. The conference suffered from a lack of a sufficiently accurate physiological model of the visual system and from a poor definition of the terms involved. The models were largely conceptual and floating. The preface by the organizers describe the less than desirable framework available for the conference74. As they note, “This conference was motivated by the identification of a need to satisfy these goals.” However, some useful data was presented.

It is useful to review the relationship between dark adaptation and white light adaptation. Under dark adaptation conditions, all of the adaptation amplifiers of the eye are operating at full amplification factor (gain). The eye continues to operate in this mode as the irradiance level is increased until the variation in gain due to the avalanche gain mechanism becomes significant. This typically occurs at and defines the lower limit of the photopic region. Up to that level, the state of adaptation in each of the spectral channels will remain independent of the spectral characteristics of the illumination. Above this level, the gain of each of the spectral channels will be reduced. However, these gains tend to track each other up to the point where one of their gains reaches unity. This level defines the top of the photopic region. From that point up to higher irradiance levels, the signal level at the pedicle of the photoreceptor will change considerably between the spectral channels.

Within the photopic region, the action of the adaptation amplifiers will maintain the relative signal amplitudes at the pedicles of the photoreceptors constant for any light source that is nominally white, i. e., has a photon flux per unit wavelength that is reasonably constant --typically daylight at 7053 Kelvin. Below the lower limit of the photopic region, the square law response of the long wavelength channel will cause the signal level at the pedicles associated with that channel to drop regardless of the gain of the associated adaptation amplifiers. As a result, the eye will exhibit a scotopic spectral response at light levels significantly below the lower limit of the photopic region (even if a nominally white light sourc is used as a source).

17.2.1.3.2 A chromatic spectrum for reference

It is useful, when analyzing the spectral sensitivity of the eye, to have a continuous multicolor background spectrum available as a reference. It is virtually impossible to produce such a background using conventional “process color” printing techniques, even with the use of additional spot colors. A marginally more effective background can be provided using photographic prints of photographic negatives. In both cases, the spectrums are prepared using sampling techniques (three separate but highly overlapping channels). The best available backgrounds found by the

74Langley, K. Simmons, D. & Welchman, A. (2002) Visual Adaptation Spatial Vision vol 16(1), pp 1-3 70 Processes in Biological Vision

author are the wall chart produced by Laurin Publishing Co.75 and the plate in Dowling76 reproduced in Gouras. The difference in the intensity of the yellow region of the spectrum is pronounced between these two examples. Since the reproducible color range of both the photographic and process color techniques are limited compared to animal vision, they can not be relied upon for quantitative purposes. The region between 400 and 450 nm is particularly poorly reproduced.

All of the spectral peaks in the overlays shown in Dowling, except for the L-channel, are in agreement with this theory. The L-channel peak should be at 610 nm. The half-amplitude widths are not defined on the Dowling plate and the individual spectra are represented by approximately Gaussian waveforms. They are shown as having different half bandwidths. This theory calls for the waveforms to be shaped according to Fermi-Dirac statistics which gives them a flatter top and more defined skirts. The new half-amplitude values are at 400 & 475 nm., 500 & 565 nm., and 595 & 655 nm. the spectral peak associated with the ultraviolet sensitivity of the human retina is not available in any reference spectrum. The Laurin chart appears to be poor in the region between 650 & 700 nm. where it shows the color of red to continue to become “redder” as it fades to black, instead of reverting toward the hue of the 600-650 region.

17.2.1.3.3 Chromatic filters for laboratory use

The proper choice of chromatic filters and light source are critical in precision visual spectral measurements. When using broad band filters, it is important to use test sources with spectral content that is carefully chosen to maximize the difference in signal amplitude between the channels being evaluated. The optimum filters are different for short-wave trichromats, tetrachromats and long-wave trichromats. Livingstone & Hubel77 and Kelly & van Norren have used filters suitable for the long-wave trichromats. However, their choices did not recognize the theoretical shape of the chromophores involved. A slightly different set may be better able to avoid undesired cross- excitation of the channels by the filters. Table 17.2.1 compares the two sets.

TABLE 17.2.1 SPECTRAL FILTERS FOR VISUAL RESEARCH ON LONG-WAVE TRICHROMATS

Livingstone Kelly & This & Hubel van Norren work

UV — --- S 47B 47 30 & long wave blocker M 58 61 74 or 99 are better* L 29 29 or 70 22 & long wave blocker YELLOW 16 106 45

Numbers are for Wratten filters. All filter sets should include an IR blocker since the eyes are more sensitive in the IR than conventional photographic film.

75The Photonic Spectrum Reference Wall Chart. © copyright 1992 Laurin Publishing Co., Inc. Pittsfield, Mass. 76Dowling, J. (1987) called in Gouras, P. (1991) Vision & Visual Dysfunction, Vol. 6. Boca Raton, FL: CRC Press plate 9 77Livingstone, M. & Hubel, D. (1984) Anatomy and physiology of a color system in the primate . J. Neurosci. vol. 4., pp. 309-356 Performance Descriptors 17- 71

* Built from a #57 or #53 & a short wave blocker.

17.2.1.3.4 A light source for laboratory use

As discussed in some detail in Section 1.3.4, the use of an adequate light source is mandatory for precise spectral measurements in vision. For measurements involving the complete eye, and overlooking the residual ultraviolet sensitivity, a 7053 Kelvin black body light source is required. Such a source provides an equal photon flux per unit spectral bandwidth within +/- 5.7% across the spectrum of interest in long-wave trichromat research. If more complete measurements of the eye are desired or the response of the retina is sought, a blackbody light source with a temperature above 8000 Kelvin is required. A source with a temperature of 8683 Kelvin provides a uniformity of flux within +/- 7%. In both cases, the deviation from nominal is predictable. The use of a source of considerably lower temperature than recommended will result in significantly erroneous measurements in the short wavelength measurements. Even the C.I.E. defined “illuminant C’ is inadequate.

17.2.1.3.5 The systemic variation in retinal sensitivity with spatial position

Stiles provided Figure 17.2.1-2 which characterizes the threshold incremental sensitivity of the human retina at four different wavelengths78. The figure is important for several reasons. First, it shows the distinct separation of the foveola (nominal diameter of 1.18 degrees) and the fovea (nominal diameter of 8.68 degrees but shown here at 4 degrees). Second, it shows the relative perceptual sensitivity of the photoreceptors with position. The perceived sensitivity is strongly impacted by the number of photoreceptors that are summed in the process of generating the luminance (R-channel) signals of vision. In the area near the point of fixation, summation is minimal. In fact, this work proposes that no summation occurs within the foveola.

Many authors have referred to the absence of S-channel sensitivity in the fovea specifically and by inference the foveola. Notice this figure shows only a 2:1 or 3:1 loss in perceived sensitivity of the S-channel within the foveola relative to the fovea. It shows essentially the same loss in perceived sensitivity between the S-channel and the M- channel (using 475 nm light as a reference) for both the fovea and foveola. Thus, there is no indication that the retina is blind to blue light in the foveola or fovea under threshold conditions. The loss between the fovea and the peripheral regions is shown as near 100:1. However, this value is highly dependent on the size of the source. For point sources, the value is much closer to 1:1. This is easily demonstrated by looking at the stars at night. The stars within the foveola and fovea do not appear significantly brighter than those outside of the fovea. Wyszecki & Stiles discuss the relevance of the test protocol in determining threshold sensitivities (page 523-525)

78Stiles, W. (1949) Increment thresholds and the mechanisms of colour vision Doc Ophthalmol vol 3, pp 138-165 72 Processes in Biological Vision

Figure 17.2.1-2 Variation of increment threshold in traverses through the dark-adapted foveal and parafoveal area with monochromatic test stimuli of different wavelengths. From Stiles, 1949. Performance Descriptors 17- 73

17.2.1.3.6 The systemic variable related to ageing

In the past, it has been common to define the eyes of the subjects as “young eyes” or to give the age of the subjects without any quantification of the significance of age. The effect of Rayleigh scattering within the physiological optics of the eyes can be quantified. This effect exhibits an inverse fourth power relationship with wavelength and becomes more prominent at a rate of about 0.5% per year. Because of the fourth power relationship, it is predominant in the short wavelength spectral channel and can be largely ignored in the other channels. In practice, this change in short wavelength performance is not normally noticed. This is because of the compensation provided by the adaptation amplifiers. However, the range of the photopic region, as defined here, is systemically reduced with age. This fact should be considered in experiment planning for research purposes.

17.2.2 The relationship between brightness and luminance in vision

The relationship between the luminance applied to the eye as a stimulus and the perceived luminance, the brightness, reported by the visual system has not been discussed in detail in the literature. The major problem has been the lack of a framework within which to discuss this subject. Studies of the hearing modality have proceeded further in this area and they may offer insight. Vision involves a more complex stimulus environment than does hearing. The hearing environment can generally be resolved into a small set of individual sources within the external spatial environment. Vision, on the other hand, typically involves a large number of significant sources that exhibit spatial variation themselves, and are embedded in an even more complex background environment. However, by restricting a test stimulus sufficiently, it is possible to draw analogies between the visual and auditory sensory modes.

The additional dimensions of vision, compared to hearing as an example, make measuring and interpreting the overall amplitude sensitivity range of vision quite difficult. These dimensions result in a wide proliferation of different test stimuli.

At a very fundamental level, the difference between stimulating the visual system with an active source (a light) versus stimulating it with a passive intermediary (reflection by a surface illuminated by an unseen source) leads to additional complexity in exploring the amplitude sensitivity range of vision.

Finally, the dynamic accommodation capability of vision, known as adaptation, plays a major role in nearly all experiments related to the overall amplitude sensitivity range. While adaptation is primarily a temporal effect, it does contain a spatial component. The spatial component is due to the sharing of energy resources among the photoreceptors within the hydraulic environment of the retina.

Because of these complexities, most of the work aimed at evaluating the sensitivity performance of the visual system has been focused on a limited range (the photopic region). Even within this range, most of the activity has been restricted even more narrowly to the largely qualitative range defined by the Munsell Values of zero to ten. This range incorporates a range of only xxx:1 in luminance intensity.

Most of the activity in determining the sensitivity range of vision has involved differential tests employing pairs of test targets. These test targets generally have a minimum spatial dimension of two degrees or more in order to achieve an adequate signal to noise ratio in tests involving one individual and reasonable correlation among individuals.

The description of the test target configuration used in amplitude sensitivity experiments is itself complex. This is largely because of the number of dimensions involved, as discussed above. Historically, the test targets have been described using the terms unrelated and related. In this work, the same situations will be described by the clearer terms, isolated and embedded respectively. an isolated test target is viewed against a dark background. An 74 Processes in Biological Vision embedded test target is surrounded by a single area of either a nominal luminance level (of the same chrominance as the test target) or an even more complex surround of multiple luminance and chrominance levels. When comparing test targets in embedded environments, the data reduction and interpretation tasks become even greater.

17.2.2.1 The perceived intensity of sound versus its actual intensity

By restricting the stimulus to a single audible tone, it has been possible to describe the perceived response to that tone over a large dynamic range in humans as characterized in Figure 17.2.2-1 from Fulton79 (figure 5.4.4.-1 of manuscript).

Figure 17.2.2-1 The perceived audio loudness as a function of sound intensity in humans ADD. The thin dashed lines indicate the gain of the adaptation amplifier circuit (which varies with the state of adaptation before a given stimulus is applied). From Fulton, 2006.

The individual performance regions of the auditory system are readily distinguished in this figure. Below the adaptation range, in the scotopic region, the loudness increases in direct proportion to the intensity of the sound. Within the adaptation range, the phonotopic region, the gain of the adaptation amplifier decreases in proportion to the stimulus. This results in an apparent increase in loudness with intensity given by an exponent of 0.6. When the

79Fulton, J. (2006) Biological Hearing: A 21st Century Tutorial. Vancouver, BC, Canada: Trafford Performance Descriptors 17- 75

adaptation amplifier gain has reached its minimum value near 1.0, it can no longer suppress the loudness versus intensity function. The function proceeds to increase linearly with intensity in the hypertopic region.

17.2.2.2 The perceived intensity of light versus its actual intensity

Within broad limits, the above figure can be used to predict the performance of the human visual system. Figure 17.2.2-2 shows such a conceptual representation. The operating regions are correlated with the luminance level based on the values in Section 2.1.1. The ordinate is arbitrary but will be related to the Value scale of Munsell as the discussion proceeds. The figure will be definitized further by specifying the size of the isolated test target used to acquire the data in the figure. Based on the previous figure and the observations of Stevens, the solid curved line intersecting with the dash-dot line labeled compression can be expected to describe the overall response of the visual system to a luminance stimulus in the absence of any adaptation mechanism. If the feedback employed by the sensory neurons was 100% effective in limiting the growth in the neural signal above a specific cut-in value, the curve labeled 100% adaptation asymptote would be achieved with the introduction of adaptation. However, the feedback employed in vision, like in hearing, is not designed to provide a hard limit on the brightness response. It is designed to expand the brightness range associated with a given luminance range over a limited operating range known as the photopic region. The result is the dashed line through the middle of the shaded box labeled “Normal Operating Regime.” The following material will attempt to quantify the scales of this figure more completely. 76 Processes in Biological Vision

Figure 17.2.2-2 Proposed template for the perceived visual brightness as a function of luminance intensity in humans ADD. The dashed line within the Normal Operating Regime is called the terminal brightness locus by Stevens & Stevens. The Compression line is called the Dark adaptation line by them.

Wyszecki & Stiles have provided a broad overview of the brightness versus luminance response of human vision80. However, the material is difficult to interpret because it lacks an underlying framework. Note that no two figures among these pages use the same scales. The data of Bodmann, et. al. (W&S, page 495) shows one piece of isolated target response data and a second piece of embedded target response data, without information on the state of adaptation of the eye. The test targets had an angular subtense of two degrees. The surround in the embedded case is described as 180 degrees, which may or may not have been full field in actuality. The statement that the test target has a given subtense is incomplete. Is the target round, square or otherwise. If square, is the subtense equal to the diagonal or the side. Neither eye has a field of view of 180 degrees in either the horizontal or the vertical aspect. However the pair of eyes has a horizontal field of over 180 degrees. Was the specification meant to describe a surround covering the full field of view of the eye(s) involved. The abscissa of the data covered 1 to 105 candles per square meter without any discussion of what operating ranges this luminance range corresponds.

80Wyszecki, G. & Stiles, W. (1982) Op. Cit. pp 493-499 Performance Descriptors 17- 77

Wyszecki & Stiles have provided a figure of considerable interest that is reproduced here in modified form as Figure 17.2.2-3. The term Y is that of the CIE coordinate system for the luminous reflectance for an opaque sample or luminous transmittance for a transmitting sample.

The abscissa of the upper half of this figure only covers a linear luminance range described by 0 to 100. This half describes the relationship between the perceived brightness of a test tablet when illuminated under standardized conditions as measured by several investigators. The functions shown are actually the equations recommended by those investigators to represent this response. The mathematical description of these functions are given on page 823 of Wyszecki & Stiles. The best fit to the data is represented by curve 4. This curve was first proposed by Newhall, Nickerson & Judd using the first five terms of an infinite series and using a magnesium oxide tablet as the reflecting surface (reflectance taken as 97.5%). They used a source at a color temperature of 6700 Kelvin. As noted rather cryptically on page 823, this gives Y=102.568 for V=10 although no units were associated with this value. In the original paper, the numeric was given in percent. The proposal was part of the Renotation activity related to the Munsell Color Book. Their equation was awkward because the value was the independent variable in the equation for Y. Bridgeman attempted to provide an equivalent equation for Y in terms of β, where β was expressed in terms of each of the three CIE tristimulus values81.

Two facts need to be noted about the Wyszecki & Stiles figure. First, it is an expansion of an earlier figure in Newhall, Nickerson & Judd (figure 14). See Section 17.3.8. Second, the curves described as fitting a cube root equation well do not fit a cube root Figure 17.2.2-3 Relationship between lightness-scale value V and luminance factor Y plotted in accordance equation well by the graphic standards of today. They with different formulae. See text. Upper quadrant from were probably drawn manually. Wyszecki & Stiles, 1982.

The Newhall expression was converted to a cube root expression and adopted by the CIE in 1976 in their first excursion into a non-linear expression for brightness. They defined L* / V over a limited range. The same curve can be expressed as a simple natural logarithm (or a Briggs logarithm to the base 10) based on the theory of this work. If the limited range of V = 0 to 10 of the upper vertical axis applicable to a Relative Munsell Color Space is redefined in an Absolute Munsell Color Space, the exponent of the luminance parameter of the lower vertical axis can be used as a scale factor in a 3D Color Space as in Figure 17.4.2-1 & -2. As a logarithm, the expression precisely relates the reflectance of the achromatic set of chips in the matte version of the Munsell Color Space quite precisely over the value range from V=2 to 10 as shown in the following figure from Romney & Fulton82.

81Bridgeman, T. (1963) Inversion of the Munsell Value Equation J Opt Soc Am vol 53, pg 499 82Romney, A. & Fulton, J. (2006) xxx (In Press) 78 Processes in Biological Vision

Based on the success of the logarithm in matching the measured values of the Munsell chips, it can be said that the equations suggested by other investigators on page 492 of Wyszecki & Stiles are now obsolete. The theoretically

supported expression is V=kClnY - kClnY0+C =kCln(Y/Y0)+C where C is a scale factor related to any arbitrary

luminance level Y0. In the Absolute Munsell Color Space, Y0 is nominally equal to 300 Lux when reflected from a 100% reflective surface.

Luminance covers an immensely wider range than shown in this upper half, normally described better using a logarithmic function of much greater extent. To introduce this larger range, the figure has been extended in the bottom quadrant. This new graph provides a broader view of the operation of the visual system. It allows a discussion of the potential equations listed by Wyszecki & Stiles as candidates for describing the brightness (or lightness) versus luminance relationship in vision. The intent is to allow the operation of the visual system over its entire range of operation, including the range expanding feature of the adaptation system, to be displayed on one graph .

- - -

Wyszecki & Stiles have discussed the repercussions of using high luminance levels on visual color-matching performance in a variety of contexts (pp 374-379) including adaptation to one broadband light source followed by observing a different broadband stimulus. Their definition of a photopic Troland is a surface illuminated at 1 Candela/m2 viewed through a 1mm2 pupil. Unfortunately, this definition and their data is presented based on an embedded CIE visibility function (V(λ)) instead of a more realistic representation of the sensitivity profile of the human retina (Section 17.2.3.5.1). They do not reach a useful conclusion after presenting the data. They use a red test source at 572 nm but a white source including red source component at 645 nm without any discussion of why. Their blue and green sources were the same for both test sources and their composite white source. Neither 572 nm (a yellow or greenish-yellow) or 645 nm (a reddish-) is usually associated with a saturated red sensation. See Section 17.3.9.1. The Troland is only applicable to the on-axis (thin lens) model of the eye (Section 17.1.2.1.1).

- - - -

Romney & Indow have recently published a new calibration of the matte achromatic chips in the Munsell Color Book of 1976. Their results are in excellent agreement with the theory of this work. As a concept used by many empiricists, they attempted to fit a cube root to their data points instead of using the more appropriate natural logarithmic function suggested by theory. Figure 17.2.2-4 shows their results when their measured values are fitted with a logarithmic function, U(M) = Ln L(M) plotted on linear scales. AA1 corresponds to the xxx They originally collected and fit the data only between a Munsell values of 2 and 10 with a cube root curve. That curve (red line) is underneath the logarithmic curve and can be seen at the very toe of the curve. The logarithmic curve continues on both sides of the experimental region as shown. Using the Romney & Indow data, the value range from xxx to xxx corresponds to a reflectance change of xxx:1. This information can be used to calibrate the overall Munsell Value range. [xxx continue ] Performance Descriptors 17- 79

Figure 17.2.2-4 The human visual response based on the Munsell Color Book using a box plot. The plot shows the relationship between Munsell Value levels (the y-axis) and the axis AA1 as in the right panel of Fig. 2 (the x-axis). Values of AA1 of colors of constant Value are not exactly constant. Red dots represent means, boxes contain 50% of cases and median line, whiskers contain the range of values that falls within 1.5H spread of the hinges, and asterisks show outliers. The fitted red curved line is described in the text. [xxx put horizontal reflectance scale back in so the change in reflectance can be associated with the change in Munsell value. See text. Figure modified from shaded box and data points from Romney & Indow, 2003.

Almost simultaneously, a second Romney & Indow paper83 appeared confirming the above results in a somewhat broader context (370 color samples and the use of a D65 illuminant). They employed an extensive statistical analysis using singular value decomposition (SVD). “In the present paper, the analysis is limited to a sample of the 360 most representative Hs, namely, (5R, V/C), (5YR, V/C),..., (5RP V/C), where V covers 2, 2.5, 3, 4, 5, 6, 7, 8, 8.5, 9V, and C covers the whole range of chroma.” It confirms the axes proposed in this work for the Munsell Color Space, at a slightly less precise level, and discusses minor differences from earlier work.

“Jameson and D’Andrade have drawn attention to this discrepancy between the axes posited by opponent process theory and the axes in the Munsell color system. They say that opponent process theory ‘. . . can never be patched up as long as unique are maintained as unitary sensations and antagonist channel zero-crossings. In light of these facts it seems wise to pursue alternate hue axes that model the empirical data more closely, and we suggest that

83Romney, A. & Indow, T. (2002) A model for the simultaneous analysis of reflectance spectra and basis factors of Munsell color samples under D65 illumination in three-dimensional Euclidean space PNAS vol 99, pp 11543-11546 doi/10.1073/pnas.162368999 80 Processes in Biological Vision one such model may be provided by a maximized interpoint-distance formulation in, for example, the Munsell color space, or in some other perceptual scaling space.’”

Stevens & Stevens have provided a large volume of data supporting the proposed template for describing vision84. That paper should be reviewed in detail by the serious reader. The work provides absolute scales for both the ordinates and abscissa. However the units used are unconventional or unknown in vision research. S. Stevens had long been working in hearing at the time of this paper. In moving into vision, he did not appear to appreciate the vast difference in wavelength of the energy involved versus typical source sizes. Where point sources are the norm in hearing because the wavelength is much greater than the typical dimensions of a speaker, the situation is quite different in vision. The wavelength of light is much less than even the smallest element in a scene. As a result, sources are typically large in area and the energy radiated by these sources must be accounted for on a per unit area basis. Their use of lumens as a unit of energy, equivalent to a watt is not appropriate. This energy could be spread over an unspecified source area and result in any luminance desired. This oversight may be due to the situation highlighted by Jones in the same volume of the same journal85. “In describing the calibration or use of a radiometer, it is customary to say something like: “Basically , a radiometer measures irradiance, nor radiance, even though it is calibrated in terms of radiance.’” the proper use of such a radiometer or photometer requires careful attention to the instructions in the user’s manual. Stevens & Stevens defined a logarithmic scale, similar to that used in hearing, based on 10-10 lumens = 0 dB. They asserted this value was near the threshold of vision. They also defined a unit of psychophysical response they called a brill. They defined it as the brightness seen (? perceived) under the standard conditions when the target has a luminance of 40 dB re 10-10 L or 1 μL. (Unfortunately, they later used the term mL which is the standard abbreviation for millilambert rather than millilumen). They did not define any linearity relationship between the brill and the Lumen. However, they did present a graph of the brightness in brills (perceived luminance) as a function of the “luminance” of the source based on their dB scale. In this figure, a 10 dB change in brills equaled a 30 dB change in luminance, resulting in a slope of 0.333 for the depicted relationship. The brill has not survived in modern vision literature. It is fortunate that the data reported can be converted to a more appropriate luminance scale because of the linearity between lumens and cd/m2 for a given test configuration. The labeling of their light source as 150 watts is superfluous. This is the power into their lamp and is unrelated to the amount of light illuminating their test target.

Figure 17.2.2-5 shows figure 7 of the Stevens & Stevens paper based on their definition of luminance as related to lumens. This figure shows a strong familial relationship to the previous template. There is an asymptote labeled “dark” that corresponds to the compression line of the template. There is also a dashed line below the dark asymptote that they describe as the equilibrium condition following adaptation. It corresponds to the dashed line in the template where it has the same significance. However, in the template, any variable element in the impressed signal results in a variation in perceived brightness in accordance with this curve. The Stevens & Stevens figure shows the individual responses converging in the upper right toward a value at 130 dB luminance (1000 brill). The theoretical template was developed for isolated stimuli and does not show this condition although it does not disparage it.

The Stevens & Stevens test configuration involved an embedded stimulus of 5.7 degrees diameter within a surround described as limited by a second aperture to 58 degrees. This allowed testing under different levels of central illumination while using a controlled surround. As a result, curves were obtained similar to that of Bodmann et. al. They systematically fell below the dark line that was equivalent to Bodmann, et. al’s. isolated stimulus and the compression line of the template.

84Stevens, J. & Stevens, S. (1963) Brightness function: effects of adaptation J Opt Soc Am vol 53(3), pp 375-385 85Jones, R. (1963) Teminology in photometry and radiometry J Opt Soc Am vol 53(11), pp 1314-1315 Performance Descriptors 17- 81

The term adaptation level in this figure should probably be defined more clearly as the surround brightness level. It does not relate directly to the adaptation level of the circuitry within the photoreceptor cells.

Figure 9 of Stevens & Stevens replots the curves of figure 7 on linear-linear scales. The resulting curves show a generic exponential character and a equilibrium brightness that is essentially horizontal. This is a characteristic of the feedback loop associated with the sensory neurons which is designed to perform a clamping function (Section xxx). It suggests the clamp level is near 50-100 brill for a target luminance of 20- 100 millilamberts. (It is not clear why millilamberts are used in this figure rather than their Lumens in dB parameter). For levels above this value, the perceived Figure 17.2.2-5 Brightness functions for various levels of brightness remains nominally constant within the adaptation. The dashed line shows the terminal brightness adaptation range of the photoreceptor cell. They noted locus–the level of sensation reached when the eye comes Craik confirmed this equilibration level held up to a into full equilibrium with the luminance it is viewing. luminance of 75,000 ft-L (119 dB) using a Maxwellian view test set86.

Stevens & Stevens give no data points, other than one in their figure 8 with a wide range bar (one order of magnitude), to substantiate the verticality of the individual curves they show under low luminance conditions. However, the depiction agrees with that suggested by the theoretical template.

In discussing their figure 7, Stevens & Stevens made several critical observation (page 381). First, they noted the equilibrium curve did not follow a power law as the operating point changed. Second, they noted, “The terminal or equilibrium brightness function shows that, if the visual receptor is allowed to adapt to the level of the stimulus, the input-output relation may approximate a logarithmic function more closely tha a power function, at least over some of the range.” They also note “the changing ‘operating point’ of the visual system that results from different levels of adaptation can thus obscure the basic form of the psychophysical function.” This last statement appears to be poorly constructed. The changing of the operating point is also a fundamental property of the visual system.

17.2.2.3 Analysis of the brightness/luminance relationship

[xxx end with a new template with specific scales. Show or claim the theoretical template is exact for the isolated stimulus The Stevens & Stevens case shows the theoretical template with an embedded stimulus]

A new theoretical performance graph for the visual modality is shown in Figure 17.2.2-6. It is calibrated using the experimental data of Romney & Indow and Stevens & Stevens. It applies specifically to the isolated stimulus condition. Verification of its precision awaits further experimental investigation using modern instrumentation.

As developed in both vision and hearing, the line labeled compression is an asymptote defining the nominal maximum signal output of the photoreceptor neurons under high stimulus conditions. The heavy curved lines are actually one line that represents the logarithmic conversion performed in the axon circuit of each photoreceptor.

86Craik, K. (1940) The effect of adaptation on subjective brightness Proc roy Soc (London) vol B128, pp 232-247 82 Processes in Biological Vision

This line moves in this representation as the gain of the adaptation amplifier changes. The gain levels shown refer to the gain of the adaptation line before the latest stimulus is applied. When that stimulus is applied, the adaptation amplifier gain will change in an attempt to bring the output voltage at the pedicle of the photoreceptor into the normal operating range.

The maximum operating range is shown as 200:1. This value is in good agreement with the maximum operating range under photopic operating conditions as suggested by Munsell Color Book. Based on the work of Romney & Indow, this range corresponds to a Value range in the Munsell Color Book of about xxx.

The theoretical performance does not predict the heavy curved lines converge at a point equal to 130 dB as shown in Stevens & Stevens. However, these lines below the compression line are temporally dynamic. Second order effects may cause the curves to converge, or Stevens & Stevens may have documented a dynamic condition with a time constant of about 2 minutes.

17.2.2.4 Compression factors found in other sensory modalities

The above paragraphs have described the variation in the exponents associated with the perceived versus applied stimuli. Compression factors are found in all sensory modalities. They typically expand the area of response within the range of primary interest. Stevens has provided estimates of the slopes of the response functions within the adaptation ranges of several sensory modalities87. He lists the slopes in these areas as; loudness, 0.67; brightness, 0.33; smell, 0.6; taste based on salt, 1.4; and heaviness(?), 1.45. The precise meaning of a slope greater than one may not be interpretable using the same model as used here for vision and hearing.

87Stevens, S. (1961) The psychophysics of sensory function In Rosenblith, W. ed. Sensory Communications NY: Wiley & Sons pp 1-33. NY: Wiley Performance Descriptors 17- 83

Figure 17.2.2-6 The theoretical performance of the visual modality with adaptation as a parameter. The curved heavy lines reflect the state of adaptation prior to the application of a new stimulus. Upon application of that stimulus, the adaptation gain will change to bring the performance into the normal operating regime shown.

17.2.3 The luminance threshold (AKA luminous efficiency function) of the human eye

This section will discuss the methodology required to define the luminosity function, the perceptible luminance function and the luminance discrimination function of human vision and then review the experimental techniques required to obtain precise verification of the theoretical functions. Because of the number of variables involved, several specific forms of the above theoretical functions will be presented to allow easy comparison with the accepted functions in the literature and those standardized by the C.I.E.

It should be noted that the entire field of photometry, as opposed to radiometry, is founded on a set of highly unrealistic assumptions. First, it assumes a series of symmetry and proportionality laws based on linear addition in the signal processing channels of the eye. This condition is clearly not met except for small signal conditions. Second, it assumes a fixed relationship between the perceived spectral sensitivities of the three individual photodetection channels of vision. This condition is not met in a real eye except under totally dark adapted conditions. Because of these difficulties, it is frequently hard to correlate the psychophysical data and the electrophysical data in the literature. The psychophysical database is based primarily on photometric units and the electrophysical database is based primarily on radiometric units. 84 Processes in Biological Vision

17.2.3.1 The tetrachromatic spectral sensitivity of the human retina

Surgery to remove the lens of the human eye has frequently been necessary in the past. It has been found that the human eye exhibits significant ultraviolet sensitivity after such an operation (in the absence of a prosthetic that itself absorbs in the ultraviolet). Griswold & Stark have provided excellent spectral data on such eyes down to a wavelength of 315 nm88. Figure 17.2.3-1 presents their data, and that of Tan89, in the context of this work. Also shown are the set of theoretical absorption spectra defined in this work for the human eye. The spectra are drawn for the nominal peak wavelengths and an arbitrary quality factor of Q=4.8. The spectra must be considered illustrative until better data becomes available for the half amplitude values for each individual spectrum (Section 5.5.10).

The one data set is labeled as “with B & W.” This notation refers to the studies by Boettner & Wolter of the absorption of the other elements of the physiological optical system, Stage B, except for the lens90. The Tan data is also “with B & W.” A recent paper by Van den Berg & Tan provide additional data relative to the Boettner & Wolter paper. While published in 1994, it reports on the mining of data collected in 1967-6891. It is unknown whether Boettner & Wolter included the absorption and scattering within the neural layer of the retina (the field lens of the physiological optics, and potentially the source of macular absorption).

Griswold & Stark made considerable effort to perfect and calibrate their test instrumentation. However, there are a number of theoretical problems with their analytical procedure. First, they discuss their work in terms of scotopic sensitivity measurements. However, they use a stimulus that is only 38 minutes in diameter. This differs from the C.I.E. suggested diameter. The C.I.E has adopted a stimulus diameter of two degrees for photopic measurements and ten degrees for scotopic measurements. Their figure 1 shows the nominal C.I.E. scotopic luminosity function overlayed on some of their data. As shown in [Figure 17.2.2-9], the difference between using the C.I.E. scotopic and photopic characteristics would be small at this wavelength relative to their ordinate. Their figure 3 shows the net absorption of the lens based on their experiments. This data will be discussed in the next section. It shows a maximum absorption of slightly over 4 log units (a transmission of only 0.01% at 360 nm). This peak wavelength is consistent with other literature.

Second, they attempt to relate the absorption in the region of 350 nm to the cis-peak in the dilute isotropic absorption peak of the retinoids (not actually limited to the cis-peak of rhodopsin) in their results section. In their discussion section, they back off from this position and posit the possibility of a separate UV sensitivity mechanism (based on other work within their group). As seen from the above figure, the anisotropic absorption of Rhodonine(11) when configured as a liquid crystal within the Outer Segment of the photoreceptor cells is a much better match to the data than an isotropic cis-peak. Furthermore, the literature does not explicitly define a cis-peak for the retinoids associated with vision (See Chapter 6).

88Griswold, M. & Stark, W. (1992) Scotopic spectral sensitivity of phakic and aphakic observers extending into the near ultraviolet. Vision Res. vol. 32, no. 9, pp 1739-1743 89Tan, K. (1971) Vision in the ultraviolet. Ph. D. thesis. Utrecht, Holland: Rijksuniversiteit te Utrecht, also University of Missouri (Columbia) Library, call no. QP481.T16. Also available in a review by Stark, W. & Tan, K. (1982), Photochem. Photobiol. vol. 36, pp 371-380 90Boettner, E. & Wolter, J. (1962) Transmission of the ocular media. Invest. Ophthal. Vis. Sci. Vol. 1, pp 776-783 91Van den Berg, T. & Tan, K. (1994) Light transmittance of the human cornea from 320 to 700 nm for different ages. Vision Res. vol. 34, no. 11, pp 1453-1456 Performance Descriptors 17- 85

Figure 17.2.3-1 (Color ln) Comparison of aphakic vision and the theoretical model. The data curves were normalized with respect to each other by Griswold & Stark. The theoretical spectra are normalized with respect to each other but separately from the data. The four chromophore absorption curves are shown normalized separately as a reference. The composite theoretical curves are for a quality factor of 4.8 and are only illustrative. See text for discussion. Data points from Griswold & Stark, 1992.

While the experimental data in the figure appears to be quite good, it must be noted that at the scale of the figure, the differences between Griswold & Stark and Tan are generally greater than 2:1. Some points differ by 3:1. The theoretical curves proposed by this work can easily be drawn within the envelope of these combined works as shown. Besides the reference absorption curves at the bottom of the figure, two composite spectral sensitivity curves are shown. The upper line is for photopic vision and the lower is for pure scotopic vision. These two curves were drawn using the parameters of the Standard Eye presented in the appendices except for the following parameters.

The spectral responses for the human retina presented above are not unexpected or unusual within biological vision. In fact, they can be overlaid directly with the spectral response of the zebra fish as reported by Saszik & Bilotta92. For the size of fish used (4-5 cm in length) the absorption of their lenses in the ultraviolet would be expected to be minimal. The peak sensitivity for these fish in the UV was also within a factor of three of the peak sensitivity in the 500 nm region.

Temperature = 310 Kelvin, λss = 405 nm, λms = 505 nm, λls = 600 nm and kuv:ks:km:kl::500:330:1000:330 for the

92Saszik, S. & Bilotta, J. (1999) The effects of temperature on the dark-adapted spectral sensitivity function of the adult zebrafish. Vision Res. vol. 39, pp 1051-1058, fg 2 & 3 86 Processes in Biological Vision

photopic curve. For the scotopic curve, kl was effectively zero and the other parameters remained unchanged.

The adjustments of 5 nm in the above wavelengths were made for two reasons. The main reason was to more precisely fit the data points on the assumption that the dip in the data near 425 nm was not due to any variation in the test set. This dip is at a slightly shorter wavelength than expected by this theory. However, this theory depends on parameters for the ultraviolet chromophore that have never been measured before. The parameters chosen were developed within the theory itself. The second reason was to more precisely track the data points in the area of the potential Bezold-Brucke anomalies near 487 & 580 nm. The data of Griswold & Stark and of Tan vary by a factor of between 2:1 and 3:1 in this area. By adjusting the difference between λsl and λms, the data of either investigators can be matched precisely. However, the preferred approach is to obtain a more statistically relevant data set so the actual wavelength difference can be specified precisely.

Griswold & Stark noted that their threshold measurements always appeared colorless to their subjects. This caused them to relate their data to the C. I. E. scotopic luminous efficiency function. However, sensitivity threshold tests always appear colorless to the subject, whether scotopic or photopic. Whether the tests were performed within the scotopic range is determined by a variety of conditions. However, the primary condition is whether the long wavelength signaling channel is functional or not due to the square law mechanism in its translation process. By comparing the data points and the theoretical curves, it is clear that they were operating in the scotopic visual region. However, both their data points and those of Tan deviate from a Fermi-Dirac slope in the long wavelength skirt of the measured sensitivity functions. This deviation suggests the presence of some sensitivity due to the long wavelength signaling channel. Such sensitivity is probably due to the long wavelength signaling channel. Such sensitivity would be an example of a failure in the univariance principle.

The theoretical curve demonstrates clearly that the measured sensitivity functions contain significant components due to three of the four chromophores of vision operating via separate signaling paths. This fact completely negates their reference to the data “making it fairly certain that our spectra are largely pure rod spectra.” In fact, their data is very compatible to a tetrachromatic eye containing no achromatic photoreceptors (rods) of any kind.

It would be interesting to expose their subjects to a checkerboard or other pattern of various intensities or reflectances over the range of 320 nm to 490 nm in order to elicit the perceived colors of the patterns at higher light levels. This would allow the determination of the wavelength of the neutral point within the ultraviolet-short wavelength color space. These tests would provide a preliminary answer to the age old question of “What do animals see in the ultraviolet, and how do they describe ‘white’.” These answers would also allow a further definition of the complete tetrachromatic color space defined in Section 17.3.3.

It would also be interesting to expose their subjects to chromatic adaptation similar to that of Jacobs, et. al.93. Such a test would demonstrate that the ultraviolet sensitivity was due to a distinctly separate ultraviolet absorber. Figure 6 in Jacobs, et. al. demonstrates this clearly for the mouse. Note the very rapid fall off in sensitivity indicative of a Fermi-Dirac edge in the absorption spectrum. Such a test would quell the idea that the ultraviolet sensitivity was an extension of the short wavelength spectral channel or a b-peak due to one of the other channels.

Stark, et. al. (1994) have provided additional data based on the in-vivo aphakic subject (WSS)94. Higher stimulus levels were used that allowed chromatic adaptation to be employed. In that paper, they again suggested the UV response might be a cis–response associated with the normal three chromophores. However, they also confirmed the

93Jacobs, G. Neitz, J. & Deegan, J. (1991) Retinal receptors in rodents maximally sensitive to ultraviolet light. Nature, vol. 353, pp 6550666 94Stark, W. Wagner, R. & Martin-Gillespie, C. (1994) Ultraviolet sensitivity of three cone types in the aphakic observer determined by chromatic adaptation. Vision Res vol. 34, no. 11, pp 1457-1459 Performance Descriptors 17- 87

earlier findings of the team that the UV response exhibited a higher peak sensitivity than any of the longer wavelength chromophores. This finding is not compatible with the idea of a secondary sensitivity peak, a β-peak, whether due to a cis–response or otherwise. An unexpected feature of their protocol was the use of a “frosted UV transmitting Plexiglas.” No specifics were given concerning this Plexiglas. This product normally exhibits negligible transmission at wavelengths below 350-365 nm95.

Richard Hammond presented a TV program over the BBC on 23 March, 2010 involving a man with his biological lenses removed who discusses his resulting UV vision96. The program should be available in the USA on the Discovery Channel in the near future. He claimed that after the operation he started to see bright purplish and blue light emitting from scanners used to scan currency notes. He also said that had far more color in them now than he had seen before. This is completely expected. No information was provided on the types of replacement lenses he was using. He did not demonstrate his ability to see at wavelengths shorter than 400 nm. Hambling presented an article in the popular press on UV vision, citing Stark as a specific example97. Much of the content is anecdotal and the concepts questionable.

Anderson provided a first hand account of aphakic vision from a medical surgeon98. However, he was not an ophthalmologist or an optician. As a result, his observations are those of a educated individual but not an authority in what he is talking about. Many of his observations are useful in the hands of one with a better understanding of the eye-brain system. His observation of an exhibit of rocks under ultraviolet illumination at the Smithsonian Institution is very instructive concerning the operation of the aphakic eye versus his other normal eye. While normal observers saw a well organized display of rocks against a dark background, his aphakic eye say a highly illuminated display in total disarray (crude tables built on saw-horses for legs, electrical cords running aimlessly), and not ready for public display. His observations of the geometric performance of the human eye/brain system are even more useful and demonstrate the conformal transformation of circles on the retina into straight lines on area 17 of the cerebral cortex and the resulting perception of straight lines where intuition would say circles or circular arcs should have been observed. See Section 15.2.5.7. His familiarity with reduction telescopes as used in surgery was at best cursory from an opticians perspective. The shortcomings he discusses are easily overcome with two features he did not discuss, a telocentric telescope design and an aspheric version of a reduction telescope.

Kraft & Werner have provided extensive data comparing the sensitivity of the eye with and without the presence of the lens for 50 subjects99. [xxx may not be correct interpretation ] Their data (Figure 17.2.3-2) is reproduced (with a background) in Backhaus et al. (page 26) and follows the earlier data of Tan, of Stark and of Babucke. The graphic printing technique used does not represent wavelengths less than 460 nm and longer than 625 nm at all. Thus the color background is stretched to cover 400 to 700as an artistic devise. Note the increasing sensitivity of the retina at short wavelengths. This increase can be expected to continue with a peak near 342 nm. (in the absence of any limits within the instrumentation) and rise above the peak of the short wavelength receptors near 437 nm.

95http://www.atofinachemicals.com/atoglas/technicalinfo/Arch/PLA17c3.cfm 96http://www.bbc.co.uk/iplayer/episode/b00rqgh4/Richard_Hammonds_Invisibl e_Worlds_Out_of_Sight/ 97Hambling, D. (2002) You don't have to come from another planet to see ultraviolet light. Guardian Thursday May 30 98Anderson, R. (1983) Visual perceptions and observations of an aphakic surgeon Percept Motor Skills vol 57, pp 1211-1218 99Kraft, J. & Werner, J. (1994) Spectral efficiency across the life span: flicker photometry and brightness matching," J Opt Soc Am A vol 11, pp 1213-1221 88 Processes in Biological Vision

Figure 17.2.3-2 Heterchromatic brightness sensitivity change per decade is plotted as a function of wavelength at the cornea (black circles) and at the retina (whilte squares). The horizontal line at zero denotes no age-related change. The thicker horizontal line at +0.05 shows the mean increase in brightnes sensitivity per decade between 420 and 560 nm. Note the false color used as a background. See text. From Kraft & Stark, 1994.

17.2.3.1.1 Effect of aging on ultraviolet vision

Bowmaker & Kunz have suggested, but did not demonstrate, that tetrachromatic fish lose the ability to see in the ultraviolet as they mature due to atrophy of the ultraviolet photoreceptors100 (see Section 1.2.1.2). The data of Griswold & Stark do not support such atrophy in humans. Their aphakic subjects varied in age from 22 to 43 years of age. These subjects all had normal eyes until surgery at ages exceeding 10 years. Based on this work, the loss of UV vision in fish is due to their growth in size and the thickening of the lenses of their eyes. These lenses are particularly thick in grown fish relative to the diameter of their eyes. It is how they achieve a high f/# optical system. The lens is particularly absorbent of UV light.

The figure strongly supports the tetrachromatic hypothesis of this work based on the Rhodonines. The corrected data of both Griswold & Stark and of Tan in the ultraviolet portion of the measured spectrum match the predicted

100Bowmaker, J. & Kunz, Y. (1987) Ultraviolet receptors, tetrachromatic colour vision and retinal mosaics in the brown trout, Salmo trutta; age-dependent changes. Vision Res. vol. 27, no. 12, pp 2102-2108 Performance Descriptors 17- 89

spectrum of Rhodonine(11) very well. The match is good with respect to both center wavelength and width of the absorption characteristic. It also appears to be good relative to the quality factor, Q. For the nominal Q = 4.8, the crossover between the theoretical chromophores is lower in the 400 nm region and higher in the 600 nm region than in the region of 500 nm As a result, the theoretical luminous efficiency function (not shown) would be expected to have a larger dip in the region of 400 nm than at either 500 (494) nm or at 600 (580) nm. Of course, whether this dip is observable under dark adapted conditions would depend on the relative contributions of the spectral channels to the luminance equation. It would also depend on the statistical precision of the data. Although Griswold & Stark used only a few subjects, the error bars provided suggest their data is quite precise. Whether it is indicative of a larger population is still an open question. Their data does exhibit a number of relative maxima, relative minima and inflection points that suggest it is compatible with the complete luminous efficiency function of this work. This is even true in the long wavelength region where there appears to be an inflection point near 600 nm and a change in slope (at least in the data of Tan) supporting the presence of a long wavelength chromophore at reduced absolute sensitivity. This would mimic the situation found in normal eyes.

Griswold & Stark suggest that the sensitivity of the ultraviolet spectral channel in the aphakic human is even more sensitive than the short wavelength channel and approaches the sensitivity of the mid wavelength channel. Bennett & Cuthill summarize the work of several investigators an say that “Birds appear if anything, to be more sensitive to UV than to light in the ‘human visible’ part of the .” If both of these statements are true, one would not expect any auxiliary peak near 400 nm (due to a pseudo-Bezold-Brucke Effect) under dark adapted conditions. However, under conditions where the ultraviolet sensitivity was reduced by about a factor of five, it is possible such a peak would be observed. Bennett & Cuthill have referenced peaks in the vicinity of 380 nm that might relate to this pseudo-Bezold-Brucke Effect. A similar peak was referenced in the vicinity of 415 nm. These peaks were obtained using less precise psychophysical techniques.

The above discussion and data makes it abundantly clear that the aphakic human retina is tetrachromatic even in middle age and beyond. The performance of the overall system is limited by the absorption of the lens to wavelengths longer than 400 nm. The data strongly supports the theory and model of this work. It is particularly useful in supporting the proposed spectral performance of the Rhodonines, even supporting the Q = 4.8 proposal. Whether the O-channel of the chrominance signal processing path is functional in the human remains to be determined.

Kraft & Werner addressed the change in sensitivity of the human eye in both the broad and ultraviolet portion of the spectrum in the paper cited above.

17.2.3.2 The spectral characteristics of the physiological optics of the human eye

Figure 17.2.3-3 provides an overview of the spectral limitations of the physiological optical system. The outside envelope is due primarily to the absorption of water. This absorption limits biological vision to the region between 340 and 1400 nm. Within this range, there are a series of other absorbers that impact or control the absorption characteristics of vision. The most important of these in the large chordates (including man) is the absorption by the lens group in the region of 350 to 400 nm.

The complete description of the equivalent optical density of the physiological optics is given in Section 16.3.3.2.1. A precise description is complicated by two factors. First, the transmission path is that of a converging refracting optical path. The optics involves curved surfaces that are not properly represented by an equivalent slab of constant thickness homogeneous material. Hence, measurements are a function of the size and position of the light bundle used to calculate the optical density. These variations are codified by one of Stiles-Crawford Effects (see Section 17.3.7). Second, the portion of the overall optical system related to the macular region exhibits an additional absorption mechanism that is not shown in the above figure. 90 Processes in Biological Vision

17.2.3.2.1 The primary in-band spectral absorption of the physiological optics

As noted in Sections 16.3.3.2.1 and 17.2.2, it is the absorption of the lens, with an absorption edge overlaying almost precisely the long wavelength absorption edge of Rhodonine(11) that causes the human eye to be limited to that of a long wavelength trichromat.

The popular literature has occasional references to the ability of the human eye to see light down to 300 nm. Figure 17.2.3-3 CR Light transmission through the This feature is due to two factors. First, the presence physiological optics of humans. From Miller,1991. of ultraviolet photoreceptors in the retina, as shown in Section 17.2.3. Second, the small rise in the transmission of the lens in the area of 320 nm. This rise is more clearly identified in the following figure describing the equivalent optical density of the lens.

The equation for the optical density of the physiological optics, without the reflectance term associated with the air- cornea interface and without a scaling constant is given in the Figure 17.2.3-4. The reflectance loss is about 2.5% across the visual spectrum. The total attenuation is described by three terms. The first term is an absorption due to an alcohol ligand within the lens and humors of the eye. The second term is an absorption due to an aldehyde ligand within the lens and humors. The third accounts for the Rayleigh scattering within the medium. The two

ligand terms, ao( λ) and aa( λ), for the alcohol and aldehyde respectively, are each given by a two-sided Fermi-Dirac expression defined in terms of a quality factor of nominally Q = 15. The first term has a peak absorption near 325 nm and the second a peak absorption near 357 nm. These wavelengths are the presumed peaks for these materials in-vivo, as opposed to in ethane or hexane--the solvents associated with in-vitro spectral evaluations.

Figure 17.2.3-4 “Equation for optical density of physiological optics” Eq. 17.2.3.1

Figure 17.2.3-5 shows the theoretical loss overlaid on the data points of Griswold & Stark. The fit appears to be excellent. The fit in the area of 330 nm can be improved by adjusting the Q and peak wavelengths slightly. However, it is not likely the data is as accurate as the theoretical curve in this area. The data points were derived from measurements on only a few eyes and only a few data points in this area.

The two Fermi-Dirac expressions are not coupled. This suggests the individual ligands are not in quantum Performance Descriptors 17- 91 mechanical communications with each other, i. e., they are probably entirely separate molecular structures. The Q is probably due to the temperature of the materials.

The scatter term is the major source of loss within the visual spectrum from 400 to 700 nm. It is also the principle loss factor that is a function of age. The equivalent optical density due to this factor is believed to increase about 0.55% per year. Such a change is nearly negligible year to year.

Figure 17.2.3-5 The equivalent optical density of the physiological optics of the eye, disregarding the absorption peculiar to the macular region. The data points are from Griswold & Stark. The smooth curve is the theoretical optical density of this work. The region below 400 nm is dominated by ligand absorption. It is this absorption that limits the human eye to trichromatic performance even though the retina is tetrachromatic. At wavelengths greater than 400 nm, performance is limited by Rayleigh scattering. 92 Processes in Biological Vision

17.2.3.2.2 The spectral absorption of the macular area

The absorption of the neurological material within the optical path associated with the macular has been presented in Section 3.2.1.3. This absorption is well characterized by conventional bulk absorption by the molecules forming the layer. Figure 17.2.3-6 presents the results of the theoretical analysis. The equation of a two-stage, stagger-tuned electronic circuit well emulates this type of absorption as measured by Brown & Wald101.

17.2.3.3 The tetrachromatic spectral sensitivity of the complete human eye

With very precise theoretical relationships for the spectral absorption of both the retina and the physiological optics of the eye, it is possible to calculate the theoretical spectral absorption of the overall eye and compare it to the available empirical data. This can be done for both the macular area as well as the surrounding area.

17.2.3.3.1 The spectral sensitivity of the Figure 17.2.3-6 (Color ln)The theoretical absorption of complete human eye (except in macular) the macular. Compare with the empirical data of Wald.

By combining the theoretical spectral absorption of the retina with the optical density of the physiological optics (other than in the macular), a theoretical spectral absorption function for the complete human eye is available. This function is presented by the solid lines in Figure 17.2.3-7 along with the best available empirical data. The human eye exhibits a significant sensitivity in the ultraviolet region that is not normally measured in the laboratory because of the use of glass optics and light sources of low blackbody temperature. To measure the complete sensitivity function of the human eye, the use of quartz optics and a light source at a nominal color temperature of 8683 Kelvin is required.

The use of crystalline quartz optics is preferred since many fused quartz glasses have limited spectral transmission due to additives introduced for other purposes. The Infrared Handbook provides an easy source of data on these materials.

The ultraviolet sensitivity peaks in the vicinity of 300 nm due to the high absorption of the physiological optics in the 325-357 nm region as developed above. Note this spectral sensitivity of the human eye in the ultraviolet region is not the result of fluorescence within the materials of the eye. It is a real and conventional sensitivity.

101Brown, P. & Wald, G. (1963) Visual pigments in human and monkey retinas Nature vol. 200, pp 37-43 Performance Descriptors 17- 93

Figure 17.2.3-7 (Color ln) Calculated tetrachromatic spectral sensitivity of the normal human eye compared with the best data available. The green curve represents the scotopic response. The photopic response is given by the red extension of the green curve. The coefficients, kuv:ks:km:kl::500:330:1000:330, were used to generate this extension. The value of kl is higher than in the standard eye (typically 100) in order to emphasize the response and a small Bezold-Brucke Effect near 580 nm. When working within the macular area, the correction shown by the dotted line is appropriate. All curves include the absorption and Rayleigh scattering associated with the physiological optics of the eye. The data points of Griswold & Stark are also shown.

Figure 17.2.3-8 provides a comparison between the aphakic and phakic (normal) eyes based on the data of Griswold & Stark. The absorption of the aphakic eye has been extended based on the absorption of the viscous humor near 300 nm. The 1000:1 additional attenuation of the phakic eye in the ultraviolet is in good agreement with the estimate by Wald. As noted earlier, the label B & W refers to the data of Boettner & Wolter related to other elements of the physiological optics (the macular specifically). The axial length of the normal human lens is 4.5 mm (Section 2.4.1). Individuals with lenses of significantly shorter axial length can be considered partially aphakic (or dysphakic) from an absorption perspective. For a dysphakic eye with a lens of only 2.25 mm axial thickness, the attenuation would be expected to be only about 30:1 or one and one-half log units. Such dysphakic subjects report significant ultraviolet perception under daylight conditions (color temperature of illumination near 6500 Kelvin). 94 Processes in Biological Vision

17.2.3.3.2 The spectral absorption of the complete human eye in the macular

The macular introduces a significant attenuation of the input irradiance in the region of 430 to 490 nm. As a result, the overall sensitivity of the human eye is significantly different in the foveola and fovea than it is in the more peripheral areas. This difference is illustrated by the dashed line in the above figure. This fact requires more careful documentation of the area of the retina observed when laboratory results are presented in the literature than has occurred in the past. The macular has introduced a generally unknown factor in the performance of the eyes presented in the past. It may account for the suggested changes in the observed sensitivity reported by Judd and discussed in Chapter 17. Figure 17.2.3-8 A comparison of aphakic and phakic eyes based on Griswold & Stark. The designation w/o B & W 17.2.3.3.3 The measurement of the can be ignored. A normal eye has an axial lens thickness reflectance of the retina through the of about 4.5 mm. physiological optics

The measurement of the spectral properties of the retina by microspectrometry through the lens is clearly impacted by the absorption of the lens. The impact is compounded by the light passing through the lens twice. This limits the observed spectral characteristic to wavelength longer than 400 nm and introduces twice as much Rayleigh scattering as normally involved. The physiological optics does not attenuate the light at wavelengths shorter than 300 nm. However, the viscous humor absorbs strongly below 300 nm. As a result, a small response in the region near 300 nm may be recorded using the double pass approach if quartz optics and suitable stimuli are used.

There is an even more important consideration when observing the retina microspectrographically. It is that the impact of spectral absorption by the individual photoreceptors is merely summed algebraically. The result is a spectrum that is completely unrelated to the electrophysiological and psychophysical spectrums. It does not reflect the “filling in” of the spaces between the skirts of the spectral absorbers provided by the logarithmic processing.

17.2.3.4 Comparison with the ultraviolet research literature

The above figure shows the data points provided by figure 1 of Griswold & Stark that include the ultraviolet sensitivity of the complete human eye (curve labeled phakic w /B & W). As mentioned earlier, Griswold & Stark were very careful in the design of their experiments. The range bars associated with their data is generally smaller than the symbols in the above figure. As a result of this fact, the concordance of the theory and their data gives considerable credence to the adequacy of the theory.

Additional credence is provided by Rodieck102. He references Goodeve, et. al. of 1942 as showing that aphakics can see down to 298 nm. He also noted that Wald had shown in 1945 that the sensitivity of the aphakic at 365nm was about 1000 times higher than the normal eye.

102Rodieck, R. (1973) The Vertebrate Retina. San Francisco, CA: W. H. Freeman pg 290 Performance Descriptors 17- 95

17.2.3.5 Comparison with the photopic research literature

There is a large volume of research literature on the shape of the absorption characteristic in the photopic region. Most of it is psychophysically based and much of it relies on difference spectrums. Much of it relates to the macular area. Only a few papers, such as Griswold & Stark, et. al. recognize the ultraviolet capability of the human eye. Lacking an appreciation of the ultraviolet capability of the human visual system, most of the literature is archaic with respect to research.

Lamb provided a review of selected portions of the database with some adjustments in values as part of the interpretation103. The data is presented initially as a function of spectral frequency instead of wavelength. When the data is normalized and fit to Lamb’s series expansion in the exponential of frequency, all of the data shows a

common low frequency (high wavelength) asymptote given by 70loge units per unit of normalized frequency. When converted to a graph of normalized spectral sensitivity versus wavelength, the long wave responses all exhibit a slight curvature as found in this work (compare with Sliney in a later Section). He concludes that the half amplitude spectral width of the chromophores is a constant when calculated with respect to frequency in support of Mansfield, instead of wavelength as calculated by Dartnall and others. In this work, the spectral half amplitude bandwidths of the individual chromophores are found to vary in the manner suggested by Mansfield. However, the reasoning is quite different. The Fermi-Dirac spectral bandwidth for each chromophore is calculated with the wavelength in the denominator of an exponential expression. Thus, a variable half amplitude spectral bandwidth as a function of wavelength is obtained without resorting to a normalized calculation based on a series expansion based on frequency.

Stockman, et. al. have recently provided another series expansion as a template for the absorption characteristic of vision104. However, it is a general expansion of the second order in terms of wavelength with no theoretical relationship to absorption. They assumed the visual system was linear prior to their application of this expansion. By just letting a digital computer run, they provided 5-place accuracy parameters (based on 18 place calculations) that appear unjustified.

The isotropic absorption characteristic of the Rhodonines given by Baylor, Nunn & Schnapf can also be compared to this figure105. xxx Their data was collected using radiation with its e-vector perpendicular to the length of the Outer Segment. Although the caption of their fig. 4 says rods, the data actually represents the isotropic spectrum of all photoreceptors.

17.2.3.5.1 The photopic research literature–normal broadband

The available animal data on the individual spectral channel absorptions agree very well with the derivations presented here. Most of the human data prior to 1975 is poorer for several reasons. The general prohibition against invasive experiments has largely prevented acquisition of precise electrophysiological data. The resulting focus on psychophysical techniques has introduced its own group of problems. The psychophysical data has been collected using a variety of methods and protocols. Several of these protocols are clearly inadequate. They generally do not employ sufficient suppression of the mid wavelength spectral channel when trying to isolate the long wavelength channel. Thus, the preponderance of the putative long wavelength data shows the Purkinje Peak in the region of 580 nm. One investigator recorded a peak at 610 nm and then placed an unsubstantiated comment in the caption saying

103Lamb, T. (1995) Photoreceptor spectal sensitivities: common shape in the long-wavelength regions. Vision Res. vol. 35, pp. 3083-3091 104Stockman, A. Sharpe, L. & Gach, C. (1999) The spectral sensitivity of the human short-wavelength cones derived from threshold and color matches. Vision Res. vol. 39, pp 2901-2927 105Baylor, D. Nunn, B. & Schnapf, J. (1984) The photocurrent, noise and spectral sensitivity of rods of the monkey macaca fascicularis. J. Physiol. vol. 357, pp 575-607 96 Processes in Biological Vision

“The peak near 610 nm cannot be due to a cone pigment.106” He offered no alternate explanation for the data. In different parts of the same figure, he showed both a peak and a valley at 580 nm. This feature is easily explained by the logarithmic summation process used in chordate vision.

When collecting composite spectral data, the color temperature of the light sources used were invariably below 3600 Kelvin. As a result, the data generally under represents the performance of the human eye in the blue.

Both human and animal data recorded before 1975 usually shows significant smoothing of the spectral responses due to the use of spectral filters wider than 15 nm. The result is a broadening (and smoothing) of the recorded spectra because of the Central Limit Theorem. Most investigators did not specify the precise location of the retina explored or anticipate any effect due to a variation in the length of the outer segments in that region. The intrinsic composite spectra show detail at the 5 nm level.

One of the earliest measurements of sensitivity illustrating all three spectral peaks (ignoring the ultraviolet) was by Weale107. Figures 17.2.3-9 shows his data as presented by LeGrand108. The point of measurement was 25 degrees from the foveola and just beyond the blind spot. The long wavelength peak is at 612 nm . The state of adaptation resulting in this data was not clearly described. However, incandescent sources were used to control the background surrounding the 50 minute test apertures.

Figure 17.2.3-9 Early spectral sensitivity curves. Weale, c, shows sensitivity peaks at 612 nm, 535 nm and near 440 nm. The state of adaptation was not clearly defined. The response by Moreland clearly illustrates a Bezold- Brucke peak near 510 nm. From LeGrand, 1972.

106Boynton, R. (1979) Human Color Vision NY: Holt Rinehart & Winston fig 6.14, pg 195 107Weale, R. (1953) Spectral sensitivity and wave-length discrimination of the peripheral retina J Physiol vol 119, pp 170-190 108LeGrand, Y. (1972) Spectral luminosity In Jameson, D. & Hurvich, L. eds. Handbook of Sensory Physiology, vol VII/4 NY: Springer-Verlag pg 422 Performance Descriptors 17- 97

Neglecting the ultraviolet sensitivity defined in this work, there is excellent agreement between this work and the trichromatic based photopic research literature as shown in Figures 17.2.3-10 and 17.2.2-10. The data points in the first figure are from Wald using a 10-15 nm bandwidth spectral filter109. The theoretical curve is based on relative coefficients for the S:M:L channels of 100:1000:300. The data points differ from the theory by less than a factor of two except in the most rapidly changing area, where averaging due to the finite width spectrometer is most significant. No smoothing of the theoretical function has been incorporated into this figure. Such smoothing will be introduced below. The primary remaining question concerns the precise difference in wavelength between the long wavelength half-amplitude point of the M-chromophore and the short wavelength half-amplitude point of the L- chromophore at in-vivo temperature in human. Two cases are shown, where the difference is 30 nm. and where it is 35 nm. (a matter of 5 parts in 600 or less than one percent). The difference corresponds to a slight difference in the peak spectral height of the theoretical luminous efficiency function near 572 nm. This slight difference causes the smoothed theoretical function (discussed below) to exhibit a peak that varies but is near the C.I.E. Standard of 555 nm found using the average response over a 2° field. As calculated, this peak was for an equal flux source of illumination at 7053° Kelvin. More detailed laboratory analysis will be required to determine the precise edges of the two absorption bands. However, this data is critically important in determining that the two absorption edges are separated by less than 35 nm at 37 Celsius.

Figure 17.2.3-10 Comparison of theoretical and empirical spectral sensitivity functions (luminous efficiency functions). Theoretical functions for relative coefficients for the S:M:L channels of 100:1000:300 from Fulton (1984). Data points from Wald, 1964.

109Wald, G. (1964) The receptors of human color vision Science vol. 145, pp 1007-1016 98 Processes in Biological Vision

The highest precision spectra for the perceived spectral sensitivity of the human eye is that of Piantanida & Sperling110. Their data for a one degree diameter spot centered on the point of fixation is presented in Figure 17.2.3-11. The test set provided a 50 msec flash of light. This data was collected without reporting a color temperature (although their 1971 work was reported at a color temperature of 5500 Kelvin). A color temperature of 5500 Kelvin would account for the high sensitivity they show at short wavelengths. A 14 degree diameter background illumination, described as 3000 Trolands, was drawn from the same source. It was described as an “equal energy source” but its color temperature was not specified. The filters used had a 0.5 nm half-band width and a spacing of 10 nm was used. Although their text indicates the experiments covered 400 to 700 nm, they did not provide values at 400, 410 & 420 nm. Nor did they report values for 680, 690 and 700 nm. The figure has been replotted from a non linear abscissa. Only two subjects were evaluated and no range bars were provided. No explanation could be found in the paper as to why TP showed a sensitivity four times lower than TW at all wavelengths.

The relatively smaller downturn in the short wavelength response of TP is interesting. It would suggest that the eye of TP was somewhat smaller than the eye of TW and/or TP was younger than TW. If true, the effect could have been due to less absorption of light by the lens of the subject. The data required to answer this question was not given in their paper.

The lines drawn through the data points are obtained from the equations of this work using the coefficients and parameters shown in the figure. Even better fits could be obtained if the range bars for the data were available. At this level of precision, the length of the outer segments of the photoreceptors must be known if the actual spectral response of the average photoreceptor of each spectral type is to be calculated.

The best fit to the test data that could be obtained under the current circumstances suggests a mean spectral absorption for the spectral channels of 437.5, 531.5 & 631.5 nm and relative sensitivities of Figure 17.2.3-11 Incremental threshold spectral

kS:kM:kL::350:1000:625. This was achieved using a sensitivity of two normal human subjects (circles). theoretical calculation at five nanometer spacing and a Averaged six ascending and six descending readings for each observer after adaptation to a 3000 td white light. smoothing factor (called ksmooth in Mathcad by Lines are predicted spectra based on this work for the MathSoft) of 40 nm. The smoothing factor is the only parameters shown. Data points from Piantanida & arbitrary constant in the entire calculation. Sperling, 1973.

Note the peaks near 470 nm and 580-610 nm are not related to the presence of an actual chromophore. These peaks are due to the logarithmic summation process caused by the output structure of the photoreceptor cells. They are related to the Bezold-Brucke and Purkinje Effects discussed in the next section.

110Piantanida, T. & Sperling, H. (1973) Isolation of a third chromatic mechanism in the deutranomalous observer Vision Res vol. 13, pp 2049-2058, fig 1 Performance Descriptors 17- 99

It is important to note that the perceived luminous channel sensitivity for both TW and TP include an absolute S- channel contribution about 35% as high as the M–channel contribution. This percentage is recognized due to the high color temperature source used. It is also in great conflict with the typical psychophysical measurements reported in the literature and based on a color temperature between 2000 and 2800 Kelvin.

A larger data set and a more precise description of the light source would allow more precise definition of the mean absorptions and the variations from the mean for these two humans. The problem of a small data set is highlighted in Section 17.3.1 where the nonuniformity of the color sensitivity of the eye, in the area of the fovea is noted.

Note carefully the shoulder on the long wavelength skirt of the overall functions. This hump occurs at the actual wavelength of the L–channel chromophore. It is found in all precision spectra of all primates.

The remainder of the two papers by Paintanida & Sperling on protonomalous and deutranomalous subjects agrees well with the theory of this work presented in Chapter 18. The protonope lacked an L-channel chromophore and the deutranope exhibits normal spectral performance in the long wavelength region. The deutranope exhibits a normal spectral sensitivity (using all three chromophore types) but a failure in the signal processing associated with the Q–chrominance channel.

An earlier Sperling & Harwerth graphic of the visual sensitivity of the rhesus monkey is shown in Figure 17.2.3-12. It shows the typical “three humps” recorded by many (Thornton, 1992). All show a L-channel peak in the 607-620 nm region.

Figure 17.2.3-12 Visual sensitivity of the rhesus monkey. The vertical line at 600 nm is provided only as a visual aid for the reader. From Sperling & Harwerth, 1971 100 Processes in Biological Vision

Kurtenbach et al. have provided mean spectral sensitivity data for groups of three individuals, who were either trichromats, deuteranopes or protonopes, using 4 nm wide filters within the mesotopic regime (0.05 to 14.98 td)111. Averaging the data from three individuals obscures the spectral response slightly due to the incorporation of subject- specific variations in the absorption of the macula. However, the data does show fine variations indicative of the theoretical spectra of this work. Figure 1 of the paper shows the progressive loss in the L-channel response of trichromats with reduced illuminance (note the distinctive shelf at 575 nm and 0.47 td). It also shows that the deuteranope is not missing any spectral component (figure 2 is nominally identical to figure 1) and that the protonope is missing the L-channel spectral component (no shelf appears in the long wavelength region at any illuminance and the long wavelength sensitivity is reduced at all illuminances). Their analysis depended entirely on curve-fitting using a set of templates from Smith-Pokorny fundamentals (obtained using 7-15 nm wide filters). The cited Smith & Pokorny paper did not propose a unique set of spectral responses (see text associated with their figures 6 & 7).

Babucke has collected new data for individual single humans with a test set designed to show the fine detail in the spectrum under mesotopic conditions112. Figure 17.2.3-13 shows his data for a single subject. The collected data not only shows all of the predicted curves and shoulders in the spectrum, it clearly shows the predicted “computational peak” at 0.58-0.59 microns. This peak can only be obtained by logarithmic summation within the neurological system. A similar but less pronounced effect is seen at 0.465-0.475 microns. Additional experiments are under way to acquire more statistically relevant data for this and other subjects (note the large deviation about the mean at short wavelengths). The theory suggests the data will be different for different subjects due to minor variations in disk diameter within the retina. By collecting the data separately, it may be possible to determine the subject-to-subject variation in this experiment.

111Kurtenbach, A. Meierkord, S. & Kremers, J. (1999) Spectral sensitivities in dichromats and trichromats at mesopic retinal illuminances J Opt Soc Am A vol 16(7), pp 1541-1548 112Babucke, H. (2007) Personal communications. Performance Descriptors 17- 101

Figure 17.2.3-13 A human spectral response confirming all of the curves and shoulders predicted by the theoretical model. The data points are the average of seven readings. Additional data is needed to establish the mean and standard deviation at each wavelength. The blue curve is the absorption function developed in this work with the coefficients shown. The red curve is the absorption function after allowance for the absorption of the macular material. Except at the longest wavelengths, the data points are within +/– 26% of the theoretical function in blue. From Babucke, 2007.

Figure 17.2.3-14, from a more recent private communication from Babucke (2008), has provided some very precise spectral data for subject KM. With one exception, the data points are within ±30% of the theoretical response using the equation and standard parameters of Section 5.5.10 when using spectral filters on the order of 10 nm wide. Babucke is concerned about the data points at 590 & 600 nm and at 520 & 530 nm. The fact the points at 520 & 530 nm are above the best fit curve using the standard parameters (blue line) can not be explained by this theory and will require more analysis of the test protocol. Unusually high values have been measured on multiple subjects. At least for SG, the height of the values above the nominal blue curve are proportional to the eccentricity of the light applied to the retina.

The points at 590 & 600 nm are consistent with the Purkinje Effect described in Section 17.2), except the peak appears to be shifted slightly toward the red. 102 Processes in Biological Vision

Figure 17.2.3-14 High precision spectral data for SG. The dashed overlay shows the theoretical fit to the curve using the parameters shown in the middle of the figure. From Babucke, 2008, unpublished.

Attempts to fit the data points more closely using a different set of parameters suggests subject SG has outer segments that are smaller in diameter (and possibly shorter in length) than the subjects used to obtain the original set of parameters. As noted in Sections 5.4.2 & 5.4.3, the Pauli Exclusion Principle determines the precise width of the spectral absorption bands of the chromophores. In developing the original theoretical spectrum, it was assumed the center wavelengths of the chromophores were at 437, 532 and 625 nm. It was further assumed that the width of the absorption spectra were broadened according to the Pauli Exclusion Principle resulting in the above center wavelengths ±n nm where n equaled 25-30 nm. The best values to fit the data of Section 5.5.10 were tabulated in Table 5.5.10-1. Attempting to fit the theoretical equation to a data set using values with less than 5 nm spacing is tedious. It will not be pursued here unless the data is known to be accurate to such fine tolerances.

By changing the value of n, it is possible to move the peak of the Purkinje peak toward the red. The dashed red line shows a fit based on n closer to 20-25 nm (at least for the M- and L-channels). The parameters used are shown in the middle of the figure. A set of data developed using Mathcad and known as c_human_spec_b.MCD was used. No smoothing was used in the calculation. Several smoothing routines are available to use with the above Mathcad program. However, they do not use a kernal based on a Boltzmann Function.

The theoretical formula allows the data points to be matched arbitrarily well by the theoretical equation using Performance Descriptors 17- 103 different values for the wavelength parameters and smoothing comparable to the width of the filters used to collect the data. A better match will not be attempted until the statistical ranges for each wavelength of the data set for SG is determined. 104 Processes in Biological Vision

Sperling & Harwerth have provided data similar to the Paintanida & Sperling data for the rhesus monkey, Macaca mulatta113,114. The data shows that the spectral performance of man and the rhesus monkey are nearly identical. They extended their study to include degradation performance following intense illumination. Unfortunately, they used a two degree diameter test target (which introduces some inhomogenuity if their foveola has the same dimensions as in humans. The effect is noted in Section 17.3.1 but they did specify the color temperature of their source as 5500 Kelvin.

Unfortunately, they attempted to match their data to a linear summation of three spectral channels based only on a Dartnall nomograph and peak absorptions at 445, 535 and 575 nm. The latter number is actually associated with the Purkinje peak found in the logarithmic summation mechanism and not a chromophore of vision. Because of their assumption, a simple summation of spectral channels was not possible. They reverted to a 2x2 matrix with four additional arbitrary coefficients to take differences between the 535 and 575 nm values in order to arrive at a set of pseudo-absorbers in the long and medium wavelength regions. Interestingly, these pseudo-absorbers had peak absorptions near 625 nm and 535 nm. Under their assumptions, they had to revert to a piece-wise linear model, based on a curve fitting activity. They describe their final spectral envelope as an “upper envelope model,” to generate an overall absorption spectrum.

In 1975, Harwerth & Sperling provided additional empirical data which is excellent115. However, their curve fitting efforts used the same techniques as in the above papers. The discussion and the results based on their modeling are not satisfying to this author. Sperling et. al. provided additional data in 1978 116. The data provided both a psychophysical response as well as an electrophysical response measured at the output of a ganglion cell (their figure 12). The agreement between the psychophysical and electrophysical data is convincing that the Luminance channel measured at the ganglion cell of the luminance channel is representative of the perceived luminance of the monkey. However, they continued to employ their pseudo-absorbers. This was necessary because they continued to rely upon the data reported by Marks in 1964. Marks, in his apprentice paper as a researcher, provided one spectral trace that appeared to peak at 575 nm. As a result of this trace, Sperling et. al. assumed “the generalized absorption spectra of the three classes of primate cones” occurred at 445, 535 & 575 nm. Their larger data set is shown in Figure 17.2.3-15. The graph has been replotted with a linear horizontal scale. The vertical scale is shown as the logarithm of the reciprocal of the photon count to the base 10.

113Sperling, H. & Harwerth, R. (1971) Red-green cone interactions in the increment-threshold spectral sensitivity of primates Science vol. 172, pp 180-184 114Harwerth, R. & Sperling, H. (1971) Prolonged color blindness induced by intense spectral lights in rhesus monkeys Science vol. 174, pp 520-523 115Harwerth, R. & Sperling, H. (1975) Effects of intense visible radiation on the increment-threshold spectral sensitivity of the rhesus monkey Vision Res vol. 15, pp 1193-1204 116Sperling, H. Crawford, M. & Espinoza, S. (1978) Threshold spectral sensitivity of single neurons in the lateral geniculate nucleus and of performing monkeys Mod Probl Ophthal vol. 19, pp 2-18 Performance Descriptors 17- 105

The figure is drastically different from what would be expected based on the current CIE luminous sensitivity standard for humans. The same is true of the curves for the humans TW and TP of the previous figure. For the monkey data, the peak sensitivity in the blue, near 437 nm, is only about 25% lower than the peak in the green. Similarly, the peak near 610 nm is actually higher than the peak in the green near 532 nm. The overall plot also shows a tilt relative to the peak values that might suggest the investigators did not correct for the variation in quantum flux per unit wavelength due to the color temperature of their source. It may be they only calculated a quantum flux per unit wavelength at one wavelength and assumed it was constant at all wavelengths. This would likely be the case if they controlled the flash intensity using calibrated filters Figure 17.2.3-15 Increment-threshold spectral sensitivity alone (without an associated radiometer). Their test set for rhesus monkeys. Data points; mean and 1 standard appears to be the same as that reported earlier by deviation of 72 threshold determinations per wavelength Harwerth & Sperling in 1971. In that paper, they using 5 monkeys. Protocol used an 18 degree, 5,650 describe their test set usign terms like watts/steradian Kelvin neutral background of 3000 td and 2 degree test 2 flash for 50 msec. Xxx Continuous lines based on the and watts/cm for their measured intensity. They also parameters shown and a smoothing factor of xxx found in discuss their calibration using an integrating radiometer. MathCad. From Sperling et al., 1978. This notation and instrumentation would indicate they depended on the calibration of the counter-rotating neutral density wedge filters to control their intensity regardless of the quantum flux in the 50 msec pulse as a function of wavelength.

If their double monochrometer maintained a half-amplitude width of 0.5 nm as in the previous papers, their actual excitation was somewhat reduced at short wavelengths relative to what was intended. This is shown by the 5650 Kelvin line in the figure. It is shown for a color temperature of 5650 Kelvin although their article was somewhat ambiguous. 5650 Kelvin is the value shown in their captions but 5500 Kelvin is stated in their text.

The Sperling, et. al. paper did not present a “conclusions” section. Their conclusions were included in the running discussion. Their conclusion that “the peak at 610 nm is too narrow and much too far toward the red, and the 535 nm peak is too narrow to be accounted for as either the envelope or the sum of the cone sensitivities.” is based on their adoption of the pseudo-absorbers used in the previous papers and the . The reference to “envelope” refers to their piecewise linear model labeled “upper envelope model” of the previous papers. That model includes four additional coefficients selected arbitrarily to provide good the best fits to their data. Their concern about the widths of their peaks is based entirely on their assumption that the spectra of Marks were theoretically correct. Their continued use of a piecewise linear envelope and an auxiliary 2x2 matrix with four arbitrary coefficients appears based on the same assumption.

The theoretical spectral response of this work has been fitted to the above with a deviation of no more than a factor of two from any of the mean values. However, it is not shown here because of the following discussion. It is shown later in this chapter. Figure 17.2.3-16 shows the above figure of Sperling et al. (1978) corrected for the assumed 106 Processes in Biological Vision nonuniformity in quantum flux due to color temperature. The human and unadjusted monkey data, along with this figure, are all unusual in that they show nearly equal peak amplitude near 437, 532 and 625 nm. This is in utter conflict with the CIE Standard Luminosity Function. Granted, some of the data is for a rhesus monkey and it may also suffer from a color temperature calibration error. However, with or without the correction for color temperature, all of the data shows the same detailed features as a function of wavelength. While only for two humans and five monkeys, the separate data sets show distinctive features that have not been erased by averaging. This situation suggests that testing more individuals would not change the precision of the results from this single test set. This is not to say that more thorough calibration would not improve the accuracy of the results.

The color corrected figure no longer shows a higher peak sensitivity in the red than in the green. In fact, the three peaks achieve the same sensitivity within a factor considerably less than two (near 1.4:1). In addition, the theoretical spectral sensitivity equation of this work fits the data extremely well. It remains within the plus or minus one standard deviation limits of the data at nearly every wavelength. It also reproduces all of the features associated with the data without relying upon any arbitrary constants.

The fit of the theoretical equation to the data can be made better. However the effort is not warranted due to the limitations within the test protocol and test equipment that generated the data. The theoretical curve does not include any compensation for the absorption and scatter of light within the lens group Figure 17.2.3-16 Increment-threshold data for Rhesus and humors of the monkey eye. Because of this, the monkeys corrected for color temperature. Data as in previous figure except for adjusted quanta per flash. Solid short wavelength half-amplitude point for the S- line is theoretical performance based on parameters in channel should not be relied upon. It is probably closer Table xxx. to 400 nm as in the nominal value of this work for the human. Similarly, the peak absorption in the region of 437 nm channel is probably not 80% of that in the 532 nm region. No correction for absorption by the macular has been included.

Because of these remaining questions, the nominal values shown in the table are the best available for the rhesus monkey but differ marginally from those for the human. The mean peak absorption wavelengths, calculated from the half-amplitude values of the in-situ chromophores, are 438.5, 539.5 and 637.5 nm at the fixation point of the eye. While the photochemistry of the visual process does not support the difference in the long wavelength region from that of the human standard of 625 nm, it does support the need to repeat the tests of Sperling, et. al. under an improved protocol and calibration procedure.

Sperling, et. al. did confirm that the perceived (psychophysical) and luminous channel (electrophysical) responses are the same in the monkey. They are both given by a single function based on a logarithmic summation of the electrical response generated by the transduction process of each spectral type of photoreceptor. This fact is also useful in Chapter 15. It provides good confirmation that the stellate cells of the brain perform a linear decoding of the stage 3 signals (which are logarithmically encoded). The result is a luminance (R-channel) signal provided to the brain (after decoding) that remains a logarithmic summation of the signal applied to the photoreceptors. Performance Descriptors 17- 107

Wilson also provided a spectral response in good agreement with this theory in 1964117. It is reproduced in Krantz118 and here as Figures 17.2.3-17. Re-plotting this figure using a photon-catch criterion, rather than an energy criterion would cause the short wavelength spectra to be emphasized more in this figure. The short and long wavelength shoulders would then be of equal threshold. The spectral peaks can be determined relative to the theoretical values shown based on this work and shown by the vertical lines. Those peaks are at 437, 532 and 625 nm.

The inset shows the stimulus configuration used to achieve identical viewing conditions. During both threshold determinations and brightness matches, the surround was illuminated with 5500K light and half the bipartite field was illuminate with 550 nm light, both at 10 mL luminance.

Blackwell & Blackwell have provided a variety of spectral data related to the various illumination regions gathered in the clinical environment119. This data invariably shows detailed structure that is absent from the C.I.E. Standard and other excessively smoothed curves. It should be noted that several of their patients with achromatopsia show a relative peak near 460 nm. This does not appear to be a true Bezold-Brucke peak. It may be due to a bias error in the signal processing system of these patients as discussed in Section 18.8.2. Although their material is now dated and they discuss several features in terms of discovery, most of the features were already well documented in other communities. References to these discussions appear Figure 17.2.3-17 Comparison of luminous efficiency at appropriate points in this work. functions for absolute threshold and for heterochromatic brightness matching. The plot is for the relative energy The above data is in strong disagreement with the threshold rather than the relative photon flux threshold. psychophysical data originally published by the San The latter would cause the curve to emphasize the short spectral region and de-emphasize the long wavelength Diego school of the 1980's, typified by the data of region. See text. From Wilson, 1964. Stockman et al120. They have frequently presented spectral data that presumes to show the spectral sensitivities of the S-, M- & L-channels. The high degree of overlap between the M- and L-channels is similar to that obtained by Wald in the 1940's based on incomplete differential adaptation using an adapting light of insufficiently long wavelength (typically 485 nm to suppress the M-channel photoreceptors). The data is also similar to that obtained very early for protanopes and deuteranopes, where the assumption was made that the complete spectrum of the deuteranope represented only the L-cone sensitivity (when it in fact is the logarithmic sum of the M- and L-channel absorption spectrums). The long wave portion of the protanope’s sensitivity is represented by the M- channel chromophores only. Their calculations are based on a linear visual system consisting of a single zone

117Wilson, B. (1964) An experimental examination of the spectral luminosity construct. Ph.D. dissertation, New Your University. Ann Arbor, Mi: University Microfilm 118Krantz, D. (1975) Color measurement and . II Opponent-colors theory J Math Psych vol 12, pp 304-327 119Blackwell, H. & Blackwell, O. (1961) Rod and cone receptor mechanisms in typical and atypical congenital achromatopsia. Vision Res. vol. 1, pp 62-107 120Stockman, A. Sharpe, L. Merbs, S. & Nathans, J. (2000) Spectral sensitivities of human cone visual pigments determined in vivo and in vitro Meth Enzymol vol 316, pp 626-650 108 Processes in Biological Vision

model, linear matrix algebra, and the CIE assumption that the luminance visibility function is equivalent to the standardized mid wavelength photoreceptor function.

Several authors have commented on the less than optimum separation of the M- and L-channel sensitivities implied by the Stockman et al assertions. The most recent of these has been Lewis & Zhaoping121.

No record has been found of anyone using the putative Stockman et al. spectra in an operational robot attempting to simulate human vision. The Stockman et al. spectra are not used in television transmission systems.

Kalloniatis & Harwerth have collected Increment-threshold spectral-sensitivity (ITSS) functions and similar threshold versus intensity data using 10 nm filters at higher intensities with a uniform background of unspecified color temperature using monkeys122. The paper deserves additional editing for readability. No background color temperature was given. The stimulus interval was long, 50-500 msec (equivalent to 10 to 0 Hz flicker frequency). Figure 17.2.3-18 shows their data with overlays based on cone fundamental responses and using the logarithm of the sums and differences of these responses. The logarithm of the absolute difference describing their proposed opponent function leads to a discontinuity in the region of 570 nm that is not present in the data or the model proposed here. There is a small notch of variable wavelength in the data and theoretical model of this work that varies with adaptation level. To alleviate the significant notch, they switch to a logarithm of the sum in this interval (as opposed to the sum of the logarithms used in this work). Their final proposal uses a logarithm of the absolute difference in the cone fundamentals plus a logarithm of the sum of the cone fundamentals (with a variety of constants chosen to fit their data) to describe the spectral region from 550 to 580 nm. Outside of this region, they omit the contribution of the logarithmic summation. No explanation was provided as to how or why the neurological system would employ this methodology and introduces so many arbitrary constants. Their paper provides a background on why the earlier assertion of three fundamental cone responses near 440-460, 530-545 and 600-610 nm by Stiles and Crawford (which was correct) was dropped by Stiles in 1978.

121Lewis, A. & Zhaoping, L. (2006) Are cone sensitivities determined by natural color statistics? J Vision vol 6, pp 285–302 (avail. on the Internet) 122Kalloniatis, M. & Harwerth, R. (1990) Spectral sensitivity and adaptation characteristics of cone mechanisms under white-light adaptation JOSA A vol 7(10), pp 1912-1928 Performance Descriptors 17- 109

Figure 17.2.3-18 Piece-wise fitting of human absorption spectra using cone fundamentals. Dark lines with a significant dip at 570 nm represent attempts to emulate the measured data (crosses) using a logarithm of the absolute differences between the cone fundamentals. The notches are not present in the empirical data. Dark lines without the dip employ a logaritmic summation approach. From Kalloniatis & Harwerth, 1990.

Kalloniatis & Harwerth conclude their introduction with the statement; “The underlying mechanisms may not be the cone fundamentals; more important, however, is that the hypotheses proposed by Stiles have not been adequately tested.“ In their discussion, they assert, “It appears Stiles was correct in hypothesizing shape invariance of the individual color vision mechanisms and suggesting that the differences in adaptation characteristic of these mechanisms resulted in the overall changes in shape of the spectral sensitivity function under white-light adaptation. However, the underlying detection mechanisms are not the fundamental cone response, as was originally hypothesized.”

Kalloniatis & Harwerth encountered some of the subject to subject variation (figure 8) also reported by Babucke.

17.2.3.5.2 The photopic research literature–infrared

The performance of the visual system in the infrared is dominated by the long wavelength absorption edge of the long wavelength spectral channel combined with the losses due to absorption by the lens group. The absorption of 110 Processes in Biological Vision

the lens group has been reproduced in Charman123 based on data from Geeraets & Berry124 (See Section 17.2.2.2).

Measuring the sensitivity of vision in the infrared is difficult because of both the range and the equipment involved. Walraven & Leebeek summarize the data available prior to Sliney and assemble a curve of individual segments125. No one investigator explored the entire range prior to Sliney, et. al.

When the above factors are combined, the agreement between the measured data and the theoretical equation is quite good. Figure 17.2.3-19 presents the same equation extended into the infra-red. The equation, represented by the solid lines, is the predicted sensitivity versus wavelength. The lower curve represents the nominal equation with the long wavelength parameter of Rhodonine(5) at the nominal value of 655 nm. The upper curve is for the same parameter at 685 nm. The dashed line represents the reduction in sensitivity due to absorption by the optics. These curves agree well with the measured values of Figure 17.2.3-19 The predicted dark adapted photopic Sliney, et. al126. over a range of ten orders of luminosity function in the infra-red compared to the data points of Sliney. Upper curve for RH = 685 nm. Lower magnitude. The data points of Sliney suggest that the curve RH = 655 nm. Dashed curve shows average subject was not completely dark adapted. The low correction for seven eyes (ages 23 to 78) from Geeraets & amplitude of the data point at 480 nm suggests that the Berry, 1968. See text. subject was violet adapted with coefficients of 100:1000:400. This situation would place the long wavelength data points about 0.5 to 1.0 orders of magnitude too high relative to the peak at 550 nm. In either case, the predicted characteristic, modified by the data of Geeraets & Berry, differs from Sliney by less than 10% per decade over ten decades. Interpreting Fig 2 of Walraven & Leebeek is difficult It appears they mis-drew the loss in sensitivity due to the lens. A loss in sensitivity would normally lead to a larger number for the absolute sensitivity. It shows the sensitivity of the complete eye, with the absorption of the lens, as higher than the sensitivity of the retina in the absence of the lens. The absicca is missing a label in the published figure. This figure also shows a sensitivity about one order of magnitude less than the other investigators. See Also the data of Lamb127.

Sliney, et. al. note the many reports of perception of a blue-green color after stimulation with long wavelength infrared. They accept it as fact but question whether it can be due to frequency doubling. They say frequency

123Charman, W. (1991) Limits on visual performance set by the eye’s optics and the retinal cone mosaic, in Vision and Visual Dysfunction, vol. 5 Boca Raton, FL: CRC Press, Inc. Chapter 7 124Geeraets, W. & Berry, E. (1968) Ocular spectral characteristics as related to hazards from lasers and other sources. Am. J. Ophthalmol. vol. 66, pp 15-20 125Walraven, P. & Leebeek, H. (1963) Foveal sensitivity of the human eye in the near infrared xxx (probably JOSA) vol. 53, pp 765-766 126Sliney, D., Wangemann, R. Franks, J. & Wolbarsht, M. (1976) Visual sensitivity of the eye to infrared laser radiation. J. Opt. Soc. Am. vol. 66, no. 4. 127Lamb, T. (1995) Photorecepor spectral sensitivities: common shape in the long wavelength region, Vision Res. vol. 35, no. 22, pp 3083-3091, fig 3 Performance Descriptors 17- 111 doubling is too inefficient a process to give the result observed. This work claims that the normal S-channel response to infra-red light is due to a 2-exciton process (where the energy of two photons is summed in order to excite an electron-hole pair in the base of the adaptation amplifier Activa). Since the threshold level of all adaptation amplifier Activas are nominally 2.0 eV, the same 2-exciton process is also able to excite M-channel Activas. This mechanism does not require the matching of energy band widths and levels as frequency doubling does. However, the sensitivity of the M-channel chromophore to light at these wavelengths must be considered. While the sensitivity of the M-channel chromophore may be reduced by a factor of at least 100 at these wavelengths, its relative availability may compensate for this.

17.2.3.5.3 The photopic research literature–chromatic adaptation (A MAJOR PROBLEM)

When discussing chromatic adaptation, it is important to remember the time constants involved in vision. Measurements of the spectral response of vision under differential adaptation must be accomplished within an effective time interval of less than one minute following adaptation128.

Wald presented a series of chromatically adapted spectrums in 1964 that form a milestone in the psychophysics of vision129. Instead of the nominal two-degree stimulus field, he used a one-degree field designed to remain within the foveola. The data provides a long wavelength spectrum that is claimed to be and frequently associated with the long wavelength chromophore of vision. Although widely reproduced, that claim is erroneous. Figure 17.2.3-20 reproduces his figure 4 with a dashed overlay based on this work. He used the data points and curve labeled “green adapted” to support his claim that the peak in the long wavelength absorber was at 575 nm. The short dashed curve through these same data points uses the overall spectral response equation of this work. The equation uses ks:km:kl::1000:110:275 to fit this data at least as well as the freehand line drawn by Wald. The equation is based on peak wavelengths for the photoreceptors of human vision of 437, 532 and 625 nm. To precisely fit the data requires an exact knowledge of the difference in half-amplitude wavelengths of the middle and long wavelength absorbers for

the subject. The values used in this calculated curve were λsl = 455, λms = 490, λml = 560, λls = 595 and λll = 645 nm.. These half-amplitude difference impacts the depth of the notch near 520 nm and the shape of the peak near 600 nm. Hence, additional iterations of the calculation could provide a better fit if the data was statistically more accurate. The data of Wald does not support his claim for the peak wavelength of the L–channel photoreceptor of human vision. The overall sensitivity equation indicates that the peak near 575 nm was formed primarily by the Bezold-Brucke Peak resulting from a mixture of M– and L– receptors in the ratio of 110:275. These values suggest the “blue” adapting light only suppressed the M–channel by a factor of 10 relative to the L- channel. While Wald describes his “green” adapting light as based on a Ilford 604 filter, he fails to note that his “field lamp” was incandescent and of unspecified color temperature. Since the incandescent source is deficient in the blue, such a combination actually provides a peak radiation intensity near the long wavelength cutoff of the filter. In this case, the peak was probably near 530 nm This explains why the S–channel receptors were not significantly suppressed in his figure 4. To isolate the L–channel receptor would have required chromatic adaptation of the M–receptor by an additional order of magnitude. This is shown by the long dashed line labeled “Alternate adaptation.” At this level of adaptation, km:kl::10:275, the true peak wavelength of the L–receptor is seen. The peak absorption of the L–channel receptors is at 625 nm.

The above discussion combined with that in Section 5.5.10.4.1 have serious ramifications. Virtually all of the experiments in psychophysics of the last 50 years have assumed the long wavelength chromophores of vision peaked in the region of 575 nm. They have relied upon a false assumption! It is unfortunate that the proposal of Wald was not questioned or the experiment performed under a more strenuous protocol for over 40 years. The peak spectral

128Aurebach, E. & Wald, G. (1954) Identification of a violet receptor in Human color vision, Science, vol. 120, pp 401-405 129Wald, G. (1964) The receptors of human color vision. Science, vol. 145, pg. 1009 112 Processes in Biological Vision

absorption of the L-channel in human vision is at 625 nm. If it is not near 625 nm in humans, humans are the only known chordate exhibiting a chromophore in their long wavelength visual channel at such a short wavelength. A repetition of Wald’s experiment using a more demanding M-channel suppression protocol will clearly demonstrate the peak spectral sensitivity of the L–channel.

Augenstein & Pugh have provided a number of spectra resulting from differential bleaching that show the signature of a chromophore with a peak sensitivity near 625 nm130. These spectra cannot be synthesized using only chromophores with peak wavelengths shorter than 580 nm.

Tansley, et. al. have provided many spectrums of squirrels, based on ERG techniques, under various states of adaptation131. The work is an excellent example of exploratory research lacking an adequate model. This is highlighted by their use of the amplitude of the ERG as a reference. This approach fails to note the variability of the adaptation amplifier that is the ultimate source of the ERG waveforms. The work suffers from the instrumentation of the day, particularly the use of a “100 watt Sylvania” light source and only a few narrow band filters. The discussion is a model of objectivity. Equal quanta per unit wavelength were used to obtain the data. It clearly shows a Bezold-Brucke peak near 490 nm along with the normal shoulder near 437 nm and the normal peak at 532 nm associated with trichromatic vision. It also highlights the difference between the amplitude of these components as a function of chromatic adaptation and intensity. They describe the presence of a component in the 450-460 nm region as capricious in its appearance but statistically significant. Although the reference in Davson says Tansley, et. al. used equal quanta per unit wavelength in their experiments, no

Figure 17.2.3-20 Wald figure 4 with overlay. Wald used the curve labeled green adapted to justify his claim that the long wavelength photoreceptor had a peak absorption at 575 nm. The short dashed curve through the same points contains ks:km;kl::1000:110:275. The two peaks in the measured data are actually due to the Bezold Effect. The short wavelength peak is near 460 nm and the long wavelength peak is near 575-580 nm. The alternate (long dashes) adaptation curve correctly isolates the peak absorption of the S–channel at 437 nm and the L–channel at 625 nm. See text.

130 Augenstein, E. & Pugh, E. (1977) The dynamics of the Π1 colour mechanism: further evidence for two sites of adaptation J Physiol vol 272, pp 247-281 131Tansley, K. Copenhaver, R. & Gunkel, R. (1961) Spectral sensitivity curves of diurnal squirrels. Vision Res. vol. 1, pp 154-165 Performance Descriptors 17- 113 claim to this appears in the paper132. It is also highly doubtful based on the instrumentation used.

Stockman, et. al. have recently provided the spectrum of what appear to be true monochromats. They exhibit significant sensitivity to radiation only in the spectral region of the S-channel133. Figure 17.2.3-21 shows their data (dashed line), compared with the spectrum of Wald (crosses) and two theoretical responses according to this work. The solid line beginning at 370 and terminating near 650 nanometers represents the theoretical S-channel response only. The theoretical response beginning at 370 and terminating near 680 nanometers represents a partially adapted eye. It follows what Wald described as a yellow adapted trichromatic human eye (solid line following the data points of Wald). The data is plotted on the scales of Wald. The data of Stockman was truncated at 575 nm. for convenience. The half amplitude points of the theoretical model are 400 & 475 nm. at a temperature of 310K. The response of the theoretical normal trichromatic eye was reduced approximately 1000:1 in the M- and L-channels to correspond to the Wald data. There appears to be excellent agreement between the two sets of data points and the two solid lines. The theoretical solid line following Stockman is for the M- and L-channel coefficients set to zero. The data points would probably be in better agreement with the theoretical line if the number of adjustments to the raw data made by both Wald and Stockman in order to remove irrelevant factors were reduced. Data manipulation invariably leads to a Gaussian final shape in accordance with the Central Limit Theorem. The deviation of the data points from the theoretical line are too small to warrant a change in the half amplitude points of the theoretical curve which must also be compatible with other, particularly vernier, data. The theoretical curve as presented may be too high in the region between 380-425 nm because it does not contain any absorption term to account for the optical system of the eye.

Wald presented data on a series of individuals under different states of adaptation in the above paper. That data is well represented by the theoretical model when the coefficients describing the state of the adaptation of

Figure 17.2.3-21 The spectrum of the “blue monochromat” and a yellow adapted trichromat shown against theoretical performance. See text for details. Theoretical curve (solid line) at 10 nm. precision for both fully and partially chromatically adapted trichromat. Monochromat data (dashed line) from Stockman, et. al. (1999). Chromatically adapted trichromat data (crosses) from Wald (1964).

132Davson, H. (1990) Physiology of the Eye, 5th Ed. NY: Pergamon Press, pg 442 133Stockman, A., Sharpe, L. & Fach, C. (1999) The spectral sensitivity of the human short-wavelength cones derived from thresholds and color matches. Vision Res., vol. 39, pp. 2901-2927 114 Processes in Biological Vision

each chromatic channel are assigned appropriately134. The theoretical equation of this work can also be used to predict the set of curves for different states of adaptation presented by Wooten, Fuld & Spillman for an observer at 30 degrees retinal eccentricity135.

17.2.3.5.4 The photopic research literature–Difference spectra

Comparing psychophysical luminosity functions, acquired under different states of adaptation, algebraically has been a common technique for over a century. However, the technique fails to take into account two major considerations. First, the underlying processes involved are not linear. Second, there are multiple parallel spectrally sensitive signal paths involved in vision that do not perform in a coordinated manner. This has led to what might be called psychophysically acquired spectra. Most of these spectra have been obtained using differential chromatic adaptation techniques that were less than aggressive.

The psychophysical community has given these spectra the name fundamental cone spectra or cone fundamentals. Although these fundamental spectra are discussed in terms of specific cone spectra, they are not. These spectra generally show structure indicative of their actual origin, particularly the presence of S-channel receptor absorption in the case of the M- and L-channel fundamental spectra. They also show a strong resemblance to the underlying luminosity function. Two recent empirical difference spectra, presented by Stockman, et. al.136, are shown in Figure 17.2.3-22. The upper frame shows their data points compared to the previous curves presented by Smith & Pokorny (solid curves) and Vos & Walraven (dashed curves) for the fundamental M-cone spectrum. The C.I.E Photopic Luminosity Standard (dash-dot line) is also shown for comparison. Based on this work, it is seen that the so-called fundamental M-cone spectrum is only a luminosity function obtained under a slight condition of chromatic adaptation. This condition can be described in either of two ways. The most appropriate is the suppression of the M-channel signal by about a factor of three relative to the S-channel and an additional suppression of the L-channel by a factor of three relative to the M-channel. This explanation is consistent with their test procedure. An alternate explanation based only on the graphics would suggest the L-channel was suppressed by a factor of three relative to the M-channel while the S-channel was enhanced by a factor of three. Determination of a peak wavelength for the data points of Stockman, et. al. is difficult because of the wide spacing of the data points.

134Fulton, J. (1985) The perception of luminance under various state of adaptation. Los Angeles, CA: Hughes Aircraft Co. Research Report (available from the author) 135Wooten, B. Fuld, K. & Spillman, L. (1975) Photopic spectral sensitivity of the peripheral retina. J. Opt. Soc. Am. vol. 65, pp. 334-342 136Stockman, A. MacLeod, D. & Johnson, N. (1993) Spectral sensitivities of the human cones. J. Opt. Soc. Am. A, vol. 10, no. 12, pp. 249-2521 Performance Descriptors 17- 115

The lower frame shows their data points and the curves of the other authors, as described above, for the so- called fundamental L-cone spectrum. Stockman, et. al’s. data points (with their error bars) are seen to match the C.I.E. Standard Luminosity Function at least as well as they match the curves of the other authors. The only deviation is in the very short wavelengths where the C.I.E. function is known to be inappropriate. If the modified C.I.E. Standard as proposed by Judd is used, all of the data points and curves of other authors representing the “fundamental L-cone spectrum” display a remarkable agreement with the C.I.E. Standard. There is no sign of significant chromatic adaptation. The broadness of all of the data points and curves in this frame make determination of a peak wavelength indeterminate.

The poorly defined maxima of all of these curves, approximately 542 in the upper graph and 560-565 in the lower graph (See below) do not contribute new information to the art. The poorly defined peak in the lower curve appears to be the source of the value frequently found in the literature, of 560-576 nm for the L-cone fundamental. Stockman, et. al. used an unusual arrangement of 4 degree diameter adapting and background lights, alternating between a red light at 678 nm and a blue light at 485 nm at 0.5 Hz. The spectral width of these lights was not specified. The Figure 17.2.3-22 Comparison of difference spectra with blue light was used to suppress the putative M-cones. the CIE Photopic Luminosity Standard of 1924. Upper The red light was used to suppress the L-cones. The frame shows the “fundamental” M-cone spectrum of Stockman and others. The lower frame shows the alternative light was used as a background during “fundamental” L-cone spectrum of Stockman and others. probing with a 2 degree narrow spectral band light The dash-dot lines represent the CIE Standard. All other flickering at 17 Hz. They also introduced a second lines and data points are from Stockman, et. al. (1993). violet light to suppress the S-cones during M-cone See text. isolation. This suppression was apparently not successful. Note the plateau in the 450 nm region of the empirical data showing the functional presence of the S- channel chromophores.

Based on this work, the choice of wavelengths of the adapting and background lights as well as the rate of alternation and the intensity of the adapting light used by Stockman, et. al. appears questionable. Their logic for these choices is provided in a separate paper137. This paper is meticulous and exhaustive but based on empirical data and a conceptual rather than precise understanding of the mechanisms of the visual system. Although equation 2 of that paper includes logarithmic notation, following a proposal of Smith & Pokorny138, the summing process is a

137Stockman, A. MacLeod, D. & Vivien, J. (1993) Isolation of the middle- and long-wavelength-sensitive cones in normal thrichromats. J. Opt. Soc. Am. A, vol. 10, no. 12, pp. 2471-2490 138Smith, V. & Pokorny, J. (1975) Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm. Vision Res. vol. 15, pp. 161-171 116 Processes in Biological Vision linear one within one logarithmic term.

The Stockman paper compares their results with that of many other psychophysicists over the years. Excellent agreement is obtained. However, both groups employ a variety of adjustments to their data. Both the Stockman group (page 2476) and the psychophysicists also rely upon the linearity assumption. The first paragraph of the introduction to the paper also develops the crux of their problem. The second paragraph develops their understanding of the problem. The problem is that the psychophysical spectra assigned to the photoreceptors of the eye are grossly different than those measure by the electrophysiologists. This problem is compounded by the anisotropic absorption spectrum of the Rhodonines in the liquid crystalline state. Most of the electrophysiological measurements before 1998 were made using transverse illumination applied to an individual Outer Segment. The result was the isotropic absorption spectrum of the chromophores, with a peak near 500 nm regardless of the chromatic type of photoreceptor measured. Stockman, et. al. used narrow band filters for the probes used to establish the spectral sensitivity but only collected data at well spaced points. The filters were described as 7 to 11 nm half-bandwidths. They did not use, but their discussion supports, the more specific term, half-amplitude- bandwidths. Their data was collected at relatively wide spacings, generally 30 nm. Although they did not connect the points in their graphs, they used the lines of other investigators as overlays to connect the points. The result is that their data presentation is compatible with a smoothing of the sensitivity curve. No narrowband structure is seen in the graphs. After all data reduction, they gave the peak absorption wavelengths for their proposed 2 degree cone fundamentals as 445, 545 &570 nm.

The Stockman et al. data are combined and annotated further in Figure 17.2.3-23. Symbols have been added to describe the spatial quality of the conditioning (adaptation) and the test spectrum. The 1993 test protocol involved a very complex conditioning regime. It combined both multiple spatial parameters and multiple temporal parameters (page 2475). The spatial parameters are shown. A disk-shaped four degree conditioning stimulus was used concentric with a two degree test stimulus for the M– and L–channel tests. The test stimulus flickered at 17 Hz for the M– and L– channel tests, with a 50% duty cycle between a test wavelength and an additional background of 561 nm. The result was data based on a chromatic discrimination criteria rather than a threshold brightness criteria.

For the S–channel tests, the conditioning field was 16 degrees in diameter with a test field of two degrees flickering at 1 Hz. The parameters of the test stimulus appear to have been of variable wavelength at 50% duty cycle against a continuous conditioning field. This simpler pattern resulted in a threshold brightness criteria regardless of test stimulus wavelength.

The shape of the S–channel (S-fundamental) response agrees completely with the theoretical response of Rhodonine(9), both in center wavelength and the slope of its skirts. This response can be associated with the absorption spectra of the S– chromophore as projected to the entrance aperture of the eye, a so-called S-fundamental. Both of the M– and L– channel responses show residual S– channel sensitivity. The L–channel response short wave skirt also suggests significant M– channel sensitivity as well. These problems appear to be due to inadequate intensity in the conditioning signals and the high flicker rate causing the results to be based on chromatic difference criteria rather than an intensity threshold criteria. This difference is due to the flicker frequency exceeding the critical flicker frequency of three Hertz documented by de Lange Dzn139.

[xxx include comments brought forward from the new comparison section, 17.2.3.5 ]

139Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd Ed. NY: John Wiley & Sons pg 565 Performance Descriptors 17- 117

Contrary to the position of Stockman, et. al. in their first 1993 paper, in the absence of aggressive chromatic adaptation such as used by Wald in the 1950's and the Stockman group in their 1999 paper, the spectral response of the individual chromatic channels of subjects with normal vision cannot be obtained by psychophysical means. In the 1999 paper, the spectrum of the S-channel is easily recognized in those with normal vision by comparing the spectrum to subjects who appear to be true S-channel monochromats.

17.2.3.5.5 The photopic research literature–Foveal

Although there is considerable discussion in the Figure 17.2.3-23 Annotated Stockman et al. data literature concerning whether the fovea is color blind compared to the proposed theoretical peaks. See text. or not, there is little substantive data, at least in the last 50 years. The nominal luminous efficiency function is obtained using a two degree diameter (in object space) light source. The area of this source more than covers the fovea of the human eye and the resulting average response may be hiding important details of the function. It would be of interest to the research community to have luminous efficiency data as a function of wavelength for only the fovea (more precisely the foveola) to settle the luminosity aspect of this question. Similarly, it would be useful to have chromatic discrimination data for this same portion of the retina. Careful experimental design could produce interesting new information concerning this area. It might show that, because of the difference in the signal path for foveal photoreceptors connecting to the cortex, both the luminous efficiency function and chromatic discrimination function are fundamentally different for this region of the retina.

17.2.3.6 Interpretation of the photopic standards literature

17.2.3.6.1 State of the Photopic Standard

As indicated above, the state of the CIE Photopic Standard is poor, to the extent that some authors have begun using subscripts to denote quasi-official (?, quasi-accepted) modifications to the archaic standard. The problem is complicated by the use of questionable procedures in the collection of data for both the old and new data bases. See Section 17.2.1.3.1. It is further complicated by the communities continued reliance on a variety of questionable concepts. These include the lack of recognition of the dependence of the visual system on photon flux instead of integrated energy, the assumption that the photopic luminosity function is independent of the spectral content of the illumination used, the lack of appreciation of the importance of data smoothing in obscuring the contributions of the underlying mechanisms, and the assumption of the Univariance Principle across the visual spectrum of the eye.

The CIE has struggled for a long time over the correct name to use in describing the sensitivity of the human visual system under typical daylight operation. The original designation visibility function of 1924 was dropped in favor of photopic luminous efficiency function in 1951 concurrent with the adoption of the first scotopic luminous efficiency function. Looking closely at the visual system and the test methodology described, it is clear that the measured functions have little to do with the efficiency of the system. They in fact describe the threshold sensitivity of the system as a function of wavelength under various conditions of stimulation. Because of the concurrently operating 118 Processes in Biological Vision

adaptation process, the measurements do not reflect the efficiency of the system, only its performance under the conditions specified. Because of this situation, the term luminous efficiency function will only be used as part of the title in the official CIE Standard. A more appropriate title would be the overall threshold visibility function (as a function of wavelength). This terminology separates the performance of the eye from the photometric terminology based on the lumen.

The current standard differs significantly in the long wavelength region compared to most of the data in the research literature as suggested by the work of Wald and of Sliney reviewed above. The deviation is so large as to question whether further consideration of the C.I.E (1924) Photopic Luminous Efficiency Function is warranted in a research environment. The C.I.E140. published a summary of more recent work in 1978 that included a curve described as the Weighted Mean for each of several methods of measurement. The wide disparity of the results of individual investigators continues to disparage the concept of using a weighted mean. Several of the investigators recorded features that are instantly associatable with the theoretical function of this work. This includes the peak near 580 nm and the inflection point near 487 nm shown in the data of Sperling & Lewis using the absolute-threshold method. The absolute threshold data of both Guth & Lodge (1973), Sperling & Lewis (1959), and the Weighted Mean show peaks at 540 nm (or slightly less in the case of Guth & Lodge by interpolation). This is 15 nm lower than in the Standard and conventionally quoted 555 nm.

There have been numerous calls for revision to the Standards by researchers. However, the Standard occupies a fundamental position in the industrial applications of illumination and is not likely to be changed soon. It is probably more useful to consider a separate standard for purposes of research. This standard would recognize the variability of the results based on color temperature of the illumination and would memorialize an equal photon flux per unit bandwidth source as the test standard. The standard would also recognize the importance of data smoothing due to finite width spectrometric instrumentation. It would also redefine the Standard Observer based on this new standard luminosity function for research.

The magnitude of the deviation between the smoothed CIE luminous efficiency functions for a standard observer and those for a real person (whether using the theoretical function or modern measurements) is so large (frequently over 30% at specific wavelengths) that the CIE functions should never be used as a real standard or to represent an average subject.

Without a usable Univariance Principle, the precise conversion of the graph of the current standard luminosity function to an equal photon flux per unit wavelength basis is a significant activity. The ratio of the width of the visual spectrum to its center wavelength is significant as in the highly asymmetric contribution of the physical optics of the eye to the overall characteristic. Because of the nature of the equations, it is also necessary to consider the three absorption regions separately.

17.2.3.6.2 Individual factors not addressed in the CIE Standard

There is more than sufficient information available to demonstrate the defined luminosity function is a continuous variable with respect to spatial position across the retina, to average radiant intensity, and a complex function of the spectral content of the radiant intensity. To fully describe the luminosity function at a given instant is difficult and requires several lines of mathematical formula to be evaluated for a specific set of parameters. To avoid this problem, the luminosity function of the literature was originally restricted to a specific, normally poorly defined , set

140C.I.E. (1978) Light as a true visual quantity: Principles of measurement. Publ. CIE No 41 (TC-1.4) Paris, FR: Bureau Central de la CIE Performance Descriptors 17- 119 of parameters.

The empirical concept, if any, was that these parameters determined one particular edge of the multidimensional parameter space. It soon became clear that this was impossible and two separate and distinct edges of that space were defined, still without total definition. Thus evolved the photopic and scotopic luminosity functions. The empirical protocol for determining these functions were defined to eliminate, rather than control, as many variables as possible. There are two facets of the protocol. One defines the state of the visual system as fully dark adapted. The other specifies, at least partially, the test probe to be used. This probe employs small spatial field conditions with respect to the fovea, illumination centered on the point of fixation, and nominal duration pulses of illumination derived from a light source via a spectrometer. The diameter of the illuminating probe is usually defined in terms of angular field in object space and has converged on two values. For photopic conditions, the diameter is normally taken as 2° circular. Recognizing the significance of, and the necessity of exceeding, the noise threshold (at least implicitly) the diameter for the scotopic condition is normally taken as 10° circular. These are the sizes recognized in the CIE Standards. The parameters of the illumination source have never been adequately specified or controlled. Their specification has usually been defined as “depend on the experimenter to use the best instrumentation available based on his experience or available funds.”

Although not commonly discussed in matters involving luminance, the variation in the performance of the retina with spatial field, and the nature of the surrounding field, is widely recognized. Wyszecki & Stiles141 devote an entire chapter to the philosophy and procedures of visual sensation matching. Lacking a detailed model of the visual system, the discussion is superficial.

The signal flow schematic diagram of the eye related to the luminance channel is shown in Figure 17.2.3-24. This diagram stresses the summation process used in the luminance channel. It omits completely the discussion of the spatial encoding that occurs at the input to the parasol ganglion cells of the projection neuron subsystem. A discussion about the relative contribution of each photosensing channel in the signal sensing stage, 1, to the luminance signal in the signal manipulation stage, 2, will follow below.

141Wyszecki G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley, Chap. 5 120 Processes in Biological Vision

It is very difficult to measure the spectral sensitivity of the human eye directly, and with precision, as a function of irradiation level and spectral interval. As listed and graphed above, the human eye incorporates a variety of techniques to achieve its very wide dynamic range with respect to radiation intensity. In this situation, a psychophysical experiment must be very carefully defined. Since the eye incorporates state variables in the signal path, both a prior and an instantaneous condition must be prescribed in any experiment. There are very few clearly definable states of the eye. One corresponds to the fully dark adapted condition. Another corresponds to the boundary between the photopic and mesotopic ranges. At this level, all of the photoreceptors are operating at full sensitivity and neither the (individual) adaptation amplifiers or the iris have begun to modify the signals delivered to the brain. These are the two conditions normally chosen to measure the photopic luminosity function. The test criteria is usually based on detection of a short pulse. This criteria is basically a signal to noise ratio criteria that is a

Figure 17.2.3-24 The signal flow schematic used for calculating the luminance function of human vision. Spatial encoding is omitted from this elementary diagram. Photoreceptor cells in foveola (also) connect directly to individual bipolar and parasol ganglion cells projecting to the Pretectum. function of test exposure area. As long as the dark adapted state is not disturbed, it is possible to use short test pulses of radiation at higher irradiance levels. However, if the total flux absorbed begins to impact the amplification of the adaptation amplifiers, different psychophysical results will be obtained.

The theoretical concept derived from this work recognizes the many parameters involved explicitly and the dynamic performance of the visual system based on the instantaneous state of the variables associated with those parameters. There are substantially fixed parameters and a set of parameters that vary automatically in an attempt to provide a nominal perceptual performance optimal for the species. The key factor is the tendency of the individual Performance Descriptors 17- 121

photoreceptor channels to adjust the net amplifier gain in each stage 1 channel (using negative internal feedback) to produce a nominally constant signal level at the nodes (pedicels) of all of the photoreceptors. This tendency is strongly affected by the ability of the vascular-electrostenolytic system to maintain the quiescent condition with variations in illumination. The theoretical concept also provides an explanation of what the luminosity function actually represents from a system perspective. It represents the minimum photon flux per unit angular area (normally in object space) required to exceed the effective noise threshold of the luminance channel of the visual system (the noise threshold divided by the effective gain of the amplification system) sufficiently to be perceived by the individual. The minimum photon flux per unit area may be obtained from a source of radiation that is narrowly filtered spectrally or less narrowly filtered. Since an integral is involved, the more filtered the radiation, the greater the precision of the determination.

The theoretical concept provides a much better framework for defining one or more states for measuring a single response to a set of conditions that could be considered the nominal luminosity function of the visual system. Several conceptual conditions become clearer.

Being a function derived from psychophysical data, the luminosity function relies on five major parameters or processes; + the nature of the radiation used to excite the eye + the absorption of light by the physical optics of the eye + the anisotropic absorption of radiation by the Outer Segment (Poynting vector of radiation parallel to the long axis of the OS), + the adapted state of the photoreceptors individually, and + the logarithmic processing of the photoreceptor signals.

The luminosity function cannot be obtained by reflective microspectrophotometry through the aperture of the eye or by invasive techniques employing transverse irradiation of individual photoreceptors.

In summary, the theoretical luminosity function is the normalized reciprocal of the perceived sensitivity threshold as a function of wavelength of the human eye to pulse irradiation, of equal photon flux per unit wavelength, of a specified spatial extent, and with a specified on-pulse duration (and specified off-pulse duration if repetitive), under dark adapted conditions. In practice, the CIE Photopic Luminosity Function is a characteristic based on a smoothed and distorted version of the above fundamental function, due primarily to the limits of the test instrumentation used to determine it. The CIE Function displays filtering by a nominally 30 nm. wide spectral filter and use of a non equal-flux irradiation source, typically an incandescent lamp with a soda glass envelope. The lamp was generally operated at an effective black body temperature of about 2800 degrees Kelvin. However, it was deficient in the blue due to absorption by the soda glass envelope.

When discussing the luminosity function and the processes that contribute to it, it is important to recognize that the peak spectral response of each process is different. The peak wavelength of the cumulative response moves to longer wavelengths starting with the response of only the Outer Segments of the retina. When calculated using an equal photon flux per unit spectral wavelength, the peak absorptance of the Outer Segments of the retina as a complete in-vivo array under dark adapted conditions occurs at 537 nm. After including all of the physical optics of the eye in the calculation, the peak absorptance of the eye at its aperture, based on equal flux conditions, occurs at a slightly longer wavelength, depending on the pupil size and the age of the subject. It is only when the spectral performance is smoothed using a spectral filter of about 30 nm and then replotted on an equal energy per unit wavelength basis that the peak is seen to occur near 555 nm, the accepted value in the literature.

There are two distinctly different groups of quasi-constant contributors to the complete luminosity function. The elements of the physical optics of the eye contribute a radiation transfer characteristic that varies only slightly with 122 Processes in Biological Vision pupil size and age. They vary more significantly with the angle of the chief ray through the optical system. This variation involves the effective thickness of the outer lens group with angle and the variation in absorption of the field lens adjacent to the Outer Segments. This variation is usually described in terms of the macula or macula lutea superimposed between the vitreous humor and the retina. Most recent data shows that it is not a unique layer but a variation in the optical density of the neural tissue related to the movement of as much neural tissue as possible out of the optical path leading to the fovea. In this context, the macula lutea is a portion of a conglomerate retinal tissue in front of the photosensitive surface that contains a reduced amount of neuron material.

The lens system of the eye makes a significant contribution to the overall luminosity function of the eye. The outer lens group, the cornea and “lens,” absorb significantly in the short wavelength portion of the spectrum. The total absorption of the outer lens group is a function of angle with respect to the optical axis and the pupil diameter in precise measurements. The field lens, consisting of the neural material overlaying the photoreceptors, exhibits significant absorption as a function of retinal position, and is particularly important in the foveal area of the retina.

[xxx revise this to show aldehyde absorption in Section 16.3.3.1 ] Equations derived in Chapter 16 from the best available data for the absorption of the outer lens group (as a function of age) and the field lens are shown in Figure 17.2.3-25. See also [Figure 17.2.3-3] for alternate data in the region of 300-400 nm. The absorption of the field lens, frequently described as a separate layer known as the macula or macula lutea in early work, is seen to be quite significant in the short wavelength region of vision. The curve represents in-vitro data from only nine subjects. Only near age 63 does the absorption of the outer lens group equal that of the macula. The impact of the outer lens group on the overall absorption is more significant in the middle and long wave region as age increases.

The equations shown are based on the data presented in Adler142 and drawn from the work of Weale143 (lens) and from Ruddock144 (macula). Weale’ data is based on color differences for living subjects and not spectrographic data. By comparing Ruddock’s data to the earlier data of Wald145 that has been widely reproduced, it is apparent that Wald was using a wide spectral bandwidth spectrometer as would be expected for his time period. Wald was also working in-vitro with the macula from 9 subjects in chloroform. [this paragraph probably moves to Chapter 16] Figure 17.2.3-25 Equations for the spectral absorption of As discussed in Section 16.3.3.2.1, the more recent the physiological optics of the eye. Solid lines are data of Griswold & Stark would suggest, a different absorption of the outer lens group as a function of age fundamental equation is needed to conform to the (only applicable at wavelengths greater than 400 nm). Dashed line is the absorption of the field lens (generally Fermi-Dirac characteristic of the optical absorption of labeled the macula)in the region of the fovea. the lens group in young eyes.

The equation for the lens group absorption exhibits a single peak near 350 nm. The literature has frequently associated the retinenes with this UV wavelength peak. However, most creditable references show retinal with a

142Hart, W. ed. (1992) Adler’s Physiology of the eye. pg. 710 143 Weale, R. (1954) Light absorption by the lens of the human eye, Optica Acta. vol . 1, pp. 107-110 144Ruddock, K. (1963) Evidence for macular pigmentation from colour matching data. Vision. Res. vol. 3, pp. 417-429 145Wald, G. (1945) Human vision and the spectrum. Science, vol. 101, pp. 653-658 Performance Descriptors 17- 123 peak near 380 nm and retinol with a peak near 330 nm. Only the average of these two values would approach 350 nm. The data supporting the equation clearly show a single peak at 350 nm (see Chapter 6). The material of the macula is fundamentally different, it exhibits a double peak in its absorption spectrum. The peaks occur at 440 and 487 nm and exhibit the same resonance factor, or Q, even though their amplitudes are slightly different. Early work by Wald146 claimed “the human macular pigment was shown to be a carotenoid, apparently lutein or leaf xanthophyll.” These early demonstrations appear to have shown a degree of correlation but not exclusivity relative to the immense biochemical family.

By combining the impact of the outer lens group and the field lens on foveal vision, it is seen that the light associated with the S-channel of human vision suffers an attenuation of between 4:1 and 9:1 before reaching the photoreceptors while the M- and L-channels encounter much less attenuation depending on age. This attenuation is encountered without any additional factor due to inadequate short wavelength irradiation due to an inappropriate light source.

The synaptic network between each photoreceptor cell and each bipolar cell of the luminance channel also impacts the contribution of each chromatic type of photoreceptor cell to the overall luminance signal. It can do this in two ways. It can sum the signals from different numbers of photoreceptor cells based on their chromatic performance and/or it can employ different size synapses in order to control the amplitude of the signal passed to the bipolar cell from each photoreceptor. The synaptic size determines the proportion of the pedicel voltage that appears at the emitter terminal of the Activa of each bipolar cell.

Little data could be mined from the literature on the impact of the first synaptic network on the formation of the signal in the luminance channel. Only global estimates could be made based on the many different spectral characteristics of the visual system, under both dark adapted and chromatically adapted conditions. These estimates generally converge around ratios between the S:M:L channels of 10:100:10. More specific ratios will be reviewed in the following sections.

There are also a variety of time variant contributions to the luminous efficiency function. These have occasionally influenced the experiments revolving around this function.

The high degree of negative interior feedback in the adaptation amplifiers is the primary variable in the luminous performance of the visual system. Since these amplifiers operate independently as a function of the input current to the base terminal of each Activa, but tend to a common gain due to the hydraulic properties of the IPM, they play a crucial role in the luminosity function. The role is particularly important in explaining the role of absorption by the outer lens group. Although the absorption by the outer lens group can be described by continuous functions, the radiation transmitted by the group is absorbed differentially by three different classes of narrowband absorbers. As a result, the signal level at the base terminal of each chromophore related Activa is different. However, the negative internal feedback of these amplifier tends to eliminate this variation. As a result, the role of the absorption characteristic of the lens group, and of the macula lutea, are minimized for signals within the high gain operating range of the adaptation amplifiers.

17.2.3.6.3 Light versus dark adaptation

Based on the above discussion, it is clear that the operating conditions of the visual system are quite different under dark and light adapted conditions. Under light adapted conditions, the gain of the adaptation amplifiers associated with the shorter wavelength channels will tend to be higher in order to compensate for the absorption by the physical optics of the eye. Because of this fact, the shorter wavelength channels will transition from the photopic to the mesotopic regime at higher illumination levels. While the S-channel photopic regime will normally be narrower due

146Wald, G. (1945) Op. Cit. 124 Processes in Biological Vision

to absorption by the macula lutea, both the S-channel and the M-channel will further narrow with age due to absorption by the outer lens group. Under conditions still within the photopic regime of all of the spectral channels, the first order spectral response of the visual system will remain independent of the absorption by the physical optical elements. The shape of the luminosity function will be defined by two components; the inherent spectral absorption of the chromophores of the signal sensing stage and the logarithmic summation process within the signal manipulation stage.

Under totally dark adapted conditions, the situation is different. All of the adaptation amplifiers are then operating at maximum gain. The adaptation amplifiers do not compensate for the variation in effective signal gain due to absorption by the outer lens group and the macula lutea. This is true as long as the product of probe illumination and time is small enough that the vascular supply is not impacted. The shape of the luminosity function will now be defined by the three components; the absorption characteristics of the lens group, the inherent spectral absorption of the chromophores of the signal sensing stage and the logarithmic summation process within the signal manipulation stage.

Under fully dark adapted conditions, the recorded luminosity function will be lower in the shorter wavelength region than it will be in the longer wavelength region. If the illumination source used in the probe is at a lower color temperature than 7053° K, the recorded reduction will be exaggerated but artificial.

17.2.3.6.4 Calculation of the neural component of the CIE luminous efficiency function

The literature does not present any calculation of the CIE luminous efficiency function based on a physical model of the visual system. The previous calculations have been based on a mathematical model based on the use of conceptual (and known to be imaginary) tristimulus values.

The summing circuit shown combining the voltages at the output nodes of the amplifiers (the pedicles of the photoreceptor cells) in the above signal flow schematic is critically important in determining the neural component of the luminosity functions of vision. The fundamental summing circuit is shown in Figure 17.2.3-26. This circuit is a simplification of the right hand part of (A) and the left hand part of (B) in [Figure 11.7.2-1]. The voltage at each of the pedicles of four chromatically distinct photoreceptors are shown on the left. The 1st generic synapse associated with the pedicle of each photoreceptor cell has been replaced by a an equivalent diode labeled Zsubscript.

Similarly, the input circuit of the Activa of the first bipolar cell has been replaced by a simple diode labeled Zeg. Zeg is not a simple diode strictly speaking because, it includes the effect of the base impedance of the bipolar cell. This base impedance provides a common path for the current in both the input and output circuit of the bipolar cell and therefore contributes to a negative feedback component that is being ignored here.

Considering the impedance, Zeg, to be a simple diode here, the circuit can be seen to consist of a “soft” analog “OR” circuit. It has the same topology as the “OR” circuit found in digital combining circuits. However, the signals being summed are analog. It is important to note that if the voltage, Veg , becomes greater than any of the individual pedicle voltages, the diode in that circuit becomes a very high impedance. Of greater importance, the diodes must be considered real diodes and not idealized switching diodes. This is because the voltages involved have similar magnitudes to the equivalent threshold voltage of each diode, ηVT. Thus, the switching is labeled soft. Note that each diode is labeled. This is to emphasize that these are not ideal diodes. They each exhibit a distinct impedance characterized by their reverse cutoff current. This parameter also describes their forward current capability at a given voltage, i.e., their effective forward impedance. Performance Descriptors 17- 125

Being a psychophysical function, the luminosity function is an end-to-end representation of all of the signal detection, signal processing, and signal perception occurring within the HVS. In some cases where the subject is asked to respond to a stimulus, the measured function may even include a component related to the motor system. The complete luminosity function for human vision, ignoring the contribution of the cognitive and motor circuits, is given in closed mathematical form by a complicated logarithmic equation multiplied by a complex absorption function due to the physical optical system. This function is developed in the Block Diagram of [Figure 17.1.4-1] showing the method of separation of the luminance channels and the chrominance channels leading to the perception of a scene. Neglecting the UV-channel entirely and the physical optics for the moment, the complete function describing the sensitivity of the signal manipulation stage is derived from the photodetection signals and the synapses and is given in symbolic form as: Figure 17.2.3-26 The summing circuit at the output terminals of four photoreceptor cells. It can be described as a “soft” analog “OR” circuit. See text for details.

R = lnC = ln xL2 + ln yM + ln zS Eq. 17.2.3-2

where S, M, & L are the integrated product of the scene irradiance, the absorption of the physical optics, and the spectral absorption characteristic of the chromophores, all as a function of wavelength; x, y, and z are functions of the state of adaptation due to the magnitude of the irradiance in their respective channels. They need not sum to a specific value.

When the scene irradiance is above the mesotopic level, the above equation is transformed into:

R = lnC = ln xL + ln yM + ln zS Eq. 17.2.3.-3 by the dynamic adjustment of the adaptation amplifier in the L photodetection channel. In both of these equations, the terms are shown in the order generally agreeing with the order in the above, linear equation. In these equations, R is the signal level at the output of the bipolar cells. In the absence of any spatial encoding, it also can represent the input to the parasol ganglion cells. It represents the symbolic form of the signal that can be measured electrophysiologically by sampling the axoplasm of the bipolar cell or the dendroplasm of a parasol type ganglion cell. C is the perceived illuminance after recovery of the signal transmitted over the signal projection sub-system to the cortex, assuming the simplest possible decoder. This signal is also measurable by electrophysiological techniques at the collector (axon) terminal of the decoder neuron within the cortex.

When the above equation is multiplied by the equation for the absorption of the physical optics (for a specific region of the retina) and the resulting equation is transformed into absolute units, C describes the complete Luminosity Function as a function of illumination for the HVS. The resulting Luminosity Function is correct for any 126 Processes in Biological Vision illumination level.

To evaluate the equation under fully dark adapted conditions, it is necessary to evaluate the individual voltage levels and gain parameters associated with the above figure. Under fully dark adapted conditions, the output of the photoreceptor cells are at their dark adapted set point voltage of -25 mV relative to the INM. To a first approximation, all of the offset voltages are the same. The precise voltage of the dendroplasm of the First Bipolar Cell is not known but is more negative than the above set point. This condition assures that the 1st generic synapses are all operational and they can be represented by the diodes shown on the left.

It is necessary to assign gain coefficients to the circuit elements forming the voltages at the photoreceptor pedicels and to the diodes forming the summing network. The circuit elements associated with the transducers and the photoreceptor cells determine the signal amplitude associated with the dark adapted set point for the photoreceptor cells. It is also necessary to assign values to the input irradiance and the state of adaptation of the individual photosensitive channels. By using a 7053 Kelvin temperature source, the impact of the source of radiation is eliminated. The design of the Outer Segment insures the absorption coefficient in each chromophoric channel is greater than 95%. Similarly, the stabilizing influence of the IPM as a common vascular supply network insures that all of the gain coefficients of the adaptation amplifiers are essentially equal under dark adapted conditions. This includes the linearization, with amplitude, of the signal emanating from the long wavelength chromophoric channel. At this point, the absorption function of the lens will be assumed to be a constant of 1.0.

The only remaining variables are the actual coefficients of the diodes associated with the summing network of the bipolar cell. Each of these diodes has a coefficient, an impedance, related to the active junction area of the synapses.

The coefficient of the diodes representing the individual chromophoric channels depend on two parameters that are poorly known. The first parameter is the actual junction area of the individual synapses between the photoreceptor cells and the first bipolar cell. The second is the number of photoreceptors of a given chromophoric type that are connected to a given bipolar cell. It is the total equivalent area of the synapses associated with a given chromophoric channel that determines the coefficient of the summing diode in that channel.

There is an additional complication here. Although, it is appropriate to count all of the photoreceptors activating a single bipolar cell, normal experimental procedure is to illuminate a specified area of the retina without regard to the actual field of individual bipolar cells (or parasol cells for that matter). This introduces an additional unknown into the calculations. However, an extensive analysis of the available data for both the dark adapted and “color adapted” human eye has provided a consistent, but simplified, set of these coefficients147. For the dark adapted condition, the relative gain coefficients of 100:1000:100 can be used initially for the L:M:S coefficients in computing the photopic luminosity function, including the contribution of the physical optics. The magnitude of these values are chosen because of a peculiarity of logarithmic summation when using natural or base 10 logarithms. The absolute value of each logarithmic term in the summation must remain positive for each spectral wavelength of interest. Therefore, if the relative spectral response of a specific chromophoric channel is to be used down to the 1% point, the coefficient of this term must exceed 100. To avoid any confusion with versions of the color equation in the literature, equation 17.2.3-2 will be re-written as:

R =LnC = [Ln(KL x L) + Ln(KM x M) + Ln(KS x S)]/Const. Eq. 17.2.3-4

147Fulton, J. (1985) The perception of luminance under various states of adaptation. Unpublished, available from the author. Performance Descriptors 17- 127

This equation still suffers from one defect. Note the result of one pedicle becoming considerably more positive than

the other two. Under this condition, the node labeled Veg becomes more positive than the other two pedicle nodes and the intervening diodes become reverse biased. Only the signal from the dominant pedicel is sensed by the bipolar cell. This situation is very unlikely in nature. However, it is encountered in the laboratory and must be recognized in the protocol for determining the dark adapted photopic luminosity function.

If the diodes in the summing circuit were perfect switching diodes, the terms R = LnC could be set equal to the larger of the right hand terms. However, the resulting equation would be fatally flawed and would not represent the total dark adapted photopic luminosity function or the Purkinje and Bezold-Brucke Effects properly. The region where two or more of the terms are nearly equal is critical to the computation. The more appropriate interpretation is to discard a term on the right when it becomes less than 10% of the dominant term. Because of the logarithmic relationship, such a term becomes negligible in the summation, and subsequent exponentiation to obtain C. In the preparation of the figures in this work, a more complex approach has been used. The computer program, Mathcad Plus, version 6.0, has been used to introduce an “exclusive or” function in the equations. This eliminates the possibility of a negative value for any logarithm and essentially implements the diode relationship into the algebra.

The theoretical formulation of the above equation 17.2.3-3 is very similar to that derived empirically by Land in his Retinex Theory of vision, including the limitation to positive logarithms in the summation. This is not unexpected based on Land’s background in photography where intensity is normally measured on a logarithmic scale. Most people found it difficult to follow Land’s description of his methodology. A readable description of the methodology appears in Livingstone & Hubel148.

Figure 17.2.3-27 presents the theoretical photopic luminosity function of the Standard Human Eye based on the above scenario. Note the five individual lobes in the theoretical luminous efficiency function prior to any smoothing. Three of these are directly related to the absorption spectrums of the chromophores but two are the result of mathematical manipulation within the retina. The spectra of the three chromophores of human vision, as recorded under operational conditions, are shown at the bottom of the figure. They are all plotted to the same nominal maximum absorption. It is important to note that (contrary to remarks in the psychophysical literature related to the so-called "fundamental cone spectra") there is little overlap between the individual spectra when they are all plotted normalized to a common peak relative absorption. The horizontal dash-dot line represents the half amplitude point level. The degree of overlap is a critical parameter in the overall photopic luminosity function due to the logarithmic addition employed in the signal manipulation stage of the visual system. Since the actual densities of the different spectral types of photoreceptors within the retina are unknown, and the relative sizes of the diodes formed by the synapses are also unknown, only the relative magnitude coefficients derived above (which include the contribution of the physical optics) are available. When the relative contributions of the various chromatic channels are plotted, the overlap between the M- and L-channels and the signal processing within the signal manipulation stage results in an apparent peak in the theoretical luminosity function in the region of 579-580 nm. The presence of the physical optics in the signal channel has negligible effect on the wavelength of this peak. This peak is generally associated with Purkinje (See Section 17.2.3.5.1). The Purkinje Effect is generally associated with the transition between the mesotopic and photopic illumination regime. A similar peak is seen in the region described by the overlap of th S- and M-channels near 487 nm. This peak is one of two generally associated with the Bezold-Brucke Effect. The other peak in this effect is that associated with the above Purkinje Effect under different circumstances. The Bezold- Brucke Effect is generally associated with the hypertopic illumination regime or under abnormal mesotopic conditions. The wavelengths of these peaks are a function of the state of adaptation of the individual eye as discussed elsewhere in this work.

148Livingstone, M. & Hubel, D. (1984) Anatomy and physiology of a color system in the primate visual cortex. J. Neurosci. vol. 4, no. 1, pp. 309-356, pg. 349 128 Processes in Biological Vision

In this figure, the gain ratios are ks:km:k l::60:1000:60. The operating temperature was 310°K. The spectral parameters are those of the Standard Human Eye provided in this work. Note how narrow the notches are at 495 and 562 nm and how abrupt the corners are at 470 and 622 nm in the absorption spectrum for this set of gain parameters. The heights of the mathematically derived peaks are quite sensitive to the gain ratios and to the temperature.

The above luminosity function is calculated without regard to any source of exciting radiation. In practice, it can be reproduced from laboratory data obtained using a source of uniform photon flux per unit spectral wavelength interval and a spectrum selection filter no wider than 5 nm. Such a source has a black body color temperature of 7053 Kelvin. The theoretical curve does depend on a set of amplitude coefficients in the equation for the R channel signal amplitude. These coefficients were chosen to include the affect of absorption by the physical optics of the eye. This theoretical function can be compared with three different empirical functions, the C.I.E version based on the averaging of data aquired with 30 nm smoothing in the 1920's, the data acquired by Wald with 10-15 nm smoothing in the 1950's, and more recent data taken with 5 nm smoothing. The agreement between the theory and the data base improves as time progresses. It appears that the data at 5 nm displays all of the features predicted by the theoretical photopic luminosity function.

Because of the logarithmic summation, the theoretical function exhibits five relative maximums, that are documented in the literature based on 5 nm spectrography, and very specific slopes to the skirts of the total waveform.

If this theoretical function is smoothed by to an equivalent 25-30 nm. wide spectral filter width, the resulting curve corresponds to the C.I.E. photopic luminosity function standard. It should be noted that both of these curves exhibits a peak that is not related to the actual chromophores of vision. This peak (and others discussed below) is an artifact of the logarithmic addition employed in the signal processing circuits of the retina. In the absence of absorption due to the physical optics, the peak occurs near 537 nm. in the theoretical equation. The overall theoretical luminosity function peaks at a slightly longer wavelength for equal flux irradiation after introducing the absorption of the physical optics. It is prescribed as occurring at 555 nm. in the C.I.E. Standard. This value can be obtained after additional smoothing of the theoretical function to correspond to the bandwidth of the spectrometers used Figure 17.2.3-27 The theoretical photopic luminosity in the 1920's and earlier. function of the complete human eye. The dotted line represents the fully dark adapted relative luminosity function of the eye in response to a photopic level equal Comparing the results of this work with the literature photon flux per unit wavelength probe. The dashed line can be done under either of two conditions. The results represents the above function smoothed to correspond to of most research activity associated with the sensitivity the use of a finite spectral bandwidth probe typical of the of the visual system is presented on graphs using a 1950's. Further smoothing can be employed to achieve the equivalent of the spectral bandwidth common in the logarithmic vertical scale in order to present a greater 1920's. The result is a very good emulation of the C.I.E. dynamic range. However, the C.I.E. Standard (1924) Standard. The individual absorption spectra at the Luminous Efficiency function (1924) is frequently bottom of the figure are those of the S-, M- & L-channels presented using linear coordinates. In either case, the in human at 310° K. vertical scale is a measure of the sensitivity of the visual system to a stimulus at a particular wavelength. The linear form of the C.I.E. Standard, figure 1(4.3.2) in Performance Descriptors 17- 129

Wyszecki & Stiles, presents an impression that the photopic and scotopic spectrums are distinctly separate and that each of these portions of the visual spectrum is functionally much narrower than it actually is. It also suppresses the inflection point associated with the short wavelength portion of the photopic Standard. The similar inflection point associated with the long wavelength portion of the visual spectrum is difficult to see even in the logarithmic form of the 1924 Standard. This inflection point is omitted in figure 1(5.7.2) of Wyszecki & Stiles although it is clearly present in the tabular data in their Appendix and when re-plotted by computer.

It will be most useful in this work to utilize sensitivity graphs with a logarithmic vertical scale. When plotted in this way, the C.I.E. Standard correlates directly with the signal in the R-channel of the visual system. In its linear form, the CIE Standard correlates with the perceived signal in the cortex, but only under dark adapted conditions and small signal conditions. This signal was defined as C to conform with earlier notation concerning the archaic color equation. In that equation, C = rR+ gG + bB as discussed above. This formulation does not represent the measured data under general conditions. In this work C equals the antilog of R and R is the logarithmic sum of S-, M- & L- channel signals after adaptation and logarithmic conversion. For a limited dynamic range and conceptual discussions, the difference between these two definitions of C are small. However, the difference is large in the research arena and under large signal conditions. The expression on the right varies with both wavelength and the photon flux intensity, F, applied to the eye. To avoid confusion with other uses of the letter C, the term C will be replaced with the broader expression X(8,F) in the remainder of this work. It is worth repeating that “the sum of the logarithms is not equal to the logarithm of the sum.” Information about the visual system is lost when this inequality is ignored.

There is an additional challenge in the fact that the theoretical sensitivity of the visual system contains the illumination level in the long wavelength term. This makes the entire luminous efficiency function a function of the illumination level. It is only within the psychophysical photopic regime, where the adaptation amplifiers are controlling the signal level applied to the signal manipulation stage, that the luminous efficiency function is independent of the illumination level. This fact has not generally been acknowledged in the literature but has contributed to the difficulties of standardization between laboratories. It is also useful to note that the luminous efficiency function has nothing to do with the quantum efficiency of the chromophores while the eye is operating within the psychophysical photopic regime.

To avoid this variability introduced by the adaptation amplifiers, the so-called photopic luminous efficiency function is nearly always determined under dark adaptation conditions. Under these conditions, all of the adaptation amplifiers are operating at their maximum gain. The visual system is then probed by a short duration, narrow spectral band, illumination source intense enough to elicit a perceived response from all of the spectral channels of the eye. The diameter of the test probe was standardized at 2°. It was normally centered on the fixation point of the eye. While standardized, the sensitivity recorded under these conditions is only indicative of the performance of the eye near the lower limit of the photopic regime in response to radiation of a specified, or unspecified but controlling, color temperature. If the source is deficient at a specific wavelength, the recorded response will reflect this deficiency. The sources used in the 1920's were grossly deficient in the short wavelength spectrum. This is the fundamental fact underlying the proposal, of Judd and others coalescing up into 1950's, to update the C.I.E. 1924 Standard. The CIE chose not to act on these recommendations. To alleviate such suggested changes, the C. I. E. defined a Standard Observer in 1931 whose visual system actually performed according to the above Standard Luminous Efficiency Function. This Observer is clearly not a normal human, or the average of a group of normal humans.

In 1951, the C. I. E. introduced the Standard Scotopic Luminous Efficiency Function along with a Standard Scotopic Observer. The function was defined under the conditions defined above except the intensity of the probe had to be maintained at a level low enough to avoid exciting the L-channel photoreceptors significantly. Such a signal could not normally be perceived using a 2° diameter test field. Therefore, the field was increased to 10° diameter in order to raise the signal to noise level in the visual system and insure perception. The result was a function that described 130 Processes in Biological Vision

a fully dark adapted visual system responding to radiation of a specified, or unspecified but controlling, color temperature. This function is more in agreement with normal human vision. Although, the C. I. E. also defined a Standard Scotopic Observer, it has been much less controversial than its photopic partner.

The critical nature of the color temperature of the illumination source is seldom discussed in the literature.

17.2.3.6.5 Extended remarks on the familiar C.I.E. Luminosity Standards

[xxx condense this section ] In developing the C.I.E. Standards related to the Luminosity function (1924 & 1951for the 2° field, also 1964 for the 10° field), the community has been left with an unfortunate legacy. Following exploration of the function in a variety of subjects by different laboratories, a consensus was arrived at and the standards promulgated. In the process, the standards defined the functions with great precision as a function of spectral wavelength. This precision is hollow. The original experiments were performed with spectrometric equipment with a bandwidth of nominally 30 nm. This bandwidth integrated all of their measurements over this interval, essentially averaging out any features occurring within this interval. The resulting smoothed values from individuals were then averaged over a group of subjects. The resulting average of the smoothed responses were then accepted as the new standard. There was a significant difference in data from different laboratories, particularly in the blue region of the spectrum. That difference, as great as 9:1 at some wavelengths149, was discarded and suppressed in preparation of the final standard. Some of the data was collected with a significantly higher color temperature light source that gave more weight to the data in the blue region of the spectrum.

Following selection of the standard spectrum, tabular values were calculated by interpolation of the original data points. Whereas most of the original data was collected in steps of 10 nm. or coarser, and using spectrometers with bandwidths of 30 nm. or greater, the tabular values were presented at an interval of 1.0 nm. These values are presented in Judd150 in an official report. This report does not include his later personal comments suggesting the inadequacy of the Standard. The report does include a conceptual explanation of why the color temperature of the source and the state of adaptation of the observer is unimportant. It includes the statement, “Colorimetry is based on these properties of the normal visual mechanism which make it a satisfactory null instrument.” Unfortunately, for purposes of research, this is a naive conclusion.

Of greater importance is the accuracy of the published values for the CIE Luminosity Function. Wright has some important remarks on this subject in 1969151.

“The CIE Colorimetry Committee recently in their wisdom have been looking at the old 1931 observer and have been smoothing the data to obtain more consistent calculations with computers. This has also involved some extrapolation and, in smoothing, they have added some additional decimal places. When I look at the revised table of the x (bar), y(bar), z(bar) functions, I am rather surprised to say the least. You see, I know how inaccurate the actual measurements really were. (Laughter from audience) Guild did not take any observations below 400 nm and neither did I, and neither did Gibson and Tyndall on the V(8) curve, and yet at a wavelength of 362 nm, for example, we find a value y(bar) of 0.000004929604! This, in spite of the fact that at 400 nm the

149Wald, G. (1945) Human vision and the spectrum. Science, vol. 101, no. 2635, pp. 653-658 150Judd, D. (1931) The 1931 I.C.I. Standard Observer and coordinate system of colorimetry, J. Opt. Soc. Am. vol. 23, pp. 359-374 151Wright, W. (1969) The Origins of the 1931 CIE System Color Group Journal (G. Britain) As reproduced in Boynton, R. (1979) Color Vision NY: Holt, Rinehart Appendix, Part II Performance Descriptors 17- 131

value of y(bar) may be in error by a factor of 10 (Laughter).”

Although not addressed significantly in the early literature, there has also been a problem related to the spectrum of the light used in vision experiments. The Planck Radiation Formula was only promulgated within the theoretical physics community in 1900. It appears that most of the experimenters working in vision up through at least the 1930's lacked an adequate understanding of the importance of the spectral distribution of light in their experiments. They were primarily concerned with the total integrated energy, which might be called the photopic energy, entering the visual system and typically used lamps with a color temperature in the 2400-2800°K range. The specific problem relates to the relationship between the amount of energy radiated by a source per unit spectral bandwidth versus the number of photons, the photon flux, radiated by that same source per unit bandwidth. As late as 1963, the Committee on Colorimetry of the Optical Society of America (erroneously) defined an equal energy spectral distribution as one characterized by equal flux per unit wavelength interval. Wyszecki & Stiles gave a correct interpretation of this relationship on page 4 of their 1982 work. The term “equal-energy” source began appearing in the vision literature in the 1950's. The term was frequently shown as above in quotation marks and was seldom if ever defined rigorously. In reading the articles of that period, the typical experimenter was using a nearly fixed spectral bandwidth spectrometer to filter the luminance of a commercial tungsten lamp. The goal was to control the total integrated energy entering the eye in accordance with Stefan’s Law, rather than concern themselves with the uniformity of the flux entering the eye in accordance with the more detailed Planck Distribution Law. This lack of definition leads to considerable difficulty in correlating the early data to the real world and any theory.

As a result, the current C.I.E. Standards represent the average values obtained from smoothed data collected with inadequate light sources and interpolated to a precision exceeding that of the original data by ten to one.

The problem is actually worse if Wyszecki & Stiles are correct on page 395. Quoting, “The values adopted in 1924 were those suggested by Gibson and Tyndall (1923) who composed a smooth and symmetrical V(λ)-curve from the data cited above. The final result was not an average of the experimental data, but a weighted assembly of the different sets of data. From 400 to 490 nm, the V(λ)-curve represents roughly the results of Hartman (1918); from 490 to 540 nm, those of Coblentz and Emerson (1918); from 540 to 650 nm, those of Gibson and Tyndall; and above 650 nm, those of Coblentz and Emerson (1918).”

It is also noteworthy that there have been fundamental revisions (greater than 7%) in the relationship between the Candela and the Watt during the period 1920-1970.

More recently (1979), the appropriate national standards laboratories have chosen to re-define the standard units of luminous intensity (the candela)and luminous flux (the lumen) in terms of monochromatic light instead of a blackbody source. They chose the frequency of the monochromatic source as 540x1012 Hz. This frequency corresponds to a wavelength in dry air of 555.016 nm. This wavelength corresponds to the nominal peak in the C.I.E (1924) Standard Luminous efficiency Function.

Wyszecki & Stiles present three figures, their 1(5.7.2) through 3(5.7.2), that highlight the difficulties encountered later. Figure 2(5.7.2) illustrates the range associated with the data from 52 subjects accepted as the Standard. Figure 1(5.7.2) shows the correction recommended by Judd in 1951 (that was not adopted). The caption of figure 3(5.7.2) requires careful reading. The Judd recommendations for a 2° field are compared to the newer alternate C.I.E (1964) Standard for a 10° field. Judd’s recommendations raise the short wavelength region of the 1924 Standard but can be interpreted erroneously as lowering the alternate 1964 Standard. The situation becomes consideerably more complex if one addresses the UV sensitivity of the human retina presented by Tan and by Griswold & Stark. By combining their data (Figure 17.2.3-1) with the more current data on the absorption of the physiological optics of the human (Figure 17.2.3-4), a much more realistic estimate of the true spectral characteristic of human vision. 132 Processes in Biological Vision

152 Stockman, et. al . have discussed this issue in detail and adopted what they call the CIEJudd 2° color-matching functions153. The intent appears to be to redefine the CIE Luminosity Standards even though Judd had been unsuccessful in such an endeavor some 40 years earlier. Although they collected sensitivity data based on 7-11 nm spectral bandwidths, they reported data with error bars of ±1-2 nm precision.

Recently, C.I.E. committee TC 1-07 has proposed a C.I.E. Standard-Deviate Observer to represent the individual variations in luminous efficiency function among “color-normal” observers154. The decomposition procedure used resulted in four sets of deviate functions.

Modern statistics theory would suggest there are two additional problems with both the older and more recent luminous efficiency data155. First, the theory in this work suggests there is significant detail in the spectral sensitivity of the human eye at intervals of less than 5 nm. Most of the data in the literature has been collected at an interval of multiples of 10 nm. Generally the spectral bandwidths used have been greater than 15 nm. The early data was collected with bandwidths that appear to be about 30 nm. Considering the spectral bandwidth equal to the statistical binwidth, a binwidth greater than the interval suggests considerable loss in information. An interval greater than the minimum detail spacing also suggests considerable loss in information. In addition, it suggests that the data points cannot be connected by straight lines, or even gently curving lines. The graphic presentation should be limited to range bars, and confidence bars if available, at the test intervals.

Second, the various features of the theoretical luminous efficiency function are not well correlated with a scale given by multiples of 10 nm. As Hardle says so clearly:

“The choice of the origin, xo, of the bin mesh is arbitrary; the consequences for the interpretation of the histogram are drastic.”

His figures 1.14 and 1.15 dramatically illustrate this problem. It would be useful to collect new data in support of a new luminous efficiency function at a bin mesh of less than 5 nm. and a spectral width of less than 5 nm. If a bin mesh of 5 nm is used, it might even be useful to collect some of the data at the same bin mesh but with an offset of 2.5 nm from the previous set to uncover any significant detail. The expected improvement in the resulting data is illustrated in figure 1.16 of Hardle.

152Stockman, A. MacLeod, D. & Johnson, N. (1993) Spectral sensitivities of the human cones. J. Opt. Soc. Am. A, vol. 10, no. 12, pp. 2491-2521 153Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley, pg. 331-410 154Special metamerism index: change in observer. CIE Publ. no. 80. Vienna: Central Bureau of the CIE 155Hardle, W. (1991) Smoothing techniques with implementation in S. NY: Springer-Verlag Performance Descriptors 17- 133

The following discussion will address two additional aspects of the problem, how the theoretical luminosity functions can be degraded in order to emulate the current Standards or how the current standards should be recast for purposes of research to better represent the real world of vision. This problem is complicated by the many nonlinearities in the system. An ideal situation would allow the original data from a large number of investigators to be reprocessed in order to recover the original spectral absorption function in spite of the above problems with the database. This appears to be impossible. The interval in the database is too large relative to the expected underlying function. An alternate approach is to attempt to degrade the theoretical function marginally until the resulting function passes within the confidence interval associated with all of the data points in the above database. Unfortunately, it appears the systemic errors among the different experiments occupy a significant portion of the individual data ranges. The only option left is to degrade the theoretical function until it passes within the range bars at each data interval. Because of the size of these range bars (See Wyszecki & Stiles, pages 402 and 405), this is not a difficult task. When degrading a function, it is very important that the main features of the original function be retained to the greatest extent possible. Hardle156 explores this problem in some detail. Of the half dozen kernels that could be used to emulate the shape of the spectral passband of the filters used in the 1920's, the Gaussian, the uniform (rectangular) and the triangle are not likely candidates. However, most researchers will be tempted to use the Gaussian kernel. Before doing so, they should review Hardle & Schimek157. The extreme sensitivity of the smoothing parameter, h, for a Gaussian kernel is demonstrated in figures 2.10 & 2.11 of Hardle. Three digit accuracy and a nominal value near 0.500 is required. If a relatively large amount of degradation is used (a deviation of only 0.007 from 0.500), the function can be made to pass through the median value of nearly every range bar of the above data. The resulting function would then correspond to the weighted mean in the 1978 CIE data on page 402 and/or 405, or the Standard Observer of the 1924 CIE Standard. However, this function and the weighted mean have little relevance to the intrinsic luminous efficiency function of human vision.

17.2.3.6.6 Obtaining the familiar C.I.E. Luminosity Function by smoothing T(8,F)

As an example of the above discussion, Figure 17.2.3-28 shows the results of smoothing a specific theoretical luminance threshold sensitivity function (reflecting the Bezold-Brucke Effect, see Section 17.2.3.5) until it resembles the C.I.E. (1924) Luminosity Function for the Standard Observor. The figure shows two degrees of smoothing with common smoothing functions provided in the MathCad package. The function labeled ui + 3 is named ksmooth and uses a Gaussian kernel to compute the local weighted average of the input waveform. The

function labeled yi + 2 is named supsmooth and uses a more complicated kernal based on a symmetric k-nearest neighbor linear least square fitting procedure to compute the local weighted average of the input waveform. In both cases, the kernal represents the spectral bandwidth of the spectral filters used to collect the empirical data. Both examples will lead to a smoothed graph with a nominal peak near 580 nm even though the underlying function exhibits no peak associated with this wavelength.

156Hardle, W. (1991) Smoothing techniques with implementation in S. NY: Springer-Verlag, Chap. 2. 157Hardle, W. & Schimek, M. ed. (1994) Statistical theory and computational aspects of smoothing. NY: Physica-Verlag, a Springer-Verlag imprint. 134 Processes in Biological Vision

17.2.3.7 Comparison with the photopic standards literature

The theoretical visibility function is seen to include a variety of variables that suggest there is no one standard function that fits all variants of the HVS. The most significant variables appear to be those related to age and the source of illumination used in testing. The absorption of the outer lens group Figure 17.2.3-28 Comparing a theoretical human spectral sensitivity function and its smoothed counterpart (omitting appears to increase at 0.55% per year across the visual any ultraviolet contribution) to illustrate how a spectrum spectrum compared to the reference year of age 21. similar to the C.I.E. Luminosity Function is obtained from Due to the nature of Rayleigh scattering, this a much more complex data set. Note the convergence absorption is of primary importance with respect to toward a peak near 580 nm (the Purkinje Peak) as smoothing continues and the complete obliteration of the the short wavelength portion of the visual spectrum. contributions related to the short and long wavelength Within the photopic illumination range, the adaptation absorption spectrums. amplifiers of the S-channel photoreceptors can accommodate almost completely for this shortfall. However, at lower illumination levels, complete compensation is not available. At levels above the photopic range, the saturation inherent in the adaptation amplifiers lead to significant narrow peaks in the overall absorption spectrum that are not represented in the C.I.E. Standards at all. Performance Descriptors 17- 135

17.2.3.7.1 State of the theoretical description

The theoretical description developed in this work is an analytical expression that can be evaluated with any desired degree of granularity. The basic form of the expression applies to the retina and neural system without the physical optics of the eye or the illumination source. Expressions for the absorption parameters of the physical optics are available and can be combined with the basic expression. The visual system is fundamentally a photon detector and not an energy detector. If a non-equal-photon-flux per unit wavelength source is used in empirical measurements, a correction factor for this source can also be calculated.

The photopic luminosity function is basically a description of the signal to threshold ratio relationship of the eye in perceptual space under a specific set of conditions. The conditions are that the threshold level is determined by the dynamic range of the signaling channel, and not quantum noise or a cortical threshold, and that the adaptation amplifiers in all of the three spectral channels are maintaining a constant average signal level at the pedicels of the photoreceptors. Under these conditions, the gain coefficients maintain a fixed relationship with each other. This relationship is typically kS:kM:kL::50:1000:30 when including the absorption of the lens group. Since the adaptation amplifiers have a dynamic range of about 10,000:1, the achievable photopic range is approximately 10,000:1 in intensity.

All of the parameters in the analytic expression of the human luminosity function are readily measurable. Those related to the chromophor controlled absorption spectra have been determined, based on data in the literature, to better than ±2 nm. The analytical expression makes it clear that the Uni-variance Principle is only applicable to the P/D process within the individual S- and M- absorption channels of vision. It does not apply as a single Principle applicable to the overall visual process. It does not apply to the individual or groups of complete photoreceptor cells.

The above corrections can be calculated individually and then combined, or the total effective signal gain of each photodetection channel can be determined by curve fitting to the best available empirical data. This latter approach was used in Section 17.2.3.2.1 using the empirical data of Wald. It appears that this data was obtained with a spectrometer bandwidth of 10-15 nm, considerably better than the data of Gibson & Tyndall that was used in the C.I.E. Standard. Many other data sets are available, some using spectrometer bandwidths slightly better than Wald’s, based on a variety of test methodologies. Wyszecki & Stiles provide comparisons between and references to these studies through 1982. The data from some of these studies exhibit the fine detail predicted by this work, particularly Sperling & Lewis (1959).

From Section 17.2.3.2.1, the relative gain coefficients for the human eye, operating within the photopic regime and for the illumination conditions used by Wald, are for the S:M:L channels respectively 100:1000:100. More than one place accuracy is difficult to justify without repeating the experiment, and those mentioned above, under more stringent conditions of control. See the results of similar NTSC studies in Section 17.3.3.1.4.

17.2.3.7.2 Comparison of the theory and empirical data

Because of the poor state of the Standards for the human photopic luminosity function, some assumptions must be made concerning any comparison between the theoretical photopic luminosity function of this work and the empirical data base. Comparing the theoretical function and the current standard is awkward. The theoretical function does not exhibit any dependence on the illumination environment. The measurement of an equivalent function depends on the use of an equal photon flux per unit bandwidth source, nominally at 7053° Kelvin. The current standard has (at least in the recent literature) assumed an equal energy per unit wavelength illumination source. 136 Processes in Biological Vision

Several comparisons are illustrated in Figure 17.2.3-29. The unfiltered theoretical luminosity function is shown by the short dashed line. This function is the result of logarithmically summing the individual absorption functions, shown at the bottom of the graph all normalized to the same maximum value and a set of spectrally specific absorption coefficients, kS:kM:kL. The curve is computed at a spacing of 0.5 nm with straight line segments connecting the data points and spectral coefficients in the ratio of 50:1000:30.

Note the distinct separation of the three chromophores as plotted at 10 nm spectral interval. The curves were plotted for the half amplitude wavelengths documented in the Standardized Human Eye and a body temperature of 310 Kelvin (37 Celsius). The individual spectral curves also illustrate the variable Q (average, or peak wavelength divided by width between half amplitude values) associated with these spectra using the best available half amplitude values. Note also the appearance in the theoretical luminosity function of two additional features due to the logarithmic summation. The higher peak near 590 nm is due to the slightly greater overlap between the M- and L-channel chromophores. The lower peak near 490 nm is due to the overlap between the S- and M-channel chromophores.

Smoothing of the theoretical photopic luminosity function has been performed using a variety of mathematical filters found in Mathcad Plus, ver. 6.0. Using this program and the filter “ksmooth,” the theoretical photopic luminosity function can be fit with precision to the C.I.E. (1924) Standard and to Judd’s recommended (1951) modification. This requires that the same assumptions be used with regard to the source temperature used to collect the data. The long dashed line represents the above theoretical function smoothed using a Gaussian kernel with a parameter of b=0.06 (~30 nm). The Gaussian function appears to be a reasonable approximation of the spectral filter characteristic implicitly included in the C.I.E. (1924) Luminosity Function. Note how all of the distinct peaks and plateaus of the original function are lost at this degree of smoothing. The two theoretical curves have been adjusted in amplitude so that the smoothed curve has a peak value of 1.0.

The C.I.E. (1924) Luminous efficiency function was plotted as a solid line after conversion to an equal flux per unit wavelength condition. This calculation was based on the assumption that the original C.I.E. function was obtained under true equal-energy conditions. The dash-dot line is the above luminous efficiency function modified as recommended by Judd. Both of these functions are for a 2° diameter illumination field in object space. This size was determined to be the smallest field giving consistent results in the laboratory.

Note how the smoothed theoretical function falls between the C.I.E. and Judd functions in the short wavelength region when they are all plotted with the same peak amplitude. It is clear that the smoothing parameter, b, need be adjusted only slightly to cause the smoothed function to emulate either the C.I.E. or Judd function.

After smoothing of the theoretical function to approximate the spectral bandwidth of the instrumentation used to prepare the standard, there is good agreement between the form of the graphs but there is a systematic error. On the short wavelength side of the graph, both the C.I.E. and Judd functions tend to be lower than the theoretical functions. On the long wavelength side of the graph, both the C.I.E. and Judd functions are higher than the two theoretical functions by a factor that grows with wavelength. The presence of this difference questions the recent association of the term equal-energy with the C.I.E. (1924) Luminosity Function. It would suggest that the original data obtained to define the function were not obtained under equal-energy conditions but with light sources that were of distinctly lower black body temperature, probably near 2400 Kelvin on average. There is negligible difference between the original C.I.E. function and the smoothed theoretical function in the long wavelength region if the 2400 Kelvin assumption is used. However, this assumption would require replotting of the short wavelength portion of this function. The resulting difference between the C.I.E. and the smoothed theoretical function can be made quite small by selecting the parameter, b. If the proposed Judd modifications are included, an even better fit can be obtained in the short wavelength region. If the data of Sperling & Lewis is accepted, the deviation in the short wavelength region is negligible and the predicted inflection point in the long wavelength region is seen in the data. By replotting Performance Descriptors 17- 137

the C.I.E. Standard, the Judd modification, and the Sperling & Lewis data for the equal flux condition based on a reasonable estimate of the source temperatures used to collect the data, it becomes difficult to see the difference between the smoothed theoretical function and these data.

The peak of the smoothed theoretical and the C.I.E. Standard luminosity functions occurs at a wavelength independent of that of any of the chromophores present. The standard graph of the C.I.E (1924) function exhibits a peak near 555 nm. If the data for this graph had been collected under truly equal energy conditions, the peak would have been nearer 551 nm. Under equal flux conditions and a narrower spectral passband spectrometer, the peak would have depended on the state of adaptation. It would have approached the peak of the M-channel chromophore, 532 nm, in the absence of the peak at 590 nm (See the following Section on the Purkinje Effect).

In 1964, the C.I.E. issued another Photopic Luminosity Function, or Luminous Efficiency Function, based on a 10° field stimulus in object space, V10(λ). It is interesting to note that this function has been smoothed to the point that it does not show any inflection points, even those of Judd. This function has little theoretical significance.

In summary, the luminosity standards of the C.I.E. are now 50 to 75 years old. The theoretical luminosity function shows a number of inflection points not found in the C.I.E. Standard. It is clear that the C.I.E. (1924) Standard was promulgated before the vision community understood the impact of quantum physics on the performance of the human eye. The Standard includes the implicit assumption that the eye is responding to an incandescent light source with a color temperature near 2400 Kelvin.

By smoothing the theoretical function, and incorporating the absorption of the physical optics and the color temperature of the source explicitly, a very good agreement with the C.I.E. Standard can be obtained.

The methods of empirically determining the photopic luminosity function also play an important role. The test results may be significantly skewed by a light source with a true blackbody temperature of less than 7053 K. It is also clear from the graph that the logarithmic summation process leading to the luminosity function of the human eye is not compatible with the so-called Univariance Principle. 138 Processes in Biological Vision

Figure 17.2.3-29 Comparison of the theoretical and empirical Photopic Luminosity Functions. The individual human absorption spectra (for the Rhodonines) have been shown on a relative basis at the bottom of the figure for reference. The horizontal dash-dot line represents the half amplitude level. The theoretical function (short dashed line) has been calculated using the absorption coefficients, kS:kM:kL::50:1000:30. The theoretical function has been mathematically smoothed (long dashed line)using a 50 nm. Gaussian filter. The difference between the C.I.E. Standard (solid line) and the modification of Judd (dashed-dot line) is highlighted by these comparisons.

17.2.4 Resolving the difference between spectra of the chromophores and other spectra

17.2.4.1 Comparing the long pulse versus flicker photometry

King-Smith & Carden have provided valuable data comparing the spectra recorded psychophysically under both pulse photometry and flicker photometry158. They suffered from the lack of a theoretical model. Hence many of their

158King-Smith, P. & Carden, D. (1976) Luminance and opponent-color contributions to visual detection and adaptation and to temporal and spatial integration J Opt Soc Am vol 66(7), pp 709-717 Performance Descriptors 17- 139

propositions are not supported by this work. They did rely upon a zone model to generate a luminance signal and two chrominance channels. They did note there was no accepted understanding of how the threshold detection function was accomplished in the CNS, whether it was based on luminance or chrominance channel information.

They did present a figure 2 describing the detection thresholds and color determination thresholds being essentially the same as a function of wavelength for 200 ms test flashes. Both functions showed a 3-peaked response. They described their criteria for determining the color of the test flashes and how they arrived at the conclusion the results were valid.. Their figure 4 showed that the peak at 530 nm moved to 555 nm and the peak at 440 nm (due to the S–channel photoreceptors) is eliminated for either brief or small flashes. The 555 nm peak is obviously a combination of the M– and L–channel responses.

Their figure 5 is particularly important and is reproduced as Figure 17.2.4-1. This figure is important because it was based on only one individual being evaluated under both conditions in only one laboratory. Only a few questions can arise regarding the differences in the protocols used. The data was collected using nominally 10 nm wide (at half transmission) filters. However, data was only collected at roughly 20 nm intervals so some information may have been lost. The important point is that there is a significant loss in sensitivity in the blue region, and quite possibly in the red region (see their figure 6), when using flicker photometry at 25 Hertz compared to the single pulse technique. King-Smith & Carden associate this loss with a difference in integration time for the blue and red photoreceptors. This work describes a different situation. It shows all types of photoreceptors exhibit the same temporal characteristics (except for the 2–exciton process associated with the L-channel photoreceptors). However, the subsequent signal propagation techniques used for the luminance and the chrominance channels within stage 3 of vision are totally different. These techniques provide a longer time constant circuit for the recovery of an adequate copy of the signal originating at the S–channel and the L–channel photoreceptors relative to the M–channel photoreceptors.

Figure 17.2.4-1 Comparing spectral sensitivity based on 1o 10 ms test flashes and flicker photometry. The 10 ms flashes (open squares) were centered on a four degree diameter, 3200 Kelvin, 1000 td, white background. The thick line (labeled L) determined from thresholds for detecting 25 Hz flicker on a similar 1000 td white background. The thin line determined from flicker photometry on a dark background. Both curves shifted vertically to match the squares at about 555 nm. From King-Smith & Carden, 1976. 140 Processes in Biological Vision

Their figure 6 is more complicated. However, it does clearly show the presence of three spectral peaks in the pulse photometry spectra but only a single-peaked broad response based on their deduced spectrum from flicker photometry data. This representation would support the assumption that both the blue and red channel responses were suppressed in flicker photometry spectra. their figure 2 also shows three spectral peaks obtained based on a one degree field stimulus of longer (200 ms) pulse duration.

In 1979, Kranda & King-Smith provided another paper that included a graph of the suppression of the S– and L– channel sensitivities under flicker at 25 Hz159. They were using 16 nm FWHA filters at 10 nm spacings. As a result, their data integrated out the finer variation in the overall spectra compared to the work of Babucke using narrower filters. Their figure 13 shows a three-peak overall spectrum with peaks at ~440, ~530 & ~610 nm. The various solid and dashed lines appear to have been extended arbitrarily without any data points in the segments below the overall response. While not presenting a graphical model of their work, they were clear that they “assumed a multiple channel system, responding linearly to threshold stimuli, up to the visual stage where the responses to different colours are combined.” This appears to conform to the small signal model of signaling. They also assumed the XYZ chromaticity diagram was linear in X and Y and draw straight loci representing various color mixtures. They did a lot of curve fitting and determined the luminance function was the sum of the R and G fundamentals of Vos & Walraven.

The conclusion proposed here, confirmed largely by the work of King-Smith’s team, is that spectra obtained using flicker photometry suppress the blue and red spectral channels in flicker photometry in the 25 Hz region. The spectra obtained by pulse methods in the 10 ms to 200 ms more correctly represent the actual spectral sensitivity of the human eye. This proposition divides the following discussions into two distinct classes. The results based on pulse photometry appear to provide more complete and less adulterated spectra reflecting the individual spectra of the three spectral classes of photoreceptors.

17.2.4.2 Reviewing other the measurements based on long pulse photometry

[xxx edit into above theme ] 17.2.5 Predicted versus measured spectra and color-matching functions

The subjects of this section are color-matching functions as opposed to the color-difference functions appearing widely in the literature. Wyszecki & Stiles review various matching experiments on pages 278-306.

Thornton has recently obtained a large set of color-matching functions (CMF) of vision aimed at extracting the spectral parameters of the visual process. His methodology employs a different protocol and more modern equipment than that of previous investigators. They consist of six papers in 1992 reporting on laboratory work performed in 1990 plus additional discussion in 1999. His important series of papers are cited in the culminating paper of 1999160. The 1992 papers share a common outline and list of figures and can only be considered as a group. In addition, certain abbreviations such as to Color Science, 2nd Ed. by Wyszecki & Stiles (describes as CS followed by a page number) and to Sources of Color Science by MacAdam (described by SCS followed by a page number) are used throughout the set but only defined when first used.

It is important to know that the Thornton data carries with it at least two technical problems that are not

159Kranda, K. & King-Smith, P. (1979) Detection of coloured stimuli bey ndependent linear systems Vision Res vol 19, pp 733-745 160Thornton, W. (1999) Spectral sensitivities of the normal human visual system, color matching functions and their principles . . . . Color Res Appl vol 24(2), pp 139-156 Performance Descriptors 17- 141

obvious. The simplest problem involves the age of his limited number of subjects. Their average age was 56 with only one subject younger than 35. Their data skews the S-channel peak significantly from the area of 437-445 nm to his claimed peak at 452 nm. The more sophisticated involves his use of metameres in his color matching function experiments. Most modern spectral data is obtained by direct psychophysical or electrophysical measurements using either dark adapted eyes or uniform white backgrounds illuminated with a source with a color temperature near 6500 Kelvin, Thornton takes a different approach. He seeks complete metameric matches between two reflected lights. What he refers to as a standard light may consist of metameres of a 6500 Kelvin source, specifically fluorescent sources or a mixture of three 15 nm wide lights from a stabilized xenon lamp source. This methodology introduces additional variables into the problem. His procedure can be described as matching complete metameres where one of the metameres is itself a complete metamere of a 6500 Kelvin source.

He makes a very important observation (p. 153). “The practice of freely transforming these CMF’s (associated with the CIE 1931 & 1964 Standard Observers) among primary sets has, I think, led to a widely held notion that the true spectral sensitivities of the normal human visual system are unknowable and even irrelevant.” It has also led to the common assumption that the peaks in the normalized color-matching functions of the Standard Observers (based on the CIE 2° color matching procedure), or of a selected set of these transforms (445, 545, & 570 nm according to Stockman, MacLeod, Johnson161) derived from these two sets represent the absorption spectra of the photoreceptors. His set of papers describes the differences (and relationships) between CMF’s and photoreceptor spectral responses. When adjusted as described below, his values and those of this work are in excellent agreement.

Thornton has pointed out some important conditions present in the earlier work of the community, starting with Maxwell’s paper of 1857. “Maxwell credits Young as the first to look toward the human visual system to suggest that each of three types of nerves in the eye is affected chiefly by rays from one sector of the , ‘but to some degrees also by those of every other part of the spectrum.’”

Thornton takes time to stress how much manipulation was performed on the spectral power distributions (SPD) collected during the first half of the 20th Century to reach a consensus that could be memorialized in the current CIE Standards. He references an important review by Fairman, Brill & Hemmendinger162. As a result, he notes several key points (p. 140). “ These manipulations, along with several at-the-time inspired assumptions have led to a difficult situation.” “. . . today the investment of a large amount of intellectual labor on the part of an individual determined to understand the system often fails to be adequate.” He notes his purpose is to clarify the situation and ease the problem of understanding it.

Thornton makes two important assessments of the currently accepted CIE methods. “One problem is that perceived brightnesses are not even approximately additive.” “The second problem is that when the use of the CMFs of either Standard Observer as weighting functions on the SPD of a viewed light is stressed by strong metamerism the Standard Observer often fails.”

Thornton reviews the Maxwell-type of color match (using a broadband source in a bipartite field as a reference) to compare with a an alternative known as the maximum-saturation color match method (where the reference was a mixture of “colors of the spectrum” in a bipartite field) The spectral lines were as narrow as he could produce with adequate brightness. In both cases, the reference light was called the “standard light.” He noted that a variant of the maximum-saturation color match method is the basis of the current CIE Standard Observers. This variant uses only narrow band spectral colors. Thornton explored two experiments. The first matched three narrow band lights to a

161Stockman, A. MacLeod, D. & Johnson, N. (1993) Spectral sensitivities of the human cones J Opt Soc Am vol 10(12), pp 2491-2521 162Fairman, H. Brill, M. & Hemmendinger, H. (1997) How the CIE 1931 color-matching functions were derived from Wright-Guild data. Color Res. Appl. vol. 22, no. 1, pp 11-23 142 Processes in Biological Vision

standard light from a fluorescent source. Using a fluorescent source as a surrogate for a broadband equal energy per unit wavelength source is unusual. He justifies the surrogate on the basis that it looks “white” and apparently excites the spectral photoreceptors to the same degree as a broadband source. Such a surrogate cannot generally be used in metameric experiments because of its non-uniform energy spectrum. The second involved matching two pairs, “doublets,” of narrow band lights in a bipartite field. This technique does not attempt to match a standard light to the sum of three spectral lights. As he notes, this technique avoids the awkward idea of negative powers frequently encountered when the experiment seeks to sum three lights to match a fourth. It avoids the awkwardness by the obvious solution of rearranging the individual lights so that the appropriate two are on each side of the matching equation.

[xxx does the following need to be split into two parts; standard light and the doublet matches. ] Thornton introduces a variation that is key to the success of his work. While earlier methods have kept the power of the three test lights constant and varied their wavelength to achieve a match. He keeps the power of the Standard Light constant and varies its wavelength. To achieve a match, he varies the power of the three other spectral lights. As a result, he obtains a spectral power distribution for each of the three test lights as a function of wavelength during a color match with the standard light. While certainly conventional, Thornton errors in measuring the power in watts in his matching experiments, rather than the applied photon flux applied. While, making his matches while reading a power meter does not affect the individual match, it does distort the relative powers needed to achieve a match (since power is not a constant as a function of wavelength in a photon detection experiment). The effect of this problem will be developed below.

While Thornton attempts to define some of the parameters of the visual system (and their relationships to each other), he does not define any model of the visual system. He only briefly refers to a Stiles-Aguilar model163. This was a very early model assuming a linear visual system. A description of the characteristics of the filters used in their early apparatus has not been located.

Thornton makes a number of sweeping statements designed to build confidence in his analyses. However, these also point to the lack of any model of the visual and neurological system behind his assertions. This work takes exception to his plea to “. . . recognize that the operating point of ‘trichromacy’ (again from the standpoint of colorimetry) is at the rear of the visual system.” His desired to “discuss the colorimetry that goes on deep in the normal human visual system” in the context of R, G & B signals (p. 153) can not be supported. An appropriate model of the visual system shows these signals are converted to P & Q difference signals before the information leaves the retina. This work also takes exception to several of his fundamental assumptions, whether stated or implied.

While these constraints are significant, his work still provides a clear mechanism for determining the approximate spectral peaks of the S-, M-, and L-channel photoreceptors of the visual system. With straight forward modifications, his values will be shown to agree well with the theoretical values provided in this work. However, a larger data set than that from only six elderly subjects (only three subjects in many crucial experiments) is needed to achieve the statistical accuracy he suggests for his current values.

163Aguilar, M. & Stiles, W. (1954) Saturation of the rod mechanism of the retina at high levels of stimulation Optica Acta vol 1. pp 59+ Performance Descriptors 17- 143

Figure 17.2.5-1 (top) shows his approach in caricature using the solid lines. The vertical line at 500 nm was used to describe his approach at a specific wavelength in detail. The standard light was held at a fixed power (normalized here to one watt) and the three spectral sources were adjusted in power to achieve the best bipartite color match. The field diameter was described in the 1992 paper as xxx. The actual power level used for the standard light was xxx. Under the linearity assumption, the concept is clear. When the power required for two of the three lights is zero, the power of the third light should equal the power of the standard light. This should occur at the wavelength of the underlying photoreceptor channel. In this case, the wavelength of the S-channel photoreceptor would be 444 nm. The M-channel photoreceptor peak response would be at 526 nm and the L-channel peak response would be at 645 nm (although the last value is poorly delimited). At other wavelengths, one of the test lights must be added to the standard light to achieve a match with the remaining two test lights.

Figure 17.2.5-1 (bottom) shows Thornton’s actual test data averaged for six subjects. The null points are quite clean suggesting the underlying photoreceptors have peak sensitivities (prior to any other adjustments) at wavelengths of 452, 533, & 607 nm. However, the location of these null points is highly dependent on the precision of the curves of low slope near the null. His expanded graphs show he is relying upon these crossing to a precision of better than one percent. If his measurements from six subjects have a statistical error in amplitude of over one percent, he should be reporting a range of null wavelengths rather than a specific number. He defines wavelengths determined using this method as the prime colors of human vision. The broadness of the absorption characteristics of the photoreceptors in the 1964 CIE data set are shown in his figure 22. The same broadness is shown in his Figure 25 using his modern data set. These curves show broad spectral peaks (in the absence of any correction for lens absorption) centered within 15 nm of the theoretical values of this work.

Thornton isolated the color reversal phenomenon found in the extreme red region of human vision. His figure 10 gives the wavelength of the color reversal as 645 nm. It is 607 nm in figure 13 and 610 nm in figure 17. He also stresses the importance of the short wavelength light in achieving a match in the spectral region associated with deep red. This requirement is in good agreement with the new Perceptual Chromaticity Diagram of this work.

Thornton compared his 1990 data with that of the CIE 1931 and CIE 1964 Standard Observers in a table and was astounded by the agreement. Figure 17.2.5-2 summarizes his data and some other relevant material. Figure 17.2.5-1 Three-color matching functions for a The electrophysiological data from the monkeys is fixed power “standard light.” Top; a caricature of the technique described in the text. Bottom, raw un- normalized unmanipulated modern (1990) visual data collected from six subjects as described in the text. Dotted lines show the relative number of photons per watt of light as a function of wavelength. Each of the curves needs to be adjusted in height to reflect the match points based on photon flux instead of power and new null points determined. Original data from Thornton, 1999. 144 Processes in Biological Vision

quite rare164. This data shows the R-channel (brightness) of vision as recorded at the occipital lobe of the cortex.

Govardovskii et al. have recently measured the spectra of a variety of fresh water fish (based on vitamin A2 chemistry)165. Their spectra were not statistically different from that of humans and other saltwater-based species (based on vitamin A1 chemistry).

164Padmos, P. & Norren, D. (1975) Increment spectral sensitivity and colour discrimination in the primate, studied by means of graded potentials from the striate cortex Vision Res vol 15, pp 1103-1113 165Govardovskii, V. Fyhrquist, N. et al. (2000) In search of the visual pigment template Vis Neurosci vol 17, pp 509-528 Performance Descriptors 17- 145

Figure 17.2.5-2 Tabular comparison of peak absorption wavelengths. The psychophysical data assumes a linear visual model and includes the absorption of the lens system. The electrophysiological data includes the lens and assumes a linear visual model. The theoretical values assume a square-law model for the L channel and do not include any lens absorption.

The precision of the psychophysical values should not be taken too seriously based on the absorption characteristics of the photoreceptors. Figure 17.2.5-3 shows the shape of these characteristics based on power measurements made by Thornton. An overlay has been added to show the situation if a constant photon flux criteria had been used. Small but significant changes in the location of the equal signal crossover points are involved. Additional modifications to the graph are needed to account for lens absorption and the 2-photon requirement of the L-channel. The lens absorption is comparable to the change introduced by the power to flux conversion. Accounting for this absorption would shift the empirical crossover points farther to the long wavelength by a similar increment. 146 Processes in Biological Vision

Figure 17.2.5-3 Absorption spectra based on power measurements. The crossovers at 487 and 568 would move to the right (489 & 570) if the measurements were based on equal photon flux measurements as shown by the dashed construction lines. Data (solid lines) from Thornton, 1999.

Thornton noted (p.155) that the shape of the absorption characteristics were crucial to his analyses. Figure 17.2.5-4 shows a comparison of his spectra and the theoretical spectra of this work. Although he did not measure the skirts of the characteristics in detail, the spectra are quite similar. The short wavelength skirt of the S-channel was either limited by the optics used or his subjects had excessive absorption in their lenses at wavelengths shorter than 440 nm. This assertion is supported by the fact his subjects had an average age of 56 (only one subject was under 53). “Young eye” played no role in this study. The shape of the two M-channel spectra are quite similar. The two L- channel spectra are quite similar although the measured curve occurs at a shorter wavelength. The reduced amplitude of the theoretical curve (also seen in the M-channel characteristic) is due to the narrowness of the spectra in relation to the Fermi-Dirac defined edges of the characteristic.

[xxx working here ]

17.2.5.1 Interpretation of the Thornton work

[xxx begin my interpretation of the situation.

Thornton has offered a massive psychophysical investigation of the spectral performance of the human eye. Its content within that field is of monumental Figure 17.2.5-4 Comparison of measured and theoretical spectra. Solid lines are spectra from Thornton, 1999. importance. His background in lighting and Dashed lines are theoretical values from this work. The knowledge of the idiosyncracies of the CIE Standard differences between them are discussed in the text. Observer are if great value to the community. The Performance Descriptors 17- 147 meticulous repetition of experiments, both of his own and others, in order to confirm specific characteristics is seldom found in the vision literature. This is particularly apparent in his repetition of certain experiments to seek or demonstrate the absence of “rod intrusion” into his data. However, he has occasionally strayed from his area of study and made remarks in the vernacular that are uncalled for. For example, his repeated statements concerning the seat of chromaticity being located at the rear of the visual system (implying the rear of the brain). His interpretation of a paragraph from Wyszecki & Stiles is similar. “The careful choice of words in the Wyszecki-Stiles quote suggests that deposing the retina as the seat of trichromacy is timely.”

He has made a number of statements that are blatantly unsupported. The last paragraph on page 253 of his Part III is an example. “The Stiles-Wyszecki attempt to correlate the tristimulus values of colorimetry to retinal absorptions resulted in a persistent sensitivity much deeper in the red than a retinal cone absorption can be.” He did not describe what the limit was that he invokes.

In the realm of statistical analysis, he has provided nominal values with deviations attached. However, no definition of the meaning of these deviations was offered. In general his deviations represent deviations in repeatability of the experiment and do not represent the precision of the data. This becomes obvious when deviations of one or two nanometers are attached to a value obtained from a binning operation using spectral filters with widths and mean separations of 15 nanometers.

As seen in the discussions of visibility functions (Section xxx), the use of filters wider than 5 nm at their half- amplitude point can introduce significant errors into spectral diagrams obtained by binning. The Fermi-Dirac function describing the edge of all known “undoped” photo-electric devices changes by 80% within 15 nm in the red region of the spectrum.

As in any major study (and this work), the results point to a specific set of values that become the cornerstone of the work. Thornton settled on the spectral values of 452, 533 & 607 and reiterated these specific values throughout the material as his prime color regions (PC). His figure 65, reproduced as Figure 17.2.5-5 with a reference line added at 611 nm, is highly instructive. It shows that his values of 450 and 533 are sharply defined (repeatable) by dual crossings of the abscissa while the value in the long wavelength region can vary considerably. Note also the unexpected amplitude of the functions in the long wavelength region determining the nominal sensitivity of that channel (the values go off the expected grid). The confluence of the curves in this figure might suggest a null in the red region closer to 625-650 than to 607. The value of 452 is obviously determined by the age of his subjects as noted above.

Thornton presented a table including the systematic change in parameters reflected in the figure. The long wavelength primary varies between 580 and 650 nm in that table while the short and medium wave primaries are fixed at 450 nm and 530 nm. Thus, each curve in Figure 17.2.5-5 Color matching functions of eight this figure is the metamere of a set of his primaries and primary-sets (J-Q of his Table XV) obtained by not matched to a fixed source. The curves passing transformation from the PC primary-set averaged observer through the reference line at 611 nm begin at the top A. A vertical line has been added at 611 nm for reference. See original for details. From Thornton, 1992, fig.65. 148 Processes in Biological Vision

matching a 650, 640, 630, 580, 590, 620, 600, 610 nm source. Placing a grid over the figure and enlarging it, as Thornton has done for other figures, it is seen that the long wavelength crossover occurs at the value of the primary used in the patching experiment. There is no convergence on a unique solution other than that of the three primaries used as a reference. However, this convergence appears quite distinct.

Thornton also settled on a set of four wavelength that he defined as anti-primes (AP) This set consists of a region in the violet, the blue-green near 500 nm, the yellow near 570-580 nm and the deep red. He frequently defines the two dips in the visual spectrum as near 497 and 579 nm. These psychophysical values are in good agreement with the theoretical values of 494 and 572 developed in this work.

His discussion of the goal and reality of defining metameres in terms of the CIE Chromaticity Diagram is of great value since it is virtually unique in the published literature. The discussion appears in his section IV. Discussion and the graphics extend from his figure 11 to figure 30.

His development of an alternate description of brightness (discussion in his section IVB, with concept development in his section IVD3 & IVD4) is of immense value to the theoretician. It offers an entree into the empirical description of brightness not found elsewhere in the literature. His analyses is nearly a perfect overlay (except for a lack of boundaries) to the theory of this work. His descriptions and relationships on pages 246-250 will be explored more fully in Section 17.4.2. That section develops a new three-dimensional color space compatible with, but providing new levels of detail concerning the Munsell Color Space. It does not pursue the modified CIE color space that Thornton suggests.

Thornton actively pursued, and did not find any rod intrusion into his experiments166, by repeating them at 30 cd/m2 and 100 cd/m2 (regions associated with and typical indoor reading environments in Section 2.1.1.1).

His figure 67 is of great value to the community in allowing comparison between the various color indices currently in use. It shows significant differences between the color-discrimination index (CDI), the color-rendering index (CRI) and the color-preferences index ((CPI).

Thornton’s comments on page 183 of the 1992 set of papers surfaces something not previously found in the literature.

“The wonder is that, in view of the three independent channels in the human visual system, recognized since Palmer (1777) and Young (1802), we have countenanced not only the concept but the prescription of a one- component, one-dimensional visual-sensitivity curve. The promulgation of a one-component weighting function. representing visual sensitivity, as characteristic of a visual system with three independent inputs, has always been insupportable. To teach that a one-input device, as the foot-candle meter, can substitute for the three-input normal visual system has caused enormous confusion.”

His practical answer to this problem was the development of a three channel “brightness-meter” with a sensitivity profile (his figure 74) equivalent to the theoretical profile of this work for the human as a blocked tetrachromat, shown in Figure 17.2.1-1 xxx.

17.2.5.2 Reviewing the measurements supporting “cone-fundamentals”

The vision community is divided into two groups with grossly different estimates of the peak wavelengths of the

166Thornton, W. (1997) Toward a more accurate and extensible colorimetry: Part IV Color Res Appl vol 22(3), pp 189-198 Performance Descriptors 17- 149 spectral mechanism of vision. The one group has obtained spectra using physiological techniques and relying upon differential adaptation to separate the spectra. Various titles have been used for these spectra, including action spectra, cone sensitivities and cone fundamentals. Schanda, in reviewing recent CIE committee work, has defined the concept of “fundamentals” as the spectral sensitivities obtained psychophysically and referred to the outer layer of the eye167. He defines “photopigment absorption spectra or cone-excitation spectra” as the spectra associated with the physico-chemico-biological photopigment absorption/photo-signal excitation process.

Stockman, MacLeod & Johnson have been the most active investigators in this area in recent times. They have focused primarily on re-computing earlier results of several groups relying upon psychophysical experiments. The other group has used both psychophysical and electrophysical techniques to obtain total spectra exhibiting the individual peaks associated with each spectral channel. Thornton168 and Ikeda & Shimozono169 have been active in this group recently. This author has also offered theoretical spectra based on the photo-chemistry of the photoreceptor neurons (Chapter 5).

Textbooks commonly cite one of three groups when discussing the spectra obtained from psychophysical experiments; Smith & Pokorny170, Vos & Walraven171, or Wald, Brown & Smith172. Each of these investigators followed a different experimental protocol. As a rule, these groups did not factor out the role of the lens in limiting the spectral performance of the intrinsic chromophores. However, this factor is only important in defining the difference between the psychophysical performance of the S-channel and the actual absorption spectra of the chromophore.

Wald, Brown & Smith explored visual performance of trichromats under differential adaptation conditions sufficient to eliminate the S-channel, but apparently not sufficient to eliminate the M-channel, from their psychophysical experiments. This shortcoming has been demonstrated by the more recent controlled differential adaptation experiments of Sperling & Hawerth that will be discussed below.

Neither Smith & Pokorny or Vos & Walraven based their work on trichromats. They both accepted the spectra obtained from protanopes and deuteranopes and relied upon the early concept of color blindness attributed to Helmholtz. While Helmholtz suggested deuteranopia as due to the absence (or possibly the failure) of the M- channel photoreceptors, Fick suggested an alternative. Fick suggested the cause of deuteranopia could be due to a failure in the signal processing associated with the “red/green” Hering type signaling channel. His proposal suggested the fusion of the M – and L–channels. Both the Helmholtz hypothesis and the Fick Hypothesis were based on the original trichromatic theory. A variety of intermediate situations can be defined between the hypothesis of Helmholtz and that of Fick. Stiles addressed the fact that erythrolabe and chlorolab were both known to be present in deuteranope retinas. This fact led him to the idea that the M-channel photoreceptors contained a mixture of the two chromophores, leading to a failure in the ability of the subject to resolve and , depending on the ratio of the two chromophores within the outer segment of the photoreceptors.

The Vos & Walraven paper was an entirely mathematical analysis based on a significant variety of arbitrary (but carefully drawn) qualitative choices and the use of a zone theory model of vision that is more complicated than that

167Schanda, J. (1998) Current CIE work to achieve physiologically-correct color metrics In Backhaus, W. Kliegl, R. & Werner, J. eds. Color Vision” Perspectives from different disciplines. NY: Gruyter Chap 17 168Thornton, W. (1999) Spectral sensitivities of the normal human visual system . . . Color Res Appl vol 24(2), pp 139-156 169Ikeda, M & Shimozono, H. (1981) Op. Cit. 170Smith, V. & Pokorny, J. (1971) Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm Vision Res vol 15, pp 161-171 171Vos, J. & Walraven, P. (1970) On the derivation of the foveal receptor primaries Vision Res vol 11, pp 799-818 172Wald, G. Brown, P. & Smith, P.(1955) Iodopsin J Gen Physiol vol 38, pp 623-681 150 Processes in Biological Vision of this work. Their spectra (“experimental courses not data points”) were obtained from Hecht (1949), Wright (1947), Hsia & Graham (1957) and Boynton et al. (1959). The additional complexity of their model was because of a lack of definition of the names and spectral range of colors and their specific role in the zone theory. It was based entirely on linear matrix algebra and did not account for the square-law performance of the L-channel photoreceptors. Their proposed spectra in figure 5 shows a component of the short wavelength spectra incorporated in the proposed L-channel spectra. Their proposed L-channel spectrum is essentially the full spectrum of a deuteranope. This spectrum is shown to consist of both the L- and M-channel photoreceptor channels in this work (and in agreement with the Fick hypothesis). Their M-channel spectrum is nominally that of a protanope. Their S- channel spectrum appears to be that of a normal subject limited by the lens of the eye at short wavelengths. All three of the spectra show this limitation at wavelengths shorter than 420 nm.

A second Vos & Walraven paper promised in 1970 finally appeared in 1990 as Vos, Estevez & Walraven173. This is an important paper corroborating the work presented here. It addresses the potential for the luminance channel of vision to be represented by the sum of the logarithms of the individual spectral responses for the first time outside the writings of this author dating from the 1960's, although this mechanistic approach was mentioned in a 1982 paper by Vos174. However, the concept is only described superficially and their figure 6 should not be relied upon. Their formulations do not address adaptation within the visual system. While continuing to rely upon the Helmholtz Hypothesis, the work relies upon a negative S–channel input, or no S–channel input, to achieve a satisfactory description of the visibility function.

Vos, Estevez & Walraven also identify the Bezold-Bruecke hue shift region in close association with the peak region of their putative L–channel spectrum (figure 5). Their putative L–channel spectra is actually the summation of the real M–channel and real L–channel spectra under one state associated with the Bezold-Bruecke effect. Their analysis also surfaces the fact that the exponent associated with the photon to electron conversion process in the L–channel of vision is twice that associated with the M–channel (0.68 versus 0.34 or 0.34x2 versus 0.34). This feature of vision is discussed in Section 12.5.2.4. The factor 0.34 is actually an approximation to the natural logarithm conversion. This approximation has frequently been described as the 1/3 power rule.

The Smith & Pokorny paper also relied upon the spectra of protanopes and deuteranopes. While the paper included the results of original work, the choice of filters used was unfortunate. While narrow band filters were used, their spacing was not contiguous or adequate in the critical 496-658 nm region. Thus, they were unable to resolve the fine details in this region of the spectra. While they did not rely upon differential adaptation as part of their test protocol, the use of a Kodak (Wratten) #47B filter leads to un-quantified differential adaptation. The spectral peak for their protanope was at 540 nm with no other measured value within 38 nm of that value. The spectral peak for their deuteranope was at 580 nm with no other value within 40 nm of that value. While their spectral data was collected in terms of energy versus wavelength, they converted the data to quantal sensitivity as a function of wavenumber in their concluding figures.

Two major problems appear in the Smith & Pokorny paper. The first concerns the precision of their empirical curves. It is critically important to note their figures 6 & 7 describing the “quantal sensitivity of the proposed human visual photopigments” do not contain any data points. The curves are smoothed and populated with open and closed circles for identification. More circles are included than there were filters in the original experiments. Only two curves are shown in each figure. The long wavelength curve is that of a deuteranope, which they propose is the theoretical spectral response of the L-channel chromophore of a normal trichromat. The shorter wavelength curve is

173Vos, J. Estevez, O. & Walraven, P. (1990) Improved color fundamentals offer a new view on photometric additivity Vis Res vol 30(8), pp 937-943 174Vos, J. (1982) On the merits of model making in understanding color-vision phenomena Color Res Appl vol 7, pp 69-77 Performance Descriptors 17- 151 that of a protanope, which they propose is the theoretical spectral response of the M-channel chromophore of a normal trichromat. No discussion of failure modes within the visual system leading to color blindness appears in the paper. The Helmholtz hypothesis is implicit in their proposals.

The second problem concerns their assertions concerning figure 6. Their figure 6 has the title, “Panel (a) Log relative quantal sensitivity of the proposed human visual photopigments.” This figure has been widely reproduced based on this inappropriate assertion. In their discussion, they say, “Figure 6 shows the proposed visual pigment absorption spectra and their predicted tritanopic coefficients without a differential macular pigment correction. It is clear that these coefficients are completely incorrect, the pair of pigments lie too close together to predict the tritanopic coefficients.” They refer the reader to a corrected figure 7. In both figures 6 & 7, the labels are reversed between the long and mid wavelength sensitivity functions! Figures 6 & 7 are arrived at from figure 1 where the curves were calculated, using a template, and “are slid along the horizontal axis to provide a good fit to the symbols ont eh long-wavelength slopes.” This data hardly qualifies as a reference source for the spectra of the chromophores of human vision.

Several authors have provided data that can help resolve this situation. Padmos & Norren have provided a paper showing electrophysiological data that displays both types of data from the same subjects and describes the way the data was obtained175. Similarly, two papers by King-Smith have presented both types of data from the same subjects176,177. Sperling & Harwerth have provided key data from their experiments involving differential adaptation to show the spectra of Stockman et. al., originating with Smith & Pokorny in 1975, can be obtained from the more fundamental spectral channel data of Thornton, Ikeda & Shimosono and others 178. However, they assert, and this author concurs, the opposite is not true. The real long wavelength spectral characteristic of the photoreceptors can not be obtained from the smoothed spectra peaking in the 575 nm and 555 nm regions. The broad spectra of the so- called mid wavelength cone spectrum (mws) and long wavelength cone spectrum (lws) generally attributed to Smith & Pokorny, are not the spectra of the actual photoreceptors of vision.

A careful examination of the documents referenced in the previous paragraph, from the perspective of the model described in Section 17.1, will show that the composite visual spectrum, that is the R-channel or brightness channel of vision, can be measured directly under photopic conditions without requiring any form of adaptation. Because of ethical problems, it is more direct to perform the direct experiments on other primates. However, the results are the same. The human visual spectrum exhibits four peaks in sensitivity in the absence of the lens and three peak sensitivities in the presence of the lens. These peaks are found in the vicinity of 342, 437, 532 & 625 nm. If the light level is reduced to scotopic conditions, the long wavelength sensitivity is lost due to the square-law operation of the L-channel photoreceptors.

By introducing differential adaptation at either the photopic or scotopic level, it is possible to suppress either one or two of the spectral channels of the human and thereby isolate the remaining spectra. Completely suppressing the L- channel artificially under photopic conditions will result in obtaining the scotopic spectral response and the chromatic sensitivity of a protanope. Completely suppressing the S-channel artificially under photopic conditions will result in both an abnormal spectrum and chromatic sensitivity generally associated with a tritanope. Completely suppressing both the S- and M-channels under photopic conditions will isolate the L-channel and result in the chromatic performance of a true long wavelength monochromat (if such exists). However, this condition has seldom

175Padmos, P. & Norren, D. (1975) Increment spectral sensitivity and colour discrimination in the primate, studied by means of graded potentials from the striate cortex Vision Res vol 15, pp 1103-1113 176King-Smith, P. & Webb, J. (1974) The use of photopic saturation in determining the fundamental spectral sensitivity curves Vison Res vol 14, pp 421-429 177King-Smith, P. (1975) Visual detection analysed in terms of luminance and chromatic signals Nature vol 255, pp 69-70 178Sperling, H. & Harwerth, R. (1971) Op. Cit. 152 Processes in Biological Vision

been achieved in the past because the adapting light wavelength has been significantly shorter than 510 nm. If a shorter wavelength is used under photopic conditions, a hybrid spectrum not unlike that achieved with total S- channel suppression will be reported and color performance similar to that of a tritanope will be reported.

Based on this discussion, it appears clear that the human and other species share three common spectral channels (omitting the ultraviolet channel). These channels are centered at spectral wavelengths near 437, 532 and 625 nm. The spectral peaks at 505, 555, 575 are easily generated based on the 437, 532, 625 set of wavelengths. The 505 nm peak called the scotopic visibility function will be reported under dark adapted conditions where the test light level reaches the scotopic (but not the photopic) light level and the response is window filtered by a 30 nm filter. Under this condition, the L-channel is inactive because of its square-law operating characteristic. This performance is usually recorded using a 10° diameter test field to achieve adequate signal-to-noise ratio.

The 555 nm peak called the photopic visibility function will be reported under dark adapted conditions where the test light level reaches the photopic light level and the response is window filtered by a 30 nm filter. Under this condition, the L-channel is active. This characteristic is usually recorded using a 2° diameter test field because of the higher available signal-to-noise ratio.

17.2.5.3 Rationalizing “cone-fundamentals” and π-parameters with other spectral parameters

The profusion of different representations of the human visual spectrum are due to at least two distinct concepts of data gathering and a wide variety of protocols related to each of these concepts. The term fundamental sensitivity spectra (or briefly fundamentals) are used by the psychophysical community to describe spectra obtained from signals passed through the entire visual modality (stages 0 through 6, see Section 14.1.3) but referred to a plane at the external surface of the eye. These “fundamentals” are subject to any limitations imposed by the neural system (logarithmic signal conversions and spectrally asymmetrical signal processing) and cannot report on the ultraviolet performance of the retina (except in the rare case of an aphakic subject). The term absorption spectra or cone- excitation spectra are used to describe spectra obtained by more clinically intrusive techniques at the cellular or neural path level. These spectra are still frequently limited by the stimulus spectra being limited by the transmission properties of the eye forward of the retina (stage 0). Thus, the ultraviolet performance of the human eye is only available by in-vitro measurements or by using aphakic subjects.

17.2.5.3.1 The design and interpretation of spectral sensitivity experiments

The protocols used to gather spectral data vary significantly in both spatial characteristics and temporal characteristics. The spatial characteristics of the stimuli seldom are matched to the variation in retinal performance characteristics. Including the transition between the foveola and the parafovea at 1.8 degrees diameter is a particular problem). Similarly, the temporal characteristics (limitations) of the neural system are seldom considered when planning the temporal characteristics of the stimuli. The use of flicker photometry introduces a particularly limiting characteristic into obtaining realistic fundamental and excitation spectra. In addition, the precise state of adaptation of each spectral group of sensory neurons must be known if meaningful overall spectra, or relative spectra, are to be obtained.

When discussing any conditioning, or pre-adapting, broadband stimulus, it is critically important that the color temperature of that stimulus be described. The chordate eye is subject to chromatic (differential) adaptation. Thus, the relative quantum flux at a given wavelength is critical to the adaptation or conditioning process. An adapting light at 6500 K for the complete eye (or 7053 K for the aphakic eye) provides near uniform quantum flux stimulation at all visible wavelengths. Performance Descriptors 17- 153

The temporal limitations of the mammalian eye must be understood if maximally precise measurements are to be obtained. The visual modality involves a considerable number of time constants, particularly related to the sensory neurons.

The longest time constant is the second time constant of the hydraulic system controlling the dark adaptation process. It is on the order of 20-30 minutes. For subjects who have recently been exposed to conditions leading to “snow blindness” or “beach blindness,” it is appropriate to wait for multiples of 30 minutes before attempting any high precision measurements. The next longest time constant due to lesser bright light is on the order of three minutes. A dark adaptation time of ten minutes is needed and conventional in this case. The first Activa of the sensory neurons of vision includes a low pass filter with a time constant of about 1.6 ms. Following any pre-test conditioning or adaptation stimulus, it is desirable to wait at least 8 ms after stimulus termination before applying any test stimulus in order to allow the output potential of the neuron to stabilize. For a lesser period, the experiment should be interpreted as measuring incremental sensitivity rather than absolute threshold sensitivity.

The spectral channels of vision are uniquely designed to integrate the photo current related to short flashes and present an appropriate signal at the pedicle of the sensory neurons. However, the achromatic and chromatic channels of vision propogate signals to the CNS using different modulation techniques. The achromatic (brightness) channel can deliver an initial action potential to the CNS (stage 4) with a delay determined primarily by the distance between the retina and the stage 4 element (either the PGN or the LGN) of the diencephalon. However, the chromatic channels operate differently. They typically require the delivery of multiple action potentials, at pulse intervals of 20 ms or longer in the M– spectral ranges (60 ms or longer in the S– and L– spectral ranges). Thus a test stimulus of at least 200 ms is needed to precisely notify the brain of a change in chromatic stimulation. A test stimulus interval of at least 60 ms is required to precisely notify the CNS of a change in achromatic stimulus.

Flicker colorimetry experiments introduce a more complex situation. The above test and conditioning stimulus intervals can be obtained at low flicker frequencies; and by operating at lower than 100% duty cycle, dark intervals of 8 ms can be achieved between the stimuli to allow settling of the output of the sensory neurons before beginning the next stimulus interval. However, at flicker frequencies above even three Hz, these conditions cannot be achieved. As a result, the experiments must be considered either incremental threshold measurements or more likely incremental color discrimination sensitivity experiments.

The protocol must make clear whether it is attempting to determine the threshold sensitivity or the incremental sensitivity associated with the brightness (luminous) channel of the neural system, or whether it is attempting to determine the chromatic difference sensitivity of the chromatic channels of the neural system.

In comparing the various spectral characteristics in the literature, the above considerations must be respected. Section 17.2.5.5.4 [xxx ] will illustrate some of these differences following the discussion in this section.

17.2.5.3.2 Background from the literature

Sharanjeet-Kaur et al.179, Foster180 and Foster & Snelgar181,182 have provided a set of papers that help rationalize the

179Sharanjeet-Kaur, (no initial). Kulikowski, J. & Walsh, V. (1997) The detection and discrimination of categorical yellow Ophtha Physiol Opt vol 17(1), pp 32-37 180Foster, D. (1981) Changes in field spectral sensitivities of Red-, green- and blue-sensitive colour mechanisms obtained on small background fields Vision Res vol 21, pp 1433-1455 181Foster, D. & Snelgar, R. (1983) Test and field spectral sensitivities of colour mechanisms obtained on small white backgrounds: action of unitary opponent-colour processes: Vision Res vol 23, pp 787-797 182Snelgar, R. Foster, D. & Scase, M. (1987) Isolation of opponent-colour mechanisms at increment threshold Vision Res vol 27, pp 1017-1027 154 Processes in Biological Vision

various visual spectra found in the literature, and the theoretical spectra of this work. The Foster paper is extensive and comprehensive. As noted earlier, Foster and Snelgar have discussed the separation of the descriptors of vision in order to relate to the chromatic-opponent and achromatic (luminosity) mechanisms. This separation is important in the following discussion. Figure 17.2.5-6 from Sharanjeet-Kaur et al. shows human luminosity spectra obtained under two different flicker-photometry conditions. The upper curves at 1 Hz show the typical spectral response also reported by Thornton, and most recently with excellent precision by Babucke (Section 17.2.1.3 xxx). Spectral peaks are reported in the regions of 437 nm, 532 nm and 600-625 nm. Using 2700 K background, the notch, which is the approximate location of the null in the M–L chromatic channel, occurs near 574 nm. With the 6800 K background, this notch shifts to around 565 nm. The nominal theoretical value of 572 nm at 6500 K, based on this work, is in excellent agreement with these values. “There is no appreciable effect of colour temperature on the 25 Hz curve.”

Sharanjeet-Kaur et al. assert, “The 25 Hz presentation produces a luminosity spectral sensitivity function whereas the I Hz reveals the sensitivity of the blue-yellow and red-green systems.” That is to say, the 25 Hz presentation is unable to separate the M– and L– channel signals successfully under their protocol.

When the flicker frequency is increased to 25 Hz, there is a significant loss in detail within the luminosity function at both 2700 and 6800 K. While suggested by the inflection points in the overall response, the relative peaks near 437 nm and 600-625 nm are lost in this test regime. This response corresponds to the M-channel “cone fundamental” response of Stockman, MacLeod and Johnson (1993) measured at 17 Hz flicker frequency, a two degree circular test spot at fixation, and a 4 degree diameter background field. Figure 17.2.5-6 The effects of flicker frequency on the observed spectral sensitivity curves in humans. The Thus, a single subject can display the multi-peaked circular test spot was 1.2 degrees in diameter centered on luminosity function found frequently in the literature the fixation point. The surrounding field was 10 degrees and the less detailed single peak response of Stockman, in diameter centered on the fixation spot at 1000 Trolands. Sharpe and MacLeod at the same time, with only a Subject; SK. From Sharanjeet-Kaur et al., 1997. change in the flicker frequency. In this comparison, the M-cone fundamental of Stockman, MacLeod and Johnson is taken to be the actual luminosity function of their subject in the presence of some, but minimal, L–channel suppression (see their isolation procedure). In subsequent experiments focused on isolating the S–cone fundamental, Stockman, Sharpe and Fach (1999) used a flicker rate of 1 Hz.

Figure 17.2.5-7 from Foster and Snelgar shows recent attempts to isolate the three spectral channels of vision while comparing them with the luminosity function of the same individual using flash techniques. The graph has been replotted with a linear abscissa to conform to the convention in this work. [The original art for figures 1 in the 1981 and 1983 papers are not clear. The notation includes a period before the last zero in each ordinate value.] The zero after the decimal point has been dropped in this reproduction. Note the straight line character of the skirts of the various functions when using this abscissa.. These skirts conform to the theoretical model based on the Helmholtz- Boltzman equation and Fermi-Dirac statistics of the absorption process (Section 5.5.10). The one exception is associated with the 608 nm experiment where the dotted line probably represents the actual situation. The top box of each inset shows the size of the test field; it was nominally 1.05 degrees (entirely within the foveola). The bottom box shows the background field diameter; it was 10 degrees. All fields were concentric and centered on the point of Performance Descriptors 17- 155

fixation. A two millimeter artificial pupil was used in all tests. The upper pair of curves shows the smoothing effect of using a large background field (during flash experiments). The “white” background had an intensity of 1000 Trolands and color temperature of 3400 K in the upper curves.. The test flash had a duration of 200 ms with rise and fall times of less than 2 ms. When appropriate for spectral isolation, a ten degree diameter variable intensity monochromatic conditioning field was used at the wavelength specified for each curve.

The upper pair of curves show the significant smoothing encountered when a large background field is used in this type of experiment. It is best to use a conditioning field the same diameter as the test stimulus. Optimally, both should be less than 1.2 degrees in diameter when presented centered on the line of fixation. The magnitude and the shape of the notch shown is predicted in detail by the “sum of the log absorptions” representation for the luminosity function proposed in this work. The specific shape of the notch can not be accounted for using a linear summation hypothesis (such as a linear differencing of the M– and L– channels defined by Stockman et al.).

Foster and Snelgar describe their lower spectra as field action spectra (using the earlier terminology of Stiles). Note the insets. Foster and Snelgar used a fixed test wavelength and a variable surround wavelength in a threshold experiment. Unlike, the Stockman group, Foster and Snelgar used conditioning fields very close to the peak sensitivity wavelengths of the spectral channels to be suppressed; they used 422 nm, either Figure 17.2.5-7 The luminosity function and partially isolated spectral responses of the human eye (with lens) 521 or 531 nm and 608 nm. They describe the based on flash stimulation. Data is for the right eye of the isolation of a specific spectral component using the subject (one author). Tics have been added along the term spectral sharpening. As the pre-adaption intensity abscissa at 437, 532 and 625 nm for reference. See text. increases, these spectra begin to approach the Redrawn with linear abscissa from Foster & Snelgar, 1983. theoretical absorption spectra of the chromatic channels (with appropriately straight skirts on a semi- logarithmic graph). The short wavelength field action spectra approaches the theoretical absorption spectra quite closely at wavelength shorter than 500 nm. Beyond that wavelength, the subject in this psychophysical experiment reports some residual sensitivity due to the M– channel. The mid wavelength field action spectra shows a peak response near the theoretical 532 nm with residual sensitivity below 475 nm due to the sensitivity of the S-channel and above 580-590 nm due to the L–channel. The long wavelength field action spectra shows a clear peak in the region beyond 600 nm. Another data point is needed between 620 nm and 640 nm to determine the precise location of the peak. The long wavelength action spectra shows a clear relative peak near 532 nm due to the residual sensitivity of the M–channel which was not suppressed adequately. Additional suppression of the M–channel would isolate the L–channel spectra completely, although the intensity of the adapting light might involve some discomfort for the subject.

Comparing the two figures, it is clear that the luminosity response of an individual is unchanged between a 1 Hz flicker based stimulation and a 200 ms flash stimulation, and the three spectral peaks of the individual absorption spectra can be isolated using appropriate differential chromatic pre-adaptation. The peaks in the field action spectra agree very well with the theoretical absorption spectra of the Rhodonines in the liquid crystalline state (Section 5.xxx) and when behind the lens of a normal eye to eliminate the UV channel sensitivity of the retina. 156 Processes in Biological Vision

Snelgar and Foster provided more data in their paper. It opens with a statement. “There are three characteristic peaks at approximately 440, 530, and 610 nm in the spectral sensitivity curve obtained by increment threshold measurements of a long-duration, circular, monochromatic test flash presented on a large white conditioning field. The three peaks have been demonstrated for the human eye in many studies (about a dozen citations).” “Evidence suggesting that the peaks at about 530 and 610 nm result from relate to (this author) activity in the red-green opponent-colour channel of an opponent-process system has been reviewed in Foster and Snelgar (1983a).” The paper focuses on the characteristics of the notch near 580 nm.

The π-parameters of Stiles have left many investigators perplexed for many years. Their traceability to the actual absorption spectra of human vision have been difficult to demonstrate. The problem began with the early Stiles work itself183,184. He began with a discussion of the foveal stimulus threshold (at a test wavelength) versus conditioning intensity with a different spectral profile. This function when plotted is known as a t.v.i. curve. It exhibited three branches. “The three branches are provisionally ascribed to three component mechanisms, denoted

by the neutral symbols π4, π1 π3 as marked in the figure.” His interpretation of the t.v.i. curve was based on the existence of a “rod mechanism” as well as multiple cone mechanisms. When the functions associated with the neutral symbols were presented on a sensitivity versus wavelength graph, the data space became confusing. While

π1 could be associated with the S-channel absorption spectra, the other symbols were more difficult to associate with any reasonable aspect of the visual system. In his table 1, he associated π0 with an undefined rod mechanism “absent

from the fovea.” π1, π2 and π3 were all associated with a “‘blue’ cone mechanism.” π4 and a π4' were associated with

a “‘green’ cone” with a maximum sensitivity in the 540 nm region. π5 and a π5' were associated with a “‘red’ cone” with maximums in the 575 and 587 nm region respectively. He left two major questions outstanding on page 109 of his 1959 paper. The specific test protocol was not clearly defined in the 1959 paper. The 1953 paper and the discussion in Wyszecki & Stiles (pages526-544) suggest the test stimulus was of short duration and imposed on a steady, larger spatial diameter, conditioning stimulus.

Foster and Snelgar also interpreted their data relative to the π-parameters of Stiles with useful results. They note, “One of us has recently shown (Foster. 1979, 1980, 1981) that if the field spectral sensitivity curves of the medium- and long-wavelength sensitivity mechanisms, corresponding normally to Stiles’s mechanism π4 and π5 are obtained with a long-duration test flash superimposed on a steady monochromatic ‘auxiliary’ conditioning field, spatially coincident with the test field. then the resulting curves may appear narrowed or sharpened with their peaks shifted in opposite directions along the wavelength scale. Thus, the field spectral sensitivity curve of the long-wavelength sensitive mechanism π5, normally rather flat-topped with maximum sensitivity at about 575 nm {Stiles. 1959). becomes attenuated on the short-wavelength side and acquires a relatively sharp peak at about 605 nm (Foster 1980,

1981). The field spectral sensitivity of the medium-wavelength sensitive mechanism π4,. also fairly flat-topped with maximum sensitivity at about 54O nm (Stiles. 1959). becomes attenuated on the long-wavelength side and peaks more sharply at 530 nm (Foster. l981).” It is proposed the same results will be obtained if the Stockman et al. experiments were repeated at lower flicker frequency and greater degrees of differential adaptation.

17.2.4.5.3 Conclusions

It is concluded that the luminosity function of the human eye is best described by flash or low frequency flicker (below 3 Hz) experiments. At higher flicker frequencies, the luminosity function becomes distorted due to attenuation of the sensitivity in both the short and long wavelength regions. At a flicker frequency in the 15 to 25 Hz region, the luminosity function can be separated into two components, a short wavelength component with

183Stiles, W. (1939) The directional sensitivity of the retina and the spectral sensitivities of the rods and cones Proc Roy Soc (London) series B vol 127, pp 64-105 (beginning on page 81) 184Stiles, W. (1959) Color vision: the approach through increment-threshold sensitivity PNAS vol 45, pp 100-113 Performance Descriptors 17- 157 energy at wavelengths shorter than 494 nm and a longer wavelength component with energy at wavelengths longer than 494 nm. The longer wavelength component can be further separated into two components, one at a wavelength shorter than 572 nm and a second at a wavelength longer than 572 nm. With more intense, differential chromatic adaptation, these two components can be sharpened significantly. The shorter wavelength component can be sharpened until it exhibits a peak wavelength at 532 nm and straight skirts when the responses are plotted on a semi- logarithmic graph. Similarly, the longer wavelength component can be sharpened until it exhibits a peak wavelength in the vicinity of 610-625 nm and straight skirts when the responses are plotted on a semi-logarithmic graph. The three resulting spectral components are in agreement with the theoretical absorption spectra of the Rhodonines of this work when in the liquid crystalline state and dimensionally configured as in photoreceptor outer segments. Both of these conditions are required.

The reason for the reduction in luminance sensitivity at large distances from 532 nm in high frequency flicker experiments is complex. For flash and low duty cycle flicker experiments (where the stimulus interval is in the 150-200 ms range), the experiment calls on the neural system to perform a threshold detection experiment based on the stage 3 luminance channels (regardless of the chromaticity present). For higher duty cycle flicker experiments (50% duty cycle and test stimulation interval less than 200 ms), the neural system is called upon to make a chromatic discrimination experiment. The stage 3 chromatic difference propagation circuits employ a biphase modulation mechanism encoding a nominally 30 Hz pulse carrier. For wavelengths shorter than 494 nm or longer than 572 nm, the performance of these circuits deteriorates in proportion to the wavelength difference from these nominal values and the amplitude of the signal at the pedicle of the photoreceptor neurons. These are the mechanisms that cause the apparent psychophysical sensitivity of the human eye to deteriorate in high flicker rate experiments. For flicker rates approaching the critical chromatic flicker frequency (CCFF), given by the above 30 Hz pulse carrier frequency, a chaotic situation arises in the stage 3 propagation channels leading to fusion of the stimulants present during the two flicker phases. The measured flicker frequency sensitivity relative to the human CCFF obtained by de Lange Dzn in 1958 is given on page 565 of Wyszecki & Stiles185. He showed an attenuation of 8:1 at 17 Hz compared to 1 Hz for a chromatic flicker consisting of alternating fields of 615 and 549 nm. A similar result can be expected for an experiment using fields near the S-channel peak at 437 nm and a more central wavelength associated with the M–channel (example, 515 nm).

The low “carrier frequency” of 30 Hz can be considered a sampling frequency based on the principles of Information Theory. Based on this interpretation, flicker frequencies above one-half of this value (15 Hz) will result in phase ambiguity (distortion) in the reconstructed signals delivered to stage 4.

The so-called cone-fundamentals of Stockman et al. are protocol limited (flicker-rate dependent) measures of perceived (psychophysical) color sensitivity. The cone-fundamentals do not represent the spectral absorption characteristics of the chromophores of vision or the output of the photoreceptors of vision. Their measurements at 17 Hz are significantly limited by the stage 3 neural pathways of vision. These pathways impose an attenuation in the apparent sensitivities of the S– and L–channels for protocols employing flicker frequencies above about 3 Hz. As a result, the L-channel cone-fundamental is actually a function of the flicker-rate given by 625 x f(flicker rate) nm. This function, and the overall L-channel cone-fundamental function is described conceptually in Section 17.2.3.5.4. The peak spectral responses of the primates are better represented by probe data obtained at the output of stage 1 or stage 2 circuits. Such data is shown for the rhesus monkey in Section 17.1.5.

The human luminance spectra measured with narrow band filters (less than 10 nm FWHA) using flash or flicker techniques below 3 Hz, correctly point toward the peak wavelengths of the underlying absorption spectra (except for the UV spectra). By employing differential chromatic adaptation within the above constraints, the individual absorption spectra can be isolated more precisely (to levels of ±5 nm or better). Precise measurement of the

185Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd Ed. NY: John Wiley & Sons 158 Processes in Biological Vision

L–channel absorption spectrum (peak and skirts of the absorption spectrum) requires careful attention to the protocol used. Effort is required to insure the measurement represents an intensity threshold rather than a chromatic discrimination. In general, the protocol should employ a chromatic adaptation interval of over 500 ms followed after at least 30 ms by a test stimulus of at least 150 ms.

17.2.4.5.4 Graphic comparison of spectral characteristics

The spectral characteristics found in the literature fall into two distinct classes.

Figure 17.2.5-8 provides a graphic comparison of the various spectra claimed to represent the performance of the human visual system. The ordinate for curves E, F, G & H are as presented by Foster. Curves A through D are scaled to the same relative scale but are displaced vertically for clarity.

The key functions to understanding these spectra are curves C and D from Sharanjeet-Kaur et al. They show a complex curve obtained using flicker radiometry (frequently mislabeled photometry but not involving the visibility function) at 1 Hz and a highly smoothed curve obtained with the same subject and test set at 25 Hz. As developed in the above discussion, both the S-channel and L-channel components of the overall curve are suppressed at higher flicker rates, with the critical flicker frequency at 3 Hz. As noted, the color temperature of the background has minimal impact on the response obtained at a given flicker frequency. Thus the overall spectral performance of the human eye is a function of both the spectral channel of interest and the flicker frequency of the protocol. The data of Sharanjeet-Kaur et al. confirms the earlier data of King-Smith &

Figure 17.2.5-8 A comparison of various spectra claimed to represent human vision. Curves C & D from the same individual are key. Curve C at a flicker frequency above CCFF is distorted compared to Curve D acquired at a frequency below the CCFF. Curve D and below provide a better representation of the spectra of vision. See text. Performance Descriptors 17- 159

Carden186.

Curves A and B were acquired by Stockman et al. using flicker radiometry at 17 Hz in a complex stimulus protocol. xxx Their selection of conditioning wavelengths was based primarily on anecdotal evidence (page 2473 & 2475). The amplitudes of these conditioning wavelengths appear to be arbitrary, and in hindsight inadequate. The preferred conditioning wavelengths would be close to the peak wavelengths of the channels to be suppressed. Some variation is desirable to avoid interfering with measurement of the skirts of the spectrum of interest.

While obtained at 17 Hz instead of 25 Hz, the Stockman et al curves are smoothed even more than curve C from Sharanjeet-Kaur et al. They give a peak wavelength of 545 nm for the M– fundamental and 570 nm for the L– fundamental at 17 Hz. These peaks were obtained using a modest degree of chromatic adaptation. They provided no curves obtained at higher degrees of adaptation. As noted above, by increasing the degree of chromatic adaptation, the peaks in the L-fundamental response moves closer to 625 nm and the peak in the M-fundamental response moves closer to 532 nm. These considerations extend the overall spectral performance of the human eye to a function of the spectral channel of interest, the flicker frequency of the protocol and the level of chromatic adaptation. The limitations are not restricted to mechanisms within the photoreceptors. The “fundamentals” of vision should not be associated with the terms “cones” or photoreceptors. The “fundamentals” of vision relate to the spectral channels of vision.

In 1999, Stockman et al. provided an S-fundamental response based on an entirely different protocol at one Hertz. The resulting curve is shown dashed. Note, the peak sensitivity occurs very near the theoretical value of 437 nm, its two skirts are symmetrical and the skirts exhibit a slope predicted by the Helmholtz-Boltzman equation. By reducing the flicker frequency below CCFF, the researchers have obtained an S-fundamental response that is dependent primarily on the characteristics of the S-photoreceptor. It is equivalent to the photoreceptor excitation spectra.

While the expression “cone” is a convenient semantic shorthand for photoreceptor, the term is misleading in that it implies there are non-cone photoreceptors.

The set of two curves labeled E and curves F, G & H were obtained by Foster and Snelgar from a single subject using 200 ms flash stimulus techniques (essentially zero flicker frequency). The complete spectrum obtained under flash conditions is very similar to curve D obtained under 1 Hz flicker conditions. The measured S-channel spectrum (curve H) peaks very near 437 nm and is equivalent to the theoretical S-channel absorber for wavelengths shorter than 500 nm. The measured M-channel spectrum (curve F) peaks very near 532 nm but its skirts are distorted by the inadequate suppression of both the S-channel and L-channel responses. The measured L-channel response (curve G) peaks near 615 nm, very near the theoretical value of 625 nm. Unfortunately, its short wavelength skirt is distorted due to inadequate suppression of the M-channel and its long wavelength skirt is distorted (not obvious in the original data plot using a different format) by one data point that is probably extraneous.

The data of Foster and Snelgar as well as the S-channel response of the Stockman group is clear; the use of flash radiometry, or flicker radiometry below the CCFF, leads to photoreceptor fundamentals that are representative of the underlying photoreceptor excitation spectra (the actual absorption spectra of the photoreceptors). Data collected under these conditions differ significantly from the M-fundamentals and L-fundamentals of the Stockman group collected at a flicker frequency of 17 Hz. The M-fundamentals and L-fundamentals of the Stockman group properly portray the overall performance of the M-channel and L-channel under high frequency flicker conditions but do not represent the performance of the photoreceptors alone.

186King-Smith, P. & Carden, D. (1976) Luminance and opponent-color contributions to visual detection and adaptation and to temporal and spatial integration J Opt Soc Am vol 66, pp 709-717 [xxx Thornton pg183 ] 160 Processes in Biological Vision

- - - - The flicker method of spectral measurement used by the psychology community is an end-to-end measurement. It is not confined to the measurement of only the spectra of the photoreceptors. The fundamental problem with the flicker method of luminance and chrominance spectral measurements is that it introduces a condition that the visual system was not designed to process. A flickering light source does not occur in the natural world (except due to forest fires and possibly the reflection of sunlight off of moving water). The visual system employs a pulse based stage 3 signaling system. The chrominance encoders of the stage 3 neural circuits employ a carrier frequency that is nominally 30 Hz and phase modulated (Section 14.xxx). This frequency is closely related to, but not the direct source of, the critical flicker frequency (CFF). It is the source of the critical color flicker frequency (CCFF) of the visual system (Section xxx or other ref). The recovery of the chrominance information by the stage 3 decoder circuits is enhanced by the use of a low pass filter with a nominal 3dB point of 3 Hz..

The mathematical description of stage 3 chrominance signaling is complex but the system can be considered an analog modulation scheme or a sampled-data modulation scheme. Consider it a sampled-data modulation scheme for the moment. When the frequency of the flickering illumination approaches the sampling frequency of the stage 3 chrominance channels (30 Hz), the output of the stage 3 system is indeterminante and the number of pulses per unit interval propagated to stage 4 tends toward zero, e. g., little or no information is forwarded to the CNS.

A feature of the stage 3 signaling system is that the more inhibiting the stage 2 signal applied to the stage 3 encoders of the O–, P– & Q– channels, the fewer the number of pulses within the nominal integration interval associated with the CNS and represented by its reciprocal, the CFF. Because of the univariance principle, this means the longer the wavelength of the L–channel stimulus or the more saturated that stimulus, the less information propagated to the CNS within the integration interval. Similarly, the shorter the wavelength of the S–channel stimulus or the more saturated that stimulus, the less information propagated to the CNS.

As seen in the discussion above, using the flicker method of colorimetry in an end-to-end psychologtical measurement leads to a change in the reported peak spectral frequency of both the M & L spectral channels as a function of the flicker frequency. Figure 17.2.5-9 shows a conceptual graph of the reported peak wavelength of the long wavelength (L–channel) photoreceptors as a function of flicker frequency. The long pulse measurements of Sperling & Harwerth, Thornton, many others and more recently Babucke (Section 17.2.1xxx) have generally given a peak wavelength in the 610-620 nm region while the higher flicker frequency approaches have reported peak wavelengths in the 560-580 nm region. The theoretical peak at 625 nm is in agreement with the values reported for a variety of non human chordates (Sections 5.5, 5.7, & 17.1.5). Any theoretical value is always subject to perfection of the model, but it appears the current value is defendable.

Figure 17.2.5-9 Predicted long wavelength peak versus flicker frequency. Performance Descriptors 17- 161

Figure 17.2.5-10 provides an alternate form showing the independent variable, flicker frequency, on the ordinate scale. The data shows the theoretical value for the peak wavelengths at zero frequency along with the reported values of Stockman et al. at 17 Hz using a 561 nm pre-conditioning stimulus and a 2 degree field centered on the point of fixation. It is interesting that the Stockman et al. values appear to be converging on the wavelength of the preconditioning stimulus. This suggests the neural system is losing its ability to ascertain individual colors as the exposure interval is being reduced. As a result, the reported wavelength is a weighted average of the pre- conditioning and test stimulus wavelengths. The curves suggest the reported stimulus for both the M– and L– channel photoreceptors would converge on 561 nm at frequencies equal to and above the critical flicker frequency.

Also shown is the 3 dB bandwidth of the stage 3 signal projection channels. As noted above, others primarily of the University of Chicago psychology school report values similar to those of Stockman et al. Many others reported values are along the curves shown at locations within the gray box. These values were obtained using long pulse or low frequency flicker techniques. Stockman, Sharp & Fach have recently provided a value for the S–channel photoreceptor at 1 Hz flicker frequency. While the data is primarily graphical, for both central and peripheral fixation, the peak value is given as 440 nm at a granularity of 5 nm in their Table 3.

No empirical values for the peak UV wavelength were found in the literature, except those deduced from the complete visibility spectra. The individual spectral responses typically have broad peaks. As a result, the reported peak wavelength is subject to the mathematical approach used to define the peak. 162 Processes in Biological Vision

Figure 17.2.5-10 The flicker frequency versus peak spectral wavelength relationship. The values at 17 Hz are those of Stockman et al. of 1993, using a 561 nm pre-conditioning stimulus. Values along the curves falling within the gray box have been reported by many investigators (see text). The tabulated 1 Hz value of 440 nm for the S–channel is from Stockman, Sharpe & Fach of 1999. The 3 dB bandwidth of the stage 3 signal projection channels is estimated from this work.

In summary, the term “cone fundamentals” is a misnomer as discussed in detail on the web page, http://sightresearch.com/files/conefundamentals.htm The spectral responses defined by this label do not relate to the intrinsic spectral responses of the chromophores or photoreceptors of human vision.

17.2.6 The performance of the eye under unusual illumination conditions

The community has found it difficult to define the transition points between the various regions of vision based on stimulation intensity. Wyszecki & Stiles review the literature. For general purposes, the transition between the photopic and mesopic regions can be defined as 3-5 cd/m2. The transition between the mesopic and the scotopic is generally taken as near 10-3 cd/m2.

17.2.6.1 The full eye at very reduced irradiance (Scotopic region) Performance Descriptors 17- 163

17.2.6.1.1 Comparison with the scotopic research literature

There has been very limited laboratory research on the scotopic performance of the human eye. Determination of the scotopic luminosity function is much more difficult than for the equivalent photopic function. It was not until the 1940's that experimentalists achieved reasonably repeatable results187. To achieve repeatable results, i. e., achieve an adequate signal to noise ratio, it was necessary to expand the size of the stimulus to a larger diameter object field. The tests were still performed with incandescent illumination sources and, as found for the photopic case, these low temperature sources were a better approximation of an equal photon flux source than they were of an equal-energy source. The current standard was derived from tests on less than 100 subjects and the statistical variation was significant188. The subjects were dark adapted for one hour before the experiments. One hour is a reasonable period for convenience but does not meet the normal criteria for full dark adaptation. Although various references suggest the C.I.E. function is for a field located at least five degrees from the fovea, the data was not collected under that condition. Crawford collected the original data using a 20° diameter bipartite field with a vertical dividing line189. The subject was asked to fixate on the top of the dividing line and compare a “white” field with the test field. The white field had a nominal luminous intensity of 3 x 10-5 candela per square meter and was viewed through the natural pupil.

The scotopic luminosity function is basically a description of the signal to threshold ratio relationship of the eye in perceptual space under a specific set of conditions. The conditions are that the threshold level is determined by the cortex, and not quantum noise, that the adaptation amplifiers in all of the three spectral channels are operating at maximum gain, but the incident radiation level is so low that the gain coefficient of the L-channel is negligible relative to the coefficient of the M-channel, due to the square-law term in the L-term in the luminance summation equation. Under these conditions, the S- and M-channel gain coefficients maintain a fixed relationship with each

other and this relationship is typically kS:kM:kL::50:1000:(<1) when including the absorption of the lens group. The absolute value of these coefficients decrease with radiant intensity level and the signal to threshold ratio of the system decreases continuously with radiant intensity. This is measurable at the output of the pedicles where the average signal level decreases with decreasing radiant intensity. The dynamic range of the scotopic region is constrained at the lower radiant intensity by the signal to threshold ratio at which the subject can perceive a change in the stimulus. Perception at this level is strongly dependent on spatial integration of the signal in the cortex. This condition is controlled primarily by the size of the stimulus in object space.

Brown & Wald190 have provided their measurement of the scotopic response in Figure 17.2.6-1. No range bars were provided. The measurement was performed under psychophysical conditions using a large field of view. Suppression of the L–channel photoreceptors was by bleaching with a “yellow light.” This curve differs considerably from the CIE adopted standard discussed in the next paragraph. It can be matched by a theoretical curve where the L–channel response was nearly completely eliminated and the M–channel response was reduced relative to its normal sensitivity relative to the S–channel. As a result, the curve shows a peak as expected by the Bezold-Brucke Effect near 494 nm. The peak would have changed to 532 nm if a bleaching light with less radiation at wavelengths shorter than 600 nm had been used, i.e., a red light. The resulting difference response would have more closely matched the calculated scotopic response and the CIE standard.

187Crawford, B. (1949) The scotopic visibility function Proc. Phys Soc B vol. 62, pp 321-334 188Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons, pp. 395-396 189Wyszecki, G. & Stiles, W. (1982) Op. Cit. pg. 396 190Brown, P. & Wald, G. (1964) xxx Science vol 144 pp 45-52 164 Processes in Biological Vision

Figure 17.2.6-1 The difference spectrum recorded psychophysically in the human retina (parafoveal region). The spectrum was obtained by recording the dark adapted spectrum and then subtracting the spectrum obtained by recording response after a brief exposure to a very bright yellow light. The .spectra were recorded in a darkened room using very low light intensities. Note the inflection points suggestive of the summation of the S– and M–channel responses. Note also the major peak near 494 nm indicative of the theoretical peak described by the Bezold-Brucke Effect. From Brown & Wald, 1964. Performance Descriptors 17- 165

17.2.6.1.2 Comparison with the scotopic standards literature

The current C.I.E. (1951) Scotopic Luminous Efficiency Function for a 10° field is shown by the long dashed line in Figure 17.2.6-2. It is slightly asymmetrical but exhibits no inflection points.

Also shown in this figure is the theoretical scotopic luminous efficiency function based on this work. This function is computed similarly to the theoretical photopic luminous efficiency function at a spectral interval of 0.5 nm. The three absorption spectrums of the visual chromophores, the Rhodonines, are shown normalized at the bottom of the graph based on the half amplitude absorptions parameters of the Standard Human Eye.. The half amplitude value for these spectrums is shown by the horizontal dash-dot line. The L-channel chromophore is shown dotted since the baseline assumption is that it does not participate in scotopic vision. Based on this assumption, the theoretical function is computed by logarithmic summation using the same absorption coefficients as for the photopic function except the L-channel coefficient has been set very low. The result is the solid line in the figure. The theoretical function shows several important features. As in the photopic case, there is a perceived peak in the spectrum near 490 nm that is not directly related to either of the absorption spectrums alone. Second and as expected, the function shows a rapid drop in sensitivity for wavelengths beyond 565 nm. Third, the long wavelength skirt of the function is defined by the Fermi-Dirac equation.

When compared to the theoretical function, the C.I.E. Standard shows two characteristics. First, the long wavelength skirt of the function cannot be represented by a Fermi-Dirac function or the templates of Dartnall. The long wavelength skirt does resemble a mesotopic luminosity function as shown by the short dashed line blending

into the solid line near 570 nm. This line was calculated for a set of absorption coefficients, kS:kM:kL::50:1000:5. The long wavelength skirt of the C.I.E. Standard matches the long wavelength skirt of this mesotopic function quite well. This suggests that the test procedure used in acquiring the data for the standard was not entirely adequate. The stimulus was in fact a factor of five too high in intensity for the purpose of evaluating the scotopic luminosity function. To achieve an accurate scotopic luminous efficiency function for research purposes, the experiments need to be repeated even if the test stimulus size must be expanded beyond 10°.

Second, the C.I.E. Standard has been smoothed to a high degree in the process of averaging the spectral responses of the individual test subjects. A theoretical function based on the coefficients, kS:kM:kL::50:1000:5 and smoothed with a 35 nm wide Gaussian filter provides an accurate portrayal of this empirical function, the current Standard. However, the calculated peak wavelength is at 525 nm, not the Standard value of 507 nm. The functions are quite flat in the region between 507 and 525 nm and the specification of the peak value is subject to how the data was interpolated.

17.2.6.2 The full eye under transition Figure 17.2.6-2 Comparison of the theoretical and other conditions (Mesopic and Mesotopic scotopic data. Solid line, theoretical scotopic luminosity function with k :k :k ::50:1000:(<1). Short dashed line, regions) S M L kS:kM:kL::50:1000:5. Long dashed line, C.I.E. Scotopic Luminosity Function (1951) The relative absorption This work makes a distinction between the overall spectrums of the Rhodonines are given in the bottom of the figure. 166 Processes in Biological Vision

mesopic region and the more carefully specifically defined mesotopic region (Section 17.1.1.2.1). The clinically defined mesopic region relates to a variety of phenomena due to a series of underlying mechanisms. The mesotopic region relates only to the neurologically based mechanisms supporting these phenomena. In the past, these regimes have been separated experimentally by using a small artificial pupil (typically 2mm in diameter). With the artificial pupil, only the mesotopic region is explored.

Discussion of all of the changes in variables occurring within the mesopic range, and only the variables changing within the mesotopic range, is complicated. While the visual system is largely dynamic range limited at the top of the mesopic and mesotopic ranges, and largely internal noise limited at the bottom of these ranges, the intermediate range exhibits limitations depending on a variety of mechanisms in the individual spectral channels and the resulting luminance channel. Precisely mapping all of these phenomena and mechanisms is beyond the scope of this work.

There is little precise data relating to the mesopic or mesotopic range in human vision. This is largely because the CIE protocol for measuring the spectral sensitivity of the human eye (the so-called luminous efficiency function) is not amenable to direct measurement as a function of stimulation level.

Recent data for DG taken by Verdon, Haegerstrom-Portnoy & Schneck have provided calibration for the loss of long wavelength sensitivity as a function of stimulus intensity. DG exhibited normal photopic spectral sensitivity at 3.4 log scotopic Trolands. However, his sensitivity in the red was reduced by between 30:1 and 100:1 at both 1.9 and 2.4 log scotopic Trolands. Figure 17.2.6-3 shows this data in greater detail. The reference spectra were not summed logarithmically to show the theoretical photopic and scotopic spectra as shown in the previous figure. No accommodation was made for the absorption of the lens of the eye in the short wavelength region. Section 18.8.3.6 discusses the vision of DG in greater detail.

17.2.6.2.1 The physiological mechanisms associated with the mesopic region.

There are two major situations related to the physiological optics that impact performance in the mesopic region. The secondary role of the operation of the iris in controlling the stimulus intensity applied to the retina has been discussed in Section 2.4.3.1. The more critical role of the iris in controlling the quality of the image projected onto the foveola, and described using the Stiles-Crawford Effect, is discussed in Sections 2.4.2 & 2.4.5. The Stiles-Crawford Effect itself is discussed in Section 17.3.7. While the diameter of the pupil determines the mean stimulus level of the image applied to the retina, it also significantly impacts the spatial contrast of that image Figure 17.2.6-3 ERG data showing the change in spectral (see Section 17.6.3.4). sensitivity with stimulus level in the achromatope, DG. No data points were obtained at wavelengths below 500 nm for the trichromat or for DG. From Verdon et al., The physiological component of the mesopic region is 1997. nominally described as beginning at 104 cd/m2 with the beginning of the iris opening and ending at 3"10-3 cd/m2 with the completion of the opening process. This is a broad range. However, the actual change in stimulus intensity at the retina due to the action of the iris alone is only a factor of 16 to 1. Performance Descriptors 17- 167

17.2.6.2.2 Brief summary of the neurological phenomonology and mechanisms

[xxx rewrite concerning efficiency ] The mesotopic luminosity region represents a major part of the transition between the photopic and scotopic regions. The performance of the visual system within the mesotopic intensity region can be described rigorously. All of the photodetectors of the eye continue to exhibit the same quantum efficiency in the mesotopic region under the theory of this work. However, the psychophysical luminosity function changes continuously in the mesotopic region as a function of the photon flux rate absorbed by the L-channel photoreceptors. As a result, the long wavelength portion of the luminosity function changes form continuously as the stimulus intensity changes. The transition between the scotopic and photopic regions is a smooth, although not linear one. The L-channel performance rises according to a square-law relationship.

The mesotopic luminosity function is basically a description of the signal to threshold ratio relationship of the eye in perceptual space under a specific set of conditions. The conditions are three. First, that the pupil size is constrained to a fixed diameter. Second, that the threshold level is largely determined by the quantum noise associated with the radiant intensity of the stimulus, on an individual spectral channel basis, and not on the threshold level of the cortex. The third condition relates to the gain of the adaptation amplifiers associated with the individual spectral channels. The loss in color constancy occurs when the adaptation amplifiers associated with at least one of the spectral channels reaches their maximum gain. This point establishes a technical definition of the photopic mesopic transition. However, there is no data showing at what point the human is able to perceive this loss in color constancy. It probably occurs at a lower stimulus.

In the mesotopic region, both the gain coefficients and the RMS noise threshold associated with each spectral channel are changing with stimulus level. The amplitude portion of the theoretical mesotopic luminosity function is easily calculated by logarithmic summation as were the photopic and scotopic functions of earlier paragraphs. Under these conditions, the gain coefficients maintain a fixed relationship with each other, however, the quantum noise is different in each spectral channel and the quantum noise in the L-channel exhibits a more complex relationship than it does in the other two. While the typical gain coefficients associated with the neurological circuitry remains near the kS:kM:kL::100:1000:300 level at the top of the mesotopic region, the “effective values” related to the L–channel begin to fall as the first power of the stimulus in that spectral region. At a level of 300:1 below the mesotopic threshold, the contribution of the L–channel signal to the performance of the luminance channel (as well as the Q–chrominance channel) is essentially negligible.

The mesotopic component of the mesopic region in humans is nominally described as beginning with the loss of color constancy. This occurs near 104 cd/m2 corneal exposure with the beginning of the closing of a 8 mm diameter iris, or at 6"102 cd/m2 using a 2mm artificial pupil.

One technical definition of the transition between the mesotopic and scotopic regions in humans is the loss of any perception of color. This normally occurs near 3"10-3 cd/m2 corneal exposure.

The transition between the mesotopic portion of the mesopic region and the scotopic region can also be defined electrophysiologically in at least two ways.

A first technical definition is that stimulus level where the signal component in the luminance channel falls below the noise component at the location of the stellate cells of the CNS. Below this level, the visual system is internal- noise limited. It can still perform, using spatial integration. However, its performance degrades rapidly.

A second technical definition, would define the transition between the mesotopic and scotopic regions as that 168 Processes in Biological Vision stimulus level where the noise contribution of the luminance channel is equal to the noise contribution of the stellate cells of the CNS. This constitutes a totally electrophysiological definition. The difference in stimulus level between these two technical conditions is not known.

These technical points are difficult to determine psychophysically and require sophisticated electrophysiological instrumentation.

The neurological (mesotopic) extent of the human mesopic range under these definitions can be as high as 2"105 to 1. Alternately, it could be lower if the CNS noise dominance should occur prior to the loss of the perception of color. It is believed the loss in color perception is defined by a specific net signal to noise ratio in the luminance channel. In man-made systems, this would generally be defined in terms of a ratio of about than 6:1 (peak signal to RMS noise).

Computation of the noise contributed by the S– and M–channel signals, as well as the noise contributed by the stellate cells of the CNS, is academic at this time. There is no available data to compare with the computations.

Neumeyer, et. al191. made a variety of measurements with goldfish and referenced similar data for honeybees that repeatedly suggested a unique range of log1.5:1 (or 30 to 1) in stimulation intensity. They labeled this range the achromatic interval and described it as the difference between the threshold for merely sensing “light” and sensing “color.” The lower limit of this range was described as 1.5 lux for the goldfish. The meaning of this narrow achromatic interval is unclear.

17.2.6.2.3 Caricature of the mesotopic luminance threshold function, T(λ,F)

Figure 17.2.6-4 builds on the baseline developed in [Figure 17.2.1-1] to illustrate the spectral response of the eye under mesotopic conditions (conditions where the pupil size is fixed)192. It uses the equations of this chapter and Chapter 16. The loss in sensitivity in the long wavelength region of the spectrum is obvious as the stimulus level is decreased. The curve mesotopic #1 represents a loss in sensitivity of 10:1 relative to the sensitivity normally observed at the lower limit of the photopic region. Mesotopic #2 represents a loss of 100:1 compared to the lower limit of the photopic region. If the eye is chromatically adapted at the top of the mesotopic region by suppressing the M-channel sensitivity, or if the spectrum of the stimulus is deficient in the M-channel region, the regions labeled the Bezold (Bezold-Brucke) Effect and the Purkinje Effect can be observed. See Section 17.2.3.4. The Purkinje Effect is ultimately lost as the sensitivity of the L–channel is lost.

191Neumeyer, C. Wietsma, J. & Spekreijse, H. (1991) Separate processing of “color” and “brightness” in goldfish. Vision Res. vol. 31, pp 537-549 192Fulton, J. (1985) The perception of luminance under various states of adaptation (unpublished) Performance Descriptors 17- 169

17.2.6.2.4 Comparison with the Mesopic literature

There is very little literature concerning the incident or perceived spectral characteristics of the Mesopic region. The CIE formed a panel (TC-1.4) in 1979 to explore the mesopic regime but it went nowhere. The CIE formed a panel in 2000 that began its work in 2004,CIE TC1-58 with the charter, ‘‘To define mesopic visual performance and related terms. To investigate performance based photometry in the luminance region below approximately 10 cd/m2. To propose a model for the basis of performance based mesopic photometry.’’ The work of this group will be discussed after the following review of earlier work.

Weaver proposed a provisional standard observer in 1949193. However, his paper provided very little documented support. Since his figure has been referenced in later works in modified form, it is Figure 17.2.6-4 Caricature of human luminance threshold important to present this curve in its original form and response under mesotopic conditions (pupil size fixed). to stress that there are no measured data points Mesotopic levels #1 & #2 are one and two orders lower in between -4 and 0 log brightness on this curve. Weaver threshold than for the lower edge of the photopic condition (lower limit of color constancy). was asked to construct an interpolated data set to cover this region for purposes of a British Standard on paints.

He wrote in 1949: “These tables were based on observational data taken at the photopic and scotopic levels, together with interpolations for intermediate levels carried out by a method which was admittedly arbitrary but was considered reasonable as a first approximation.”

He did not include any original observational data nor did he specify the characteristics of the illumination assumed. Thus, he postulated the two end points of his graph based on scotopic and photopic conditions and drew a reasonable curve between them. It appears he relied upon the peak wavelengths stipulated in the CIE Luminous Efficiency Standards. These are 555 nm for the photopic 2° (on-axis) standard adopted previously in 1924 and 507 nm for the scotopic 10° (5° off-axis) standard adopted subsequently in 1951. These are large fields relative to the foveola and to the size of typical objects in a scene. He did not address the other parameters associated with these values.

This work does not support the figure of Weaver. Weaver appears to have selected data points that are not from a consistent data set. Figure 17.2.6-5 shows the original curve of Weaver along with some additional notation. Weaver’s data is based on an equal energy assumption and used a 2360 Kelvin light source (which was in common use as a reference at the time). While his data was collected using a 2.6 degree field, it was “adjusted” to conform to the CIE Standard. He did not say which standard.

It is important to differentiate between the baselines used in the figure. This work uses the absolute peak associated

193Weaver, K. (1949) A provisional standard observer for low level photometry. J. Opt. Soc. Am. vol. 39, pg. 278 170 Processes in Biological Vision with the proposed luminance threshold function, T(λ,F), for scene objects of less than 0.5 degrees. Weaver used the centroids of the CIE Standards, V(λ) and V’(λ) for large scene objects. It is also important to recognize the considerable difference between the relative response of the CIE Standards and actual human vision in the region of 400-450 nm. This has been documented by Weaver and by Judd. The difference is discussed elsewhere in this work.

Weaver describes the transition between the photopic and scotopic regions as 0.5 foot-lamberts. Newhall194 gives the luminance at the transition between the photopic and scotopic regions as between about 0.01 and 0.1 foot-lamberts.

Figure 17.2.6-5 Theoretical and putative empirical shift in spectra going from photopic to scotopic vision. The solid curved line without data points or error bars is from Weaver, 1949. The horizontal line is based on the peak value of T(8, F) and the equal photon flux assumption of this model.

194Newhall, S. in (1963) The Science of Color. NY: Optical Society of America pg. 105 Performance Descriptors 17- 171

Ikeda & Shimozono provided data that is in complete agreement with this work if certain minor changes are made in the interpretation of their data195. Their spectral filters were nominally 10 nm wide (half width) and they reported an “almost double-peaked shape” for the overall spectrum. If their filters had been 5 nm wide (half width), their data would have been much clearer. It would have resolved the notches between both the M- and L-channels ( at 572 nm) and the S- and M-channels (at 494 nm) more clearly. Resolving these notches makes it clear that neither of the functions they used in the following equation were unitary. They used a logarithmic summation of the terms in the

luminance equation where the term SR(λ) referred to the “rod” spectrum associated with the scotopic visibility function instead of the more specific spectrum of the combined S- and M-channel photoreceptors. Their term SC(λ) referred to the “cone” spectrum instead of the complete spectrum of the combined S-, M- and L-channels.

Ideda & Shimozono did use a mathematical model of the visual system involving the sum of two logarithmic evaluations of the spectral response. In their case, they employed the logarithm of the overall luminous response rather than the logarithm of the individual spectral responses as proposed here.

Figure 17.2.6-6 reproduces figure 1 of Ikeda & Shimozono to illustrate the variation between subjects taken under as similar conditions as possible. The vertical lines at 437, 532 and 625 nm have been added to show how the data relates to these wavelengths, in some cases peaking at those wavelengths. The Ikeda & Shimozono data was acquired using 20 nm FWHA filters. They suggested that one photopic Troland equalled about 2.4 scotopic Trolands using their reference Xenon-arc light. They used a bipartite field approach and the method of adjustment. Five measurements in each of three sessions were used to characterize each data point. Approximately 30 minutes of dark adaptation preceded each data collection session. They represent that the two upper curves acquired at –2- log photopic Trolands, although demonstrably different and with both subjects still perceiving a reddish coloration to the long wavelength test fields, are characteristic of human scotopic vision. It is not clear how their –2-log photopic Trolands compares with the commonly accepted start of the scotopic region at 3 x 10–4 cd/m2 viewed with a natural pupil (Table 2.1.1-1). The scotopic region is defined as color perception free.

Figure 1 of Ikeda & Shimozono can be compared favorably with the more detailed Figure 17.2.6-7, figure 3 from Hurvich &

Figure 17.2.6-6 Luminous efficiency functions at nine retinal-illuminance levels; two subjects. Top to bottom: –2-log, –1.5-log, –1-log. . . ., 1.5-log, and 2-log photopic Trolands. From Ikeda & Shimozono, 1981.

195Ikeda, M. & Shimozono, H. (1981) Mesopic luminous-efficiency functions J Opt Soc Am vol 71(3), pp 280-284 172 Processes in Biological Vision

Jameson of 1953196. Ikeda & Shimozono operated over four log units while Hurevich & Jameson operated over 4.5 log units of luminance. The Hurvich & Jameson data are inverted as they show radiant intensity of the stimulus rather than the radiant sensitivity of the retina. This figure is in even better agreement with this work. While a bit more noisy due to the narrowness of the filters used, the location of the notches near 494 and 572 nm are shown more clearly and the saturation in the M-channel spectral response at high light levels (near the top of the figure) due to photoreceptor saturation is beginning to show explicitly. Vertical lines have been added at 437, 532 and 610 mμ for reference.

Hurvich & Jameson provided very detailed descriptions of their apparatus and calibration procedures. Their spectrally selective filters exhibited wavelength bandwidths “with the entrance and exit slits fixed at 0.2 mm ranged from 1.5 mu at 413 mu to 7.6 mu at 680 m. They also offered investigators statistical data on their measurements upon request but did not provide any hints regarding this statistical data. The jaggedness of their individual trace suggests more test data would be useful at each measurement wavelength.

“The spectral sensitivity of the fovea of the right eye of each of two practiced observers was measured at 10 m intervals from 400 mμ to 700 mμ for the dark-adapted neutral state, and from 405 mμ to 700 mμ for the bright-adapted neutral state (white, 10 mL). Ten complete luminosity functions were obtained for each observer for each of the two states of adaptation. The foveally fixated test field was elliptical in form and subtended 1° X 0.80° at the observer's eye, and the circular surround for the bright-adapted condition subtended a visual angle of 37° at the observer's eye. In the dark-adapted neutral condition central fixation was achieved by the use of a small reflected red fixation dot, and in the bright-adapted state, by fixating the dark elliptical 1° field centrally located in the illuminated surround. The test stimulus appeared within the fixated area and was exposed for 0.045 sec.

The selection of an absolute white adapting stimulus which satisfies the conditions of both perceptual and physiological neutrality was achieved separately for each observer in a similar series of steps.”

196Hurvich, L. & Jameson, D. (1953) Spectral sensitivity of the fovea. I. Neutral adaptation J Opt Soc Am vol 43(6), pp 485-494 Performance Descriptors 17- 173

Figure 17.2.6-7 Luminance sensitivity variation from photopic to scotopic regimes. Note the formation of notches near 494 and 572 nm as the light level is increased and the broadening of the central peak at high light levels due to photoreceptor cell saturation. The ordinate scale is correct for the lowest function. The other functions are displaced successively by 0.5 log unit on the ordinate scale. From Hurvich & Jameson, 1953. 174 Processes in Biological Vision

Hurvich & Jameson note the re-evaluation of the CIE Luminosity function under way in 1953 and assert, “It is amply clear that a considerable body of experimental evidence is now available which contradicts the more traditional notion that the luminosity function exhibits ‘a notable symmetry’. We are in agreement with Thomson who, on the basis of a detailed statistical analysis, concludes that ‘one can say with confidence that the spectral sensitivity of the centre of the central fovea cannot be a smooth single-humped function’.”

Thornton has overlaid the data points of Ikeda & Shimonozo for subject HS at scotopic levels with a curve generated by the sum of three Gaussian functions, with peak frequencies at 450, 530 & 610 nm with excellent empirical results. Figure 17.2.6-8 shows the same quality of results can be obtained by overlaying the data points with a spectral response formed of the sum of the logarithmic values of each spectral channel (based on the Helmholtz- Boltzman equation) using the standard wavelength values of this work (effective peaks at 437, 532 & 625 nm. The relative spectral amplitudes (inside the log) were 25, 1000, 28 ( 1.40, 3.0 & 1.45 outside the log operation) and the curve was smoothed using “medsmooth” from MathCad, with a smoothing parameter of seven, to accommodate the relatively wide spectral filters of the investigators.. Various other smoothing, interpolation and regression formulas can be used to smooth the underlying functions, but the theoretical function is entirely adequate recognizing the variations from subject to subject and even session to session for one individual. The large 10 degree visual angle bipartite field also suggests some variation of sensitivity within this large retinal field (the non-uniformity of Maxwell’s spot as a minimum).

The fit of the theoretical function in the figure to the measured data can be optimized further by adjusting the wavelength parameters of the chromophores in steps of one or two nm. However, the variation between individuals (both in the average diameter of their outer segments and between states of adaptation achieved in different test sessions by the same individual) makes this an unproductive approach. The diameters of the outer segments of the photoreceptors have been shown to be significant in the Stiles- Crawford Effect (Section 17.3.7) measurements from individuals.

Kurtenbach Meierkord & Kremers have provided an analysis of data collected from trichromats, deuteranopes (red-green colorblind but with full spectra, including an L-absorber) and protanopes (lacking an L-absorber)197. While the paper is well crafted, and employs 4-nm half-bandwidth filters and a Figure 17.2.6-8 Overlay of measured data with theoretical 6000 Kelvin adapting background, their protocol function from this theory. Dotted curve from theoretical introduces problems. Their measurements were made calculation of this work, with peak spectral wavelengths at intervals much wider than 4-nm. Their empirical at 437, 532, & 625 nm. Data from Ikeda & Shimonozo, equation for trichromats employs a linear summation 1981, solid curve from Thornton, 1992. based on six explicit and two implicit free parameters. Their measurements were made at five degrees eccentricity. Their measured data appears to be noise limited at low mesopic intensities. At high intensities, they report spectral responses for the trichromats exhibiting three peaks at 450, 540 and 610 nm.

197Kurtenbach, A. Meierkord, S. & Kremers, J. (1999) Spectral sensitivities in dichromats and trichromats at mesopic retinal illuminances J Opt Soc Am A vol 16(7), pp 1541-1547 Performance Descriptors 17- 175

Babucke198 has compared his measured mesotopic data with the empirical equations from the MOVE-project and from Kurtenbach et al. and the theoretical equation of this work. He found the theoretical equation provides a better fit as shown in Figure 17.2.6-9. The Kurtenbach et al. data was best fit by eliminating the L-M term (setting their

coefficient fD to zero) from their overall equation.

CIE panel TC1-58 recently released an interim report with data in exceptionally good agreement with this work. The report is called the MOVE (Mesopic Optimisation of Visual Efficiency) report and is available on the Internet199. The report provides data and modeling at an intensity level of 0.1 cd/m2 (0.03 foot-lamberts) at an eccentricity of zero degrees. Data was also collected at 10, 1 & 0.01 cd/m2 for eccentricities of zero and ten degrees and for targets of two and 0.3 degrees diameter.

Figure 17.2.6-10 shows the excellent agreement between figure 10 of the MOVE report and this work. It specifically shows the peaks in the luminous efficiency spectrum resulting from the short, medium Figure 17.2.6-9 A comparison of theoretical and and long wavelength photoreceptors at 437, 532 and empirical curve fitting to mesopic measurements. As 610 nm (indicated by the vertical indicia), with the noted, the best fit to the measured data was achieved without using the subtractive term in the Kurtenback et al. effect of the lens absorption impacting the short analysis. From Babucke (personal communication, 2008). wavelength response in the region of 437 nm slightly. The “chromatic model” was developed by the MOVE team is a simple linear empirical model. The luminance level used is at the transition between the photopic and mesotopic regimes. The amplitude of the long wavelength peak may be reduced marginally at this intensity level, and will begin to drop precipitously as the luminance level is reduced further. This fact is not considered or predicted by the MOVE chromatic model.

198Babucke, H. (2008) In German www.dgao-proceedings.de ISSN: 1614-8436 199www. lightinglab.fi/CIETC1-58/files/MOVE_Report.pdf dated (2005) ISBN: 951-22-7566-X 176 Processes in Biological Vision

Figure 17.2.6-10 Recent MOVE data on luminous efficiency. Spectral sensitivity measured directly using contrast threshold techniques (eccentricity 10o) compared with that generated using a linear chromatic model at 0.1 cd/m2 (0.03 foot-lamberts). The linear model was developed by the MOVE team. Note the linear vertical scale. The measured spectral peaks at 437, 532 and 610 nm are quite distinct. From the CIE committee report, MOVE, 2004.

Trezona has presented an interesting method of defining the mesopic region based on bipartite photometry200. It is based on the concept that “As long as the spectral luminous efficiency function is unchanged with radiance then a

plot of log Eref versus log Etest is a straight line of unit gradient.” If the luminous efficiency should change, a new plot is obtained. It will also be a straight line of unit gradient. Figure 17.2.6-11 shows this relationship and the measured data points for observer #9. The units are radiometric millitrolands. The10° bipartite matching was

between a D65 source and a 588 nm reference light. The performance of the system is defined by the intercept of the V’ locus and the V locus and the value on the vertical axis of the intersection of the transition curve and the reference line drawn equidistant from the two loci. The V locus is traditionally associated with the luminance function due to the summation of the three spectral channels of vision. The V’ locus is traditionally associated with the luminance function due to the rods. However, in this work, it is just as reasonably associated with the luminance function at low levels in the absence of the L–channel signal, i.e., the logarithmic summation of the S– and M– channels.

Note the transition from photopic to scotopic vision is accomplished over less that two log units change in illumination. for this subject, the midpoint of the transition occurs at about -0.3 = log radiometric millitrolands.

200Trezona, P. (1991) A system of mesopic photometry Color Res Appl vol 16(3), pp 202-216 Performance Descriptors 17- 177

Figure 17.2.6-11 Plot of logEref versus log Etest. Note the use of D65 illumination. The short diagonal line between V and V’, and through 0,0 on these scales, could define the transition between the photopic and scotopic regions. This would define the middle of the mesotopic region. From Trezona, 1991.

The plot does not suggest any mechanism that could be called rod intrusion into the photopic portion of the response. The two portions of the graph operate at two independent levels of luminous efficiency.

Trezona tried again to describe rod intrusion in a short communication in 1995201. The paper did not reach any major new conclusions.

17.2.6.3 The full eye at excessive irradiance (Hypertopic region)

While of largely academic interest (and clinically dangerous to explore), the transition between the photopic and hypertopic regions can be described in terms of at least two technical criteria. The first technical definition of that

201Trezona, P. (1995) Problems of rod participation in large field colour matching Color Res Appl vol 20(3), pp 206-209 178 Processes in Biological Vision transition is where the gain of the adaptation amplifiers of at least one of the spectral channels has reached its minimum value. This corresponds to the initial loss of color constancy at high stimulus levels. Operation above this level is frequently reported as resulting in a yellowing of the observed imagery. Such a report would suggest the initial saturation of the M–channel. A second technical definition is that stimulus level where the conversion efficiency of the outer segments of one of the spectral channels has fallen to its half amplitude value. This level can be defined in terms of the complete P/D Equation of this work.

17.2.6.4 The full eye with enhanced long wavelength irradiance (Purkinje Effect)

When there are significant changes in the relative amounts of illumination falling on the M- and L-channel chromophores of the eye, the visual system performs in an unexpected manner. This effect has been associated with Purkinje who described it from the behavioral perspective.

The Purkinje Effect is the result of the unique confluence of two static and one dynamic mechanisms associated with vision. The existence of the Effect is a result of the logarithmic nature of the signal summing to form the luminance signal in the R–channel. Its existence is also dependent on the relative degree of overlap between the long wavelength skirt of the mid wavelength and the short wavelength skirt of the long wavelength absorption spectrums. The reason the effect is so elusive is its time dependency and its operational complexity. The effect is dependent on the rate of change in sensitivity associated with the dark adaptation amplifier (related to its time constant) being slower than the rate of change in the illumination during sunset. If the rate of decrease in the mid wavelength illumination is greater than the rate of increase in sensitivity due to adaptation by the mid wavelength channel, the sensitivity in this channel relative to the long wavelength channel is reduced. The result is a suppression of the mid wavelength component of the overall response. This leads to an enhancement in sensitivity at a wavelength between the two nominal absorption bands due to the logarithmic mechanism. the overall

Barlow & Levick have provided electrophysiological data on this effect at the ganglion cell of the cat using broad band illumination sources202. The data suggests the transition from photopic to scotopic response occurs over a range of two log units for their filter set. Figure 17.2.6-12 presents the theoretical basis for the Purkinje Brightness Effect. When the signals are summed logarithmically, an artifact appears. The artifact is caused by the overlap in the absorption characteristics of the M- and L-channel chromophores and the relative amplitudes of the signal components in these two channels. When the product of the illumination and the sensitivity of the L-channel is higher than normal relative to the M-channel, the overall luminosity function exhibits a peak sensitivity near 579 nm. As the product of the illumination and the sensitivity of the L-channel decreases relative to the M-channel, as it does with the approach of darkness, the peak in the luminosity function near 579 nm decreases in amplitude. At a certain illumination profile, the luminosity function exhibits peaks of equal amplitude at 532 and 579 nm separated by a trough. At still lower levels of illumination, the absolute peak in the luminosity function is found at 532 nm.

202Barlow, H. & Levick, W. (1968) The Purkinje shift in the cat retina. J. Physiol. (London) vol. 196, pp. 2P-3P Performance Descriptors 17- 179

This Effect is asymmetrical with the diurnal change in outdoor illumination due to the time constants and operating levels of the adaptation amplifiers. It is also a function of the absolute illumination level because of the square-law nature of the L-channel transduction process. It is most commonly observed with the change from photopic to mesotopic vision at twilight.

Note that as the overall luminosity function changes, the nominal peak spectral response shifts in an unexpected manner. As the relative sensitivity of the L-channel decreases, the absorption peak near 579 nm decreases in amplitude relative to the peak near 532 nm. When these two peaks are of equal amplitude, there is a trough between them. As a result of this Figure 17.2.6-12 Theoretical foundation for the Purkinje condition, the peak wavelength associated with the (brightness) Effect. Solid line, kS:kM:kL::50:1000:100. Purkinje Effect changes in a discontinuous manner Dashed line, kS:kM:kL::50:1000:10. Dotted line, from 579 nm to 532 nm. There is never a peak in the kS:kM:kL::50:1000:1. spectrum between 532 and 579 nm.

17.2.6.5 The full eye with suppressed mid wavelength amplifier performance (Bezold Effect)

At excessively high levels of illumination, the visual system fails to perform as discussed above. Prior to significant saturation in the photodetection process, the signal level in the M-channel becomes hard limited by the adaptation amplifier reaching current saturation. As a result of this saturation, the perceived luminosity function exhibits an unusual form due to the logarithmic summation employed in the luminance channel. A similar situation can occur under differential adaptation in the laboratory, even at normal stimulus levels. As the component due to the M- channel photoreceptors is reduced relative to the other two components, two peaks appear in the overall luminosity function as shown in Figure 17.2.6-13. These peaks correspond to the peaks associated with the Bezold- Brucke peaks in the literature. The short wavelength peak occurs near 487 nm and the long wavelength peak occurs near 579 nm for the values assumed here, kS:kM:kL::100:1000:100. This set of constants only represents a 3:1 suppression of the mid wavelength channel. Unlike the Purkinje Effect, the Bezold- Brucke Effect is not transient in character.

It is interesting that this effect appears to be important in the tropical rainforest. Where there is an excess of material in the scene that reflects in the “green” portion of the spectrum, the absorption function of the human eye is broadened and the relative sensitivity of the eye to and aquas is increased disproportionately. Figure 17.2.6-13 Theoretical foundation for the Bezold- Brucke Effect. Absorption coefficients of the Rhodonines 17.2.6.5.1 Background shown on a relative basis at the bottom of the figure. Luminosity function shown for absorption coefficients of kS:kM:kL::100:1000:100. 180 Processes in Biological Vision

The Bezold-Brucke Effect dates from the 1870's. While frequently discussed qualitatively, Walraven is one of the few that have addressed it more quantitatively203. Walraven provides a brief review of the sparse and widely spaced literature. Hering claimed in 1880 that the effect could be explained best using his opponent theory. In 1987, Pierce first attempted a conceptual explanation in terms of the Young-Helmholtz theory. However, the Pierce approach was criticized by Purdy in 1931 because it was not in accordance with the Abney additive laws. Purdy performed measurements increasing from 10 to 1000 Trolands in order of magnitude steps. 10 Trolands corresponds to about 3 x 10-1 cd.m2, near the lower edge of the mesotopic region. 1000 Trolands remains within the mesotopic region. Thus, he was not working in the zone of color constancy. It is not clear how Purdy insured the separation of brightness perceptions from chrominance perception in measuring the hue shifts he reported.

In 1948, Judd and in 1955, Hurvich & Jameson resurfaced the Hering approach as an explanation. In 1961, Walraven provided a conceptually based mathematical description of the Effect based on hue shifts and using the CIE V(8) curve as an absolute reference. Conceptually, he separated the luminance and chrominance channels of vision. In addition, he proposed that the contribution of the S–channel to chrominance was 10-12 times greater than its contribution to luminance. This factor is similar to the 10-16 proposed in this work.

Although Walraven did not include any equations in his paper, he did provide a discontinuous theoretical curve fitting the data of Purdy. The data and curve show no hue shift at 476 and 570 nm and a discontinuity in the region of 503 to 520 nm (Purdy used 508 nm) when the stimulus was raised from 100 to 1000 Trolands in the mesopic region. Walraven noted that his results depended on the selection of appropriate “fundamental sensitivity curves,” reliance on the absolute accuracy of the CIE V(8) function, the introduction of a nonlinearity in each spectral channel, and then a set of arbitrary assumptions concerning the white point. His analysis does revolve around the “interaction” between the integrals associated with the red and green spectral channels and the “interaction” between the integral associated with the blue channel and the integral associated with the sum of the red and green channels. He did not define the color temperature of his conceptual light source or the effect of such a light source on the operation of the visual system in the mesopic region. The curvatures presented by Walraven between 600 and 650 nm appear to be due primarily to the loss in L–channel response associated with the transition from the photopic to the scotopic operating regions. The discontinuity near 508 nm appears to be due to the merging mechanism employed within the CNS. These features are not related to the Bezold-Brucke Effect.

To avoid countering the Abney additive law, Walraven concludes that the nonlinearity causing the Bezold-Brucke Effect must reside in the chrominance channel. He notes that any nonlinearity that occurred in each of the spectral channels would not affect the additivity obtained in the luminance channels. This latter case would only be true under small signal conditions, a condition that rules out any significant differential adaptation.

17.2.6.5.2 Analysis

This work takes a quite different view than Walraven of the cause of the Bezold-Brucke Effect. No arbitrary assumptions are made, no linearity laws are imposed, and the same model is used as elsewhere in this work. The Effect clearly involves large signal conditions (changes involving orders of magnitude within the mesopic region). The Effect is examined with respect to possible causes and mechanisms in the spectral, luminance and chrominance channels. The fundamental logarithmic conversion of all spectral signals occurring at the pedicle of the photoreceptor cells appears to be the dominant feature. The subsequent sum of the logarithms of the S–, M– and L– channels gives a signal in the luminance channel (R–channel) that shows distinct peaks that develop as the ratios of M– to S– signal amplitudes and M– to L–signal amplitudes change. These peaks occur at wavelengths near those reported for the Bezold-Brucke Effect. A combination of the logarithmic conversion at the pedicles and the saturation that occurs in the output (distribution) amplifiers of the photoreceptor cells provide the very non-linearity that Waldren describes.

203Walraven, P. (1961) On the Bezold-Brucke phenomenon J. Opt Soc Am vol. 51, no. 10, pp 1113-1116 Performance Descriptors 17- 181

The situation in the chrominance channels is distinctly different. While the non-linearity introduced by the photoreceptor cells remains key, the mechanism is different. The differencing of the logarithms of the S– and M– channels and the L– and M–channels does not result in any artifacts in the signals. However, if the amplitude ratios change, a difference in the slope and null value of the P– and Q–signals as a function of wavelength will result (see Sections 17.3.2.2 & 17.3.2.3). This change in the null point is particularly important because the brain is unaware of it. The brain has learned that the null value in the decoding of the P– and Q–channel values corresponds to specific “hues (nominally 494 and 572 nm).” However, the shift in absolute signal magnitude at the output of the pedicles results in a change in the wavelengths at which nulls are encoded in the P– and Q–channels. This is the source of the chrominance portion of the “hue change” of the Bezold-Brucke Effect.

As the relative level of the M–channel is reduced relative to the S– and L–channels, the encoded null in the P–channel occurs closer to 532 nm. Similarly, the encoded null in the Q–channel also occurs closer to 532 nm. As a result, the perceived change in chrominance is the very opposite. A null closer to 532 nm is still decoded as representing the previously learned wavelengths. Thus, a relative reduction in the M–channel will cause a shift in perceived hue away from the M–channel median near 532 nm.

Based on this model and analysis, the Hering school more correctly defines the Bezold-Brucke Effect. The Bezold- Brucke Effect (specifically the null points reported near 571 and 475 nm) is due primarily to the logarithmic signal summation process in the luminance channel and secondarily to the change in the chrominance channels. The changes are associated with a change in the relative signal amplitudes associated with operation in the mesopic region of vision as well as the color temperature (spectral content) of the radiant energy presented to the eye. A more precise agreement between the values mentioned here and the values of Purdy will require a much more careful analysis of the experimental conditions used by Purdy.

The null observed by Purdy near 507 nm is not associated with the Bezold-Brucke Effect. It is accounted for in this work by two mechanisms, the transition within the brain between depending on the P– and Q–signals to define the perceived color of the scene element and the relative insensitivity of both the P– and Q–channel signals to changes in wavelength in this wavelength region.

17.2.6.5.3 A projected Bezold-Brucke Effect near 395 nm

It can be predicted that an additional hue shift can be induced in the region of 395 nm that can be considered an additional Bezold-Brucke Effect. The Effect could be elicited by a change in the relative signal level in the short wavelength channel relative to that in the ultraviolet wavelength channel. It could result from a change in balance between the short wavelength and ultraviolet sensitivity favoring the short wavelength component. This Effect would be easily recognized in the aphakic eye and could account for part of Judd’s findings related to the short wavelength sensitivity of young eyes. For complete young eyes, it would appear as an increased sensitivity in the region between 400 and 420 nm. If evaluated in the same manner as Purdy, a hue shift would be reported by the subject.

In the aphakic eye, it should be possible to cause the spectral response function to exhibit three anomalous peaks, at 395, 487 and 580 nm, for a short period by suddenly reducing the illumination 10:1 in the mid wavelength region and by 3:1 in the ultraviolet region relative to a nominal pre-adaptation with a sufficiently broad spectral band source (Nominally 8683 Kelvin). Figure 17.2.6-14 illustrates in caricature the expected results. When combined with the effect on the O–, P– and Q– channels, hue shift nulls near 385, 476 and 571 nm could be expected.

The peaks in this figure actually reflect the nulls in the O–, P– & Q– channels at about 400 nm, 494 nm and 572–578 nm respectively. The last range is due to the uncertainty in the peak wavelength of the L–channel at the current time.

182 Processes in Biological Vision

Figure 17.2.6-14 (Color ln) The proposed three peaks in the aphakic human spectral sensitivity function under forced conditions. Vertical indicia have been added at 0.342, 0.437, 0.532 and 0.610 microns for reference. Note the residual presence of the long wavelength absorption characteristic near 0.625 microns.

17.2.6.6 The so-called Purkinje Shifts of the literature

In the recent literature, writers have not always clearly differentiated between the Purkinje Effect and the Bezold- Brucke Effect. Furthermore, they have spoken in terms of a shift in the wavelength of the peak composite spectral absorption. This has caused a problem. When they speak of the normal Purkinje shift to 580 nm, they consider it normal for such a shift to be toward longer wavelengths. However, when they speak of the Purkinje shift to about 487 nm (actually the appearance of one of the Bezold-Brucke peaks), they speak of it as abnormal. Both of these Effects are caused by a rise in a local maximum due to logarithmic signal summation and not due to an actual shift in wavelength due to an underlying physical mechanism.

17.2.6.7 The use of the above Effects in precision research

The use of artificial chromatic adaptation offers a unique capability to determine the precise half-amplitude absorption parameters of the individual spectral channels. By investigating the above special Effects in detail, the height and width of the abnormal peaks could be defined. These parameters would support the precise definition of the spectral absorption of each chromophore (full width half amplitude, FWHA, values) as found configured in the outer segments.

17.2.7 Luminance threshold & other descriptors related to performance

The subject of minimum luminance differences that can be achieved as a function of average luminance level has not been an important one. However, it does provide some important information concerning the noise performance of the eye. Traditionally, the overall task has been attacked from three perspectives: Performance Descriptors 17- 183

+ Measuring the luminance discrimination capability of the eye, using either a bipartite field or two concentric fields, under full illumination using “white light.” These methods appear to provide a general profile of the function but do not appear to give precise information.

+ Measuring the luminance discrimination capability as above using some form of flicker test. As will be discussed in Section 17.3.3, this technique is fraught with difficulties related to temporal processes in the visual system.

+ Measuring the luminance threshold immediately following sustained illuminance at the desired level. The assumption being that the adaptation mechanism and any other time constants involved have not had time to change.

Wyszecki & Stiles discuss this subject in some detail204. The discussion is couched in terms of rods versus cones instead of the underlying noise performance of the eye. This alternate approach will be discussed in the following sections.

17.2.7.1 The Noise and threshold characteristics of the human eye

The evaluation of the limiting performance of the human eye requires close attention to each segment of the photodetection and the signaling systems of the retina and both the computational and cognitive systems of the brain. Convention would suggest that the eye is noise limited, like most man-made systems at low signal levels. However, personal observation of the psychophysical performance of the eye suggests it is not noise limited. Systems employing thresholding techniques need not be noise limited. They may be threshold limited to avoid needless signal processing, and in the case of animals--distraction.

Proper analysis of the noise performance of the visual process requires very detailed knowledge of that process. Many previous investigations have assumed very simple models of the signaling channel(s)205. These models did not recognize the unique nature of the long wavelength channel nor did they recognize the possibility of different noise mechanisms limiting performance in different illumination regimes.

As in any good detection system, it is important to provide signal amplification as early in the system as possible. Otherwise, later signal processing stages may contribute noise to the overall signaling channel of a magnitude approaching that of the desired signal. Figure 17.2.7-1 shows a noise model of the visual process developed in this work. The details of cortical processing have not been explored in this work. However, it appears that the noise characteristics of the cortical circuits are due to a random process rather than a hard threshold.

As will become clear, the noise contribution of elements proximal to the photoreceptor cell is negligible in vision. Two separate noise regimes are of interest in vision: the RMS noise regime associated with low illumination levels and the noise associated with the circuits of the CNS. Several investigators have shown an interest in the individual noise events associated with the photodetection process. This is a largely pathological situation of little practical value. It could have some value in determining the precise band gap associated with the first neural amplifier of the photoreceptor cell.

The eye can be shown to be photon noise limited in the scotopic illumination regime. However, photon noise quickly becomes insignificant as the illumination level increases. It achieves a S/N ratio of at least 50 dB at the mesotopic-photopic level transition. Above this level, the noise performance of the eye is of trivial concern. In the absence of any input illumination, the noise sources of the physiological materials of the eye are the primary perceived noise source. They are also of trivial practical importance.

204Wyszecki, G. & Stiles, W. (1982) Op. Cit. pg. 569 205Krauskoph, J. & Reeves, A. (1980) Measurement of the effect of photon noise on detection. Vision Res. vol. 20, pp 193-196 184 Processes in Biological Vision

There are several potential noise sources in the system related directly to the temperature of the biological tissue involved. The first is the noise associated with the liquid crystalline material of the chromophores. The second is the noise associated with the base region of each of the Activas, serving as adaptation amplifiers, found in the dendritic structure of the photoreceptor. The third potential source is in the base region of the (Summing) Activa also located within the neuron of the photoreceptor cell. It is important to note two parameters. The operating temporal bandwidth of each photoreceptor channel is quite small, typically less than 200 Hertz in animals. In calculating the amplitude of the noise current at a given point in the system, this low bandwidth is important. Second, the very high amplification of each of the adaptation amplifiers cause the signal current reaching the summing amplifier from each adaptation amplifier to be significantly higher than the noise current due to the summing amplifier. The signal current to random noise current at this point is quite high, even under very low light level conditions. This has been amply demonstrated in Figure 2 of Baylor et. al206 who present the generator waveform in response to a single photon being absorbed by the chromophore. An individual photon elicits a response that is about 18 times the RMS noise level in the case of the toad based on the suction electrode technique. Baylor, et. al. used 520 nm light applied perpendicular to the long axis of the photoreceptor and effectively employed the isotropic absorption characteristic of the photoreceptor that is not employed in vision (In later experiments, they converted to end on illumination in order to measure the anisotropic absorption actually employed in vision).

Both the adaptation amplifier and disk stack noise sources can be described as energy threshold devices. They exhibit an energy threshold of about 2.0 electron-volts or higher for the adaptation amplifier noise source. The thermal noise source attempting to generate free electrons within the base region of the Activa has an RMS energy of between 26 and 27 mV Figure 17.2.7-1 The noise model of the visual system. depending on specimen temperature. The ratio of The position of the adaptation amplifier makes the initial noise source dominant. nearly 8:1 between these values suggests that very few noise electrons are generated by this source. The situation is similar in the disk stack. The individual chromophore material has a energy threshold that determines its spectral characteristics. The threshold associated with the long wavelength absorption is also involved in the noise process. This threshold is near 2.6 electrton-volts for the S-channel, 2.15 electron-volts for the M-channel, and 1.84 electron-volts for the L-channel. These values are all much higher than the 26-27 electron-volt thermal energy of the materials. Although the L-channel is slightly more noisy, the channels also exhibit a ratio of at least 8:1 between the threshold and the RMS noise source.

Combining the two noise sources in the noise model is complicate mathematically because of the internal thresholds. However, the number of noise electrons exceeding the threshold in the combined circuit is quite small. Baylor, et. al207. have measured the rate of occurrance of noise like events at the by capturing all of the current emanating from a single photoreceptor using their suction pipette technique with monkeys. They report a rate of generation of 0.006 events per second per photoreceptor (one every three minutes). This rate is measured after the amplification of the noise signal by the adaptation amplifier. With the experiments being performed in darkness, it can be assumed that the adaptation amplifier was operating at a gain of near 3400:1. Subsequent noise sources in the visual system are of similar thermal energy, face similar threshold levels but are not amplified like the above sources. These subsequent

206 Baylor, D. Lamb, T. & Yau, K-W. (1979) Responses of retinal rods to single photons. J. Physiol. vol. 288, pp. 613-634 207Baylor, D. Nunn, B. & Schnapf, J. (1984) The photocurrent, noise and spectral sensitivity of rods of the monkey, Macaca faxdicularis. J. Physiol. vol. 357, pp. 575-607 Performance Descriptors 17- 185 sources can be and have been neglected in the figure.

Baylor, et. al. suggest there is a thresholding process in the signaling channel to account for the very low noise level and that it might be near the photoreceptors. The above model provides a more detailed description of the actual location.

The remainder of the noise model includes several other features of interest. First, the summing channels of the signal manipulation stage would increase the apparent rate of noise electron generation in each channel. However, the rate would still be quite low. Nevertheless, the parasol ganglion cells of the projection stage do incorporate a threshold and a significant capacitance in their input circuit. This capacitance acts as an integrator ahead of the voltage threshold that further suppresses the transmission of any noise through the summation channels of the system. The differencing channels of the summation stage can cause a significant increase in noise level for conventional thermal noise. However, for the individual noise pulses being discussed here, they act similar to the summing circuits. There is no threshold in the midget ganglion cells. Therefore, any noise passing through these circuits will be passed on to the brain. No analysis of the noise performance of the brain is offered here. However, it is likely that each circuit following the decoding of the projection signals does exhibit a minimum signal threshold. This is especially apparent in the chromatic circuits that cease functioning at ligher illumination levels than the luminance circuits.

A special feature of the L-channel of the visual system should be noted. In order to maintain the excellent noise performance of the eye and still detect the lower energy photons in the red end of the spectrum, a compromise was made. The energy threshold required to excite the base layer of the adaptation amplifier Activa was maintained at about 2.0 electron-volts. As a result, the energy of two photons must be accumulated in the chromophore material before the necessary energy level is achieved and excitation of the Activa occurs (coincident with de-excitation of the chromophore material). This cannot be described as a two photon process because each photon is absorbed independently. However, it can be described as a two exciton process in quantum terms since it takes two excitons changing state within a very short time interval to cause an electron pair in the base material of the adaptation amplifier Activa. In statistical terms, this causes the signal level in the L-channel to decrease faster than the equivalent signal level in the other channels. This is the ultimate reason why the animal eye losses sensitivity in the L-channel before doing so in the other channels.

Although minimal signal amplification is provided further along the signal path, the high signal level due to the adaptation amplifier makes any subsequent noise sources negligible. Based on this situation, the noise performance of the eye, particularly the human eye, can be calculated based only on the quantum statistics of the incident image and the quantum efficiency of the optical system of the eye and the Outer Segment of the photoreceptors. This has been done and scenes have been prepared to illustrate the performance of the eye under low light conditions208. It is relatively easy to demonstrate the eye operates under quantum noise limited conditions because quantum noise is defined entirely by the illumination level in the image. Under quantum noise limited conditions, the noise level changes with the square root of the input illumination level. Under thermal noise limited conditions, the noise level is independent of the input illumination level.

[xxx rewrite ] The quantum efficiency of the animal visual system, particularly in the chordate and other complex eyes, is nearly 100% because of the way the disks are stacked along the optical path followed by the incoming photons. Nearly no photons, on a percentage basis, reach the RPE or other equivalent surface behind the chromophore material. This makes the retina of the animal eye one of the most highly efficient photon detectors known. It is in the same class as the misnamed “solid state photomultipliers” which are actually quantum mechanical semiconductor absorbers just like the eye. The retina is about 10 times more efficient a photomultiplier tube based on a photoemissive surface and

208Rose, A. (1977) Vision: human versus electronic. In Vertebrate Photoreceptors, Barlow, H. & Fatt, P. eds. NY: Academic Press. pp. 1-13 186 Processes in Biological Vision

50 to 100 times more efficient than a photographic film.

It is not widely known but the “night goggles” worn by the military in this age are still not as effective in true low light conditions than the famous German naval binoculars of World War II. This is because the product of the collection efficiency of the binoculars times the quantum efficiency of the eye is higher than the similar product of the collection efficiency of the smaller aperture night vision glasses and the quantum efficiency of the photo-emissive surface used in the glasses. The true value of the night vision glasses is in two of their properties. The high signal amplification of the glasses allow a pilot or driver see an image of the scene at a similar brightness level to that of his instrument panel. This allows him to correlate the inputs from the two scenes and perform his mission. They also incorporate a saturation circuit not unlike that of the adaptation amplifier in the eye. The amplifier gain drops precipitously when a very bright illumination source appears in the field of view of the night vision goggles, therreby protecting the sensitivity of the pilots eyes. [xxx rewrite ] This is accomplished by introducing a poorly regulated power supply into the goggles electronics. This is exactly the same mechanism used to control the sensitivity of the animal eye. However, the electronic circuit has been tailored differently.

17.2.7.1.1 Critical circuit features in low light vision

There seems to be a logical set of design rules at work in the visual system that control its performance at low light levels. Individual rules apply to each portion of the visual system. The primary rule is do not process useless information in the form of ordinary data. The question to be answered is how do these rules apply to the three data streams, luminance, short wave chrominance and long wave chrominance, entering the brain?

The luminance channel has a threshold at the input to the parasol type ganglion cells. This threshold prevents action potentials from being generated in the luminance channel if the luminance signal is below a specified level when delivered to the threshold. If the illumination is so low that, even with the adaptation amplifier operating at maximum gain, the signal level is below this threshold, no action potential related to luminance is transmitted to the brain. There is no obvious threshold in the midget ganglion cells associated with the two chrominance channels. These cells produce action potentials under quiescent conditions. However, the time interval between pulses in both chrominance channels approaches the quiescent pulse interval under very low input signal conditions.

A possible operating scenario is as follows: The photodetection channels are each quantum noise limited in performance due to the high energy level required for excitation. This level is far above the thermal noise energy level at biological temperatures. The adaptation amplifiers are similarly immune to noise due to thermal energy at biological temperatures. This is due to the wide band gap of the material constituting the base region, hydronium. With the high potential amplification of the adaptation amplifier, the signal at the pedicle of each photoreceptor is always quantum noise limited. There is no noise source farther down any of the three signal chains that is of the magnitude of the amplified and quantum noise limited signal.

The noise performance of the chrominance signals created by the lateral differencing circuits is a function of the spatial integration within the retina. If only two photoreceptors were employed as inputs to a single differencing circuit, the output signal would be inherently 1.4 times noisier than the individual input signals. However, this number decreases as more photoreceptor signals are averaged in the input structures of the lateral cells. It appears to equal 1.00 in most situations. Lacking a threshold at the input to the midget ganglion cells, at sufficiently low illumination levels, noisy information will be encoded onto the action potential pulse stream and transmitted to the brain.

The luminance signal is created by combining the individual photodetection channels associated with the different Performance Descriptors 17- 187 chromophores at the photoreceptor pedicles. The summation process tends to reduce the noise compared to that in the noisiest input channel. However, the noisiest channel could be quite noisy. It can be shown that the square-law signal associated with the L-channel will be the noisiest channel at a given illumination level. It can also be shown that both the signal and noise level applied to the adaptation amplifier in this channel falls in amplitude faster than the other channels. The result is that this adaptation amplifier reaches maximum gain before the other amplifiers. Under this condition, the low signal and low noise associated with the L-channel has little impact on the combined luminance signal. The signal and noise level applied to the parasol ganglion cell threshold under low light conditions is controlled by the sum of the M-channel and S-channel signals.

Under this scenario, three performance conditions must be considered. Two are related to impaired performance. The third is shutdown of the visual system.

(1a) As the illumination level decreases through the mesotopic range, the chrominance discrimination in both chrominance channels becomes poorer and poorer. The long wavelength discrimination deteriorates faster than the short wavelength discrimination. (1b) The long wavelength sensitivity in the L-channel spectral range also deteriorates as lower level are reached within the mesotopic range.

(2) When the scotopic illumination range is reached, the illuminance channel is still well above the parasol cell threshold. Although both chrominance channels are still active, they are operating in the null condition. The action potentials transmitted to the brain have a pulse to pulse spacing that is near the quiescent spacing except for a small amount of modulation due to noise. The brain may incorporate a threshold at the output of the chrominance action potential decoder. This threshold would suppress any extraneous chrominance patterns due to different noisy signals arriving relative to different locations in the field of the retina.

(3) When, the luminance signal becomes so low at the input to the parasol ganglion cells, that it does not exceed the threshold, no action potentials are generated by the cells. No action potential pulses are received at the luminance channel decoder in the brain. The brain registers a null condition. No image is formed. There is no sensation of black. Anything perceived by the brain at this illumination level must come from internal sources.

17.2.7.1.2 A combined achromatic/chromatic threshold performance graph

Spillmann & Conlon have provided two graphs describing the measured threshold performance of the human eye attempting to separate the achromatic and chromatic thresholds209. This data is in contrast to the many verbal discussions concerning the chromatic performance of the eye as it relates to the conventional adaptation characteristic. The presentation appears to be in good agreement with the theoretical model presented here. The following Interpretation of the graph relies heavily on the signaling channels defined in this work. The most critical assumption is the separation of the signaling path into a summation (luminance) path and a differencing (chrominance) path. Based on this differentiation, the equations for the signal to noise ratio at a given point in the visual system are seen to be different and can be described. What is not known is the threshold signal to noise ratio of the human eye and the shape of the signal pulse at the output of the photoreceptor cells, the Class D waveform, at the lowest illumination levels. The data points were collected using a test light source only partially characterized, a 1° square created with a tungsten source viewed through a Wratten #61 filter (catalog half-amplitude points 503 & 556 nm. by interpolation) and measured with a Crozier-Holway three channel visual discriminometer defined in 1939. A 1.5 mm. effective aperture was used in the Maxwellian projection system. The subject experienced a 0.2 second test illumination at 6° on the horizontal meridian in the nasal field. The illumination was described as having a of 535 nm. When appropriate, a 30° circular surround was provided using a “white light” from a tungsten source. At other times, the eye was pre-exposed to a “white light” from a tungsten source providing

209Spillman, L. & Conlon, J. (1972) Photochromatic interval during dark adaptation and as a function of background luminance. Jour. Opt. Soc. Am. Vol. 62, no. 2, pp. 182-185 188 Processes in Biological Vision

a 4173 mL. luminance over a subtense of 75° by 90°. Based on the available parameters, it is reasonable to assume that an insignificant amount of radiation was applied to the S- and L- photoreceptor channel during the test interval. At the lowest levels, the time delay of the P/D equation is probably not important in the data collection. However, the rise time of the Class D waveform may be similar to the 0.2 sec. exposure interval. This condition would result in a luminance signal pulse that is non rectangular and of less than expected amplitude when perceived by the brain. In the absence of signals from the S- and L- channels, the signal in the chrominance channel would be expected to be similar temporally to that of the luminance channel. Looking forward to more precise data in the future, this analysis will focus on the concept.

The results for the steady state case are shown in Figure 17.2.7-2. Looking first at the open circles representing the luminance data, at the lowest radiance levels (only a limited region of the visual spectral range is in use and the term luminance is inappropriate), the threshold appears to be independent of the radiance. It is proposed that the threshold in this region is due to the internal threshold of the perceptual stage of vision. The theoretical threshold is therefore shown as a horizontal line (A). Above this region, the data points are well represented by a straight line with a slope of one-half (B). Such a region is indicative of a photodetection system limited by quantum noise at its input. At higher radiance levels, the data points can be represented by a straight line with a slope of one (C). In this region, and extending to higher levels as the adaptation amplifier begins to lower the overall circuit gain, the performance of the system appears to be limited by the short term dynamic range of the signaling channel. Although the data points representing the transition from the internal threshold limited case to the photon noise limited case are few, the gradual transition from one regime to the other suggests that it is also stochastic. The mathematics would imply the internal threshold is also a stochastic process.

The distance between the open circles and the closed circles has traditionally been defined as the photochromatic interval. The term has usually been loosely defined. Sometimes it is presented as a function of spectral wavelength as measured under a specific set of radiant (more often photometric) intensities. Tilton provided such a definition during the 1970's210. However, his work was more conceptual and based on the standard luminosity

functions, V(l) and V’(l) that he took to represent actual rather than smoothed spectral data.

The asymptotes drawn in the figure suggest that the crossover between mesotopic and photopic vision occurs at a relatively high level relative to the scotopic to mesotopic transition, with the mesotopic region extending over four orders of magnitude. It appears that these are not the optimum asymptotes and that additional laboratory data would probably indicate a mesotopic to photopic transition one or two orders of magnitude further to the left.

Looking at the chromatic data points, a similar situation is observed at the lowest radiance levels. The Figure 17.2.7-2 Combined chromatic and achromatic chrominance threshold can be represented by a thresholds for the steady state case showing asymptotes horizontal line. The line is at a higher threshold level describing the three operating ranges, (A), internal for at least two reasons. First, is the fact that the threshold limited, (B), quantum noise limited, and (C) short term dynamic range limited . Open circles, differencing function of the chrominance channel luminance data. Filled circles, chrominance data. Data affects the signal level applied to the perception from Spillmann & Conlon (1972)

210Tilton, H. (1977) Scotopic luminosity function and color-mixture data J.Opt. Soc. Am. vol. 67, no. 11 pp 1494-1501 Performance Descriptors 17- 189 process. Second, the amplitude of the signal in the differenceing channel is a function of the wavelength of the irradiance. As shown in Section 17.3.2, the choice of irradiance with a spectral peak near 535 nm. is less than optimum from the perspective of chromatic perception. However, its choice was a logical one on the grounds of minimizing the excitation of the adjacent chromatic channels. In their discussion, Spillmann & Conlon developed the concept of a “photochromatic interval” to describe the ratio of the achromatic to the chromatic threshold. In their paper, this photochromatic interval reached 47 dB (4.7 log units) in the region they describe as below 10-4 millilamberts. It is proposed here that the photochromatic interval is a function of wavelength. Further experiment is needed to confirm and quantify this relationship. For radiances higher than the labeled 100 millilamberts, the chromatic data points appear to follow the achromatic data points quite closely in accordance with the proposed linear threshold versus radiance relationship caused by short term dynamic range limitations in the signaling channel.

Spillmann & Conlon carefully coached their subjects concerning concentrating on reporting a threshold based on only color or only brightness. The results of such coaching are extremely difficult to quantify, especially when only a few data collection runs were made. They also discuss their difficulty in data reduction using a technique developed by Crawford in 1937. Because of these difficulties, the data points between 0.1 and 100 millilamberts will not be considered from a theoretical perspective here. It is likely that additional experimentation would show that the horizontal asymptote should be extended to the intersection with the 1:1 asymptote and the dip shown in the data points, of 10-17 dB, is due to the difficulty a human has in making independent observations in this region.

Goldberg, Frumkes & Nygaard211 performed a set of experiments similar to Spillmann & Conlon, except seven degrees temporal of fixation. However, they did so under a much less controlled environment, no definition of “green” or “yellow,” etc., and using observers with no psychophysical training, except for one of the principles. One of their curves for green light at a 5 Hz. flicker rate conforms to Spillmann & Conlons luminance curve. It would also be described as a luminance response based on Hecht’s papers. They did not present a rigorous theory on which to base their discussion and did not draw firm conclusions based on their data.

17.2.7.1.3 Discrimination of luminance differences

If one ignores the nature of the threshold for luminance perception in vision, it is possible to simplify the discussion to merely one of the perceivable change in illumination as a function of illumination. Wyszecki & Stiles reproduce an early figure from Steinhardt (1936) showing the observed characteristic under these conditions using a “‘white’ stimuli and with field sizes larger than the rod-free area.” Unfortunately, the figure does not give data points, only the proposed relationship. The relationship does show a saturation value of about 70:1 at high light levels in agreement with this work. It also shows an unexplained deviation in the region of 0.01-0.001 candela per square meter just like the data of Spillmann. However, the curve is shown proceeding toward unrealistic ratios at low light levels. The curve should become asymptotic to 0.0 at ever lower light levels. With this understanding, the curve (although representing a differential) exhibits the same functional relationships as in the previous figure from Spillmann.. In the scotopic range, the differential is limited by internal stochastic noise and approaches log Δl/l = 0 at the lowest levels. In the mesotopic regime, the adaptation amplifiers are operating at maximum gain and the luminance discrimination function has a slope of 0.5. The differential is limited by stochastic (photon in this case) noise. In the photopic regime, the adaptation amplifiers attempt to control the average signal level applied to the signal processing stage. As a result, the luminance discrimination function exhibits a very low slope. This slope is approximately equal numerically to the inverse of the exponent in the transfer characteristic of the adaptation amplifier. At maximum value, the function exhibits a value of about 70:1. In the hypertopic regime, the luminance discrimination function reflects saturation in the signal manipulation stage. It will eventually return to 0.0 (but probably not before intense pain is felt by the subject).

17.2.7.2 Thresholds as a function of field position

211Goldberg, S. Frumkes, T. & Nygaard, R. (1983) Inhibitory influence of unstimulated rods in the human retina: evidence provided by examining cone flicker. Science, vol. 221, pp. 180-182 190 Processes in Biological Vision

Liu et al212. have discussed the sensitivity of the eye based on perimetry using a colloquial expression, the “island of vision.” Figure 17.2.7-3 compares the concept using both a three-dimensional and two-dimensional presentation.

Figure 17.2.7-3 The island of vision (left) based on threshold (static) perimetry and the same information plotted as “kinetic” perimetry.. From Liu et al., 2001.

The island of vision clearly shows a peak sensitivity, along the z-axis, that is limited to a very small radius. This region is assumed to be limited to the foveola of the retina.

Aulhorn & Harms have provided provocative data on the threshold performance of the human eye as a function of field position with background illumination as a parameter213. The reference does not describe the size of the test source and most of their papers are in German. Figure 17.2.7-4 shows their data taken along the zero degree meridian. Their units of measure are archaic but the results are quite informative. As a result, the meaning of the scales and their discussion must be looked at closely. It is difficult to interpret L/ΔL in their context. It appears that it is equivalent to Lmin/ΔL since ΔL’s greater than L are present in the data. The use of (Lmax - Lmin)/(Lmin + Lmax), the modulation, would be easier to understand. The fact that the fovea goes from less than average to greater than average sensitivity as a function of background is interesting. The sensitivity appears to vary with field position in both acuity and vascular system capability.

Note the inversion of the sensitivity function as a function of background illumination. The peak sensitivity is always at the point of fixation for low background conditions. At very low backgrounds, the peak sensitivity at the fixation point may be as much as one order of magnitude poorer than that of the surrounding retina. Under high background conditions, the maximum absolute sensitivity may not be associated with the foveola.

212Liu, G. Volpe, N. & Galetta, S. (2001) Neuro-Ophthalmology: Diagnosis and Management. NY: Saunders 213Aulhorn, E. & Harms, H. (1973) Visual perimetry In Handbook of Sensory Physiology, Jameson, D. & Hurvich, L. ed. Vol. VII, No. 4 NY: Springer-Verlag, pg 118 Performance Descriptors 17- 191

Figure 17.2.7-4 Profile perimetry along the zero degree meridian for 8 different states of adaptation. Average values for 10 normal subjects. The area or diameter of the test source was not given. Units are in Apostilb (asb). One asb equals 1/π candela/m2. From Aulhorn & Harms, 1973.

17.2.7.3 Defining the quantum efficiency of vision

Many investigators have chased the holy grail, attempting to define the quantum efficiency of the visual process. Unfortunately most of them did not have an adequate model of the process they were trying to evaluate (Section 7.2.4).

Most of the investigations focused on psychophysical experiments seeking to define the probability of detection of a brief flash of only a few photons after (putative) complete dark adaptation. These investigations have failed to describe many features of the visual system that are critically important to the interpretation of these studies. xxx Inherent in these studies has been the assumption that the quantum efficiency at threshold was the characteristic 192 Processes in Biological Vision

value of the system at all illumination levels. The P/D equation derived in this work clearly shows that response of the photoexcitation/de-excitation process does not resemble or employ the photoelectric effect described in detail by Einstein in 1905. The mechanism involves the creation of bound but excited electrons within a liquid crystalline organic material at a very high absorption and hence a high quantum efficiency. However, the electrostatic fields within the material are not conducive to a rapid transport of these excitons from their point of excitation to their point of de-excitation when only a few excitons are present. As a result, the generation of free charges as a result of the excitation of the material by light is smeared out over a period of time. This situation was noted indirectly by Levick & Zacks214 as reported in Teich, et. al215. Levick & Zacks assumed the action potential generation rate at a ganglion cell had a direct relationship to the absorption of photons.

Determining the quantum efficiency of any process requires meticulous attention to the details of the experiment and how the quantum efficiency is defined (Section 7.2.4). As an example, is the loss in efficiency due to a sparse array of detectors in a two-dimensional array counted against the efficiency of the detectors or the efficiency of the array manufacturing process. This is a particular problem based on the conventional wisdom that the retina contains photoreceptors that are only active over a part of the illumination regime (the concept of rods and cones). How much of the surface of the retina in a given region is dedicated to photoreceptors active at the target illumination level used in the tests. The position of this work is that there are no achromatic photodetectors described as rods. All of the active area is filled with photoreceptors active at all light levels. The fill factor of this array based on a uniform array of adjacent two-micron diameter photoreceptors is very high. This would suggest a very high geometric efficiency if all of the photoreceptors exhibited equal quantum efficiency for the wavelength of light involved in the test.

A variety of methods of measuring the quantum efficiency of a light stimulated system exist. The most obvious is to count the charges generated at some point in response to a known number of photons stimulating the transducer. However, at the levels of interest here, that experiment becomes a study in the statistics of quantum mechanical events at best. In the case at hand, access to the initial electron stream is not available in the first place. Some of the mathematical studies in the literature, such as Teich, et. al., have employed very sophisticated mathematics and were largely limited by the quality of the data and test protocols used to collect the data.

Hecht, et. al216. and many other investigators have used the charge generation to incident photon approach at threshold levels except they operated under extreme constraints. They did not control or understand the signal processing path between the light generating test set and the response generated by the subject under psychophysical test conditions. Even under these constraints, Hecht, et. al. estimated the efficiency of the eye to be in the vicinity of 7 to 20%. More recently, Baylor, et. al. have measured similar values using an electrophysiological approach and the toad217. They concluded the quantum efficiency (photon in to total integrated charge out) is on the order of 11% to 17% when measured at the axon of the photoreceptor under near threshold conditions. However, like in the Levick & Zacks activity, the output current waveform did not exhibit a shape suggestive of the input photon flux and it occurred following a significant delay. It must be pointed out that the “rod” evaluated by Baylor, et. al. exhibited a distinctly M-channel characteristic, not a broadband achromatic sensitivity. They pondered this fact in the paper.

[xxx rewrite based on sec. 7.2.4 ] An alternate method of determining the quantum efficiency of a light related process under operational conditions

214Levick, W. & Zacks, J. (1970) Responses of cat retinal ganglion cells to brief flashes of light J Physiol vol 206, pp 677-700 215Teich, M. Prucnal, P. Vannucci, G. et. al. (1982) Multiplication noise in the human visual system at threshold: 1. Quantum fluctuations and minimum detectable energy J Opt Soc Am vol 72(4) pp 419-431 216Hecht, S. Shlaer, S. & Pirenne, M. (1942) Energy, quanta and vision J Gen Physiol vol 25, pp 819-840 217Baylor, D. Lamb, T. & Yau, K.-W. (1979) Responses of retinal rods to single photons J Physiol vol 288, pp 613-634 Performance Descriptors 17- 193 involves measuring the threshold contrast change at a given light level and relate that threshold to the RMS variation in the associated steady state light level. This method involves the assumption that the light level used causes the quantum-statistical noise of the light to be the dominant noise in the system. This is easily shown to be true experimentally and examples can be found in the research literature. The proof involves showing that the RMS noise, e. g., the variance associated with the signal is accurately described by the square root of the average photon flux. This method leads to the determination of the quantum efficiency of the initial process at levels significantly above the threshold level. The result of this process suggests the quantum efficiency of the visual system is at least as good as any man-made detection system, and is in the 80-100% range.

As an aside, the fully dark adapted human eye is still able to outperform the best available man-made imaging systems when employing optical systems of equal performance. These man-made systems, typically manufactured using silicon as a substrate, can reach an easily measured 60% quantum efficiency at wavelengths in the 500-1,000 nanometer range. They can also reach this value in the 400-500 nanometer range if special manufacturing techniques are used (known as back side thinning).

Under carefully controlled conditions, the quantum efficiency of the photodetection process of a single photoreceptor cell, PC, approaches 100% (>80% when dark adapted for over 20 minutes) through the use of a unique set of configuration and operating parameters (Section 7.2.4).

Demonstrating the quantum efficiency under specific conditions is a mathematically challenging task. The following sub-sections will outline the appropriate protocols and conditions while employing a variety of simplifications.

17.2.7.3.1 Background

Dealing with light, especially at low incident levels is an inherently statistical process. Light itself is a stochastic process, involving random events and necessarily probabilities. Importantly, the spectral channels defined by the spectral absorptions of the individual chromophores do not employ precisely the same mechanisms. The long- wavelength channel operates distinctly differently. To develop these differences, the applicable laws of probability theory are shown in Figure 17.2.8-1. The upper portion of the figure are textbook representations of the applicable laws of probability theory written for the discrete case, rather than for the distributed function case which involves integral calculus.

The additive rule can be simplified by dropping the last term if the events A & B are not mutually exclusive. As generally accepted, there is significant overlap between the spectral absorptions of the individual neural sensory receptors. In the general case, the spectra are not mutually exclusive but a specific photon can only excite one or the other of the pair. This introduces the subject of replacement or no replacement in a specific trial in an experiment but this subtlety will not be introduced here. In the following development, it will be assumed that all photon streams are monochromatic and occur at the wavelength of the peak sensitivity of one of the neural sensory receptors of stage 1.

Immediately below the additive rule is an expansion of that rule to three independent but exclusive terms. The rule can be expanded to four independent terms. In the following discussion, each of the letters A, B, C & D can be associated with a separate spectral band, UV, S, M & L. However, the mechanisms associated with UV, S & M are the same. Due to this fact, the UV term will be ignored and A will be associated with the S–channel, B will be associated with the M –channel and C with the L–channel. Each term will be considered independent. No mutual exclusion will be asserted.

The conditional rule states: the conditional probability that A has occurred relative to the hypothesis that B has occurred, is given by the joint probability that both A and B have occurred divided by the probability that B has occurred. 194 Processes in Biological Vision

The multiplication rule can be looked upon as a modification of the conditional rule by inference.

Figure 17.2.8-1 The laws of probability theory applicable to visual sensing ADD. These laws can be applied selectively to the operation of the neural sensory receptor channels. See text for their interpretation.

Bayes’s Theorem is seen to be a rearrangement of the multiplication rule using the two terms on the right.

Finally, the independent event rule shows that the probability of two independent events happening within a given time period is the product of the probability of each event occurring within the same time period independently.

- - - -

In the visual modality, the stimulation of the individual sensory neuron is a multiple step process. A photon must initially create an exciton within the electronic structure of the chromophore, a photo-exciton process. One or more excitons within the chromophore must then create a free electron in the electronic structure of the sensory neuron associated with the chromophore, an exciton-free electron process (that can be considered an acoustic transfer of a quanta of energy between two structures. The result of a photon exciting a molecule of the chromophoric coating of a disk is the creation of a single exciton. Since the chromophoric material is present as a liquid crystalline state of matter, the stimulation of a single molecule is tantamount to the stimulation of the whole liquid crystalline assembly of molecules to an initial quantum-mechanical level. The stimulation of any molecule of the chromophore in the same liquid crystalline assembly causes the stimulation of the whole liquid crystalline assembly to a higher quantum- mechanical level (Section xxx).

Each sensory neuron of the visual modality exhibits a minimum quantum-mechanical energy threshold, usually Performance Descriptors 17- 195

labeled Vγ. Vγ is believed to equal ~2.10 to 2.20 electron-volts based on the work of Sliney (Section 17.2.5.5.2 xxx). To excite a sensory neuron, the chromophoric material must be able to transfer an exciton to the neuron containing this energy, equivalent to a photon with a wavelength of less than ~590-560 nm respectively nm.

This energy requirement indicates that no single photon of light with a wavelength significantly longer than about 590 nm can not excite a visual sensory neuron. However, excitons with the energy of multiple photons can excite a visual sensory neuron. This is the mechanism used in the L–channel sensory channel of vision. The energy of two photons are summed within the energy band of the L–channel chromophore before that energy is transferred to the sensory neuron, generating a free electron. This process is described as a 2-exciton process to distinguish it from a 2-photon process as used in other applications within the light regime. Thus, in the L–channel, centered at either 610 or 625 nm (2nd order and 1st order analysis respectively), two photons must be used to create a single exciton that is capable of exciting the sensory neuron thereby creating a single “photoelectron.” This 2-exciton process has repercussions. The slope of the 2 exciton process on a graph of sensory neuron stimulation versus light stimulation intensity is twice as high as that for a S– or M–channels.

It is proposed that all electrolytic neurons of the biological system exhibit threshold values, Vγ, of the same voltage at normal exothermic biological temperatures (98.6 Fahrenheit, 37 Centigrade). The precise value of Vγ must be confirmed in the laboratory in the near future. Note, this value only affects the cut-in or turn-on of the neuron. It does not indicate a minimum signal amplitude after the neuron is biased into its operating range.

- - - -

The conditional rule will be applied to the L–channel where it will be asserted that at low stimulus intensities, two photons must excite the chromophoric material associated with one disk, or one surface of a disk if the two sides are not in quantum-mechanical contact within the time constant of the exciton excitation/de-excitation cycle. This time constant is typically quite long relative to the arrival of two photons.

- - - -

The noise performance of the human eye is described in Section 17.2.7.1.2 based on the work of Spillmann & Conlon. Their work focused on the M–channel of human vision. They identified a regime where the noise performance of the eye was independent of the stimulus intensity (internal noise limited region–as expected in the scotopic region), a region where the slope of the response was unity (photon noise limited--as expected in the photopic region), and an area of intermediate slope (as expected for the scotopic region). It is proposed that the slope in the photopic region for the L–channel would have a slope of two due to the 2-exciton mechanism.

17.2.7.3.2 Structural configuration of the outer segments

[xxx see Section xxx ]

17.2.7.3.3 Define bleaching in the context of photon absorption at the outer segment

[xxx See Section 7.2.4 ]

17.2.7.4 Defining “bleaching” in the context of the P/D equation

Bleaching of the chromophores of vision has not been a major area of research since the 1960's. At that time, most 196 Processes in Biological Vision of the data was analyzed with respect to a simple first order exponential function218. Burns & Elsner wrote on the subject in 1985219.

As described in detail in Appendix A, the Photoexcitation/De-excitation equation describes the absorption cross- section of the chromophores of vision in terms of the number of potential bound electrons within the ground state of the chromophores at a given time.

While individual chromophoric molecules have a very small absorption cross-section when illuminated axially, this is not true when they are assembled into the liquid crystalline state. When so assembled into a one molecule thick thin film, the effective absorption cross section is equal to the physical dimension of the liquid crystalline assembly multiplied by the ratio of the unexcited to the total of chromophoric molecules present.

As photons are absorbed and some of these bound electrons are transferred to the excited state, this pool of potential bound electrons is reduced--until the excited electrons can be de-excited and returned to the pool. The degree to which the pool is depleted is a direct measure of the effective change in absorption cross-section of the chromophores. This reduction in effective absorption cross-section is what is defined in empirical vision research as physiological bleaching.

Care must be taken to differentiate between physiological bleaching defined above and bleaching due to solvation or other chemical treatment. The Rhodonines only act as the chromophores of vision when they are present in the liquid crystalline state and are supported by an electrical connection providing the de-excitation mechanism required. When the photoreceptors of vision are chemically processed in the laboratory in order to separate them from the retinal substrate or chemically analyze their content, the material is inevitably solvated. In solution, the Rhodonines (like other chemicals of the cyanine family) are essentially transparent. Under these conditions, the Rhodonines are properly described as bleached by solvation, a form of pathological bleaching.

17.2.7.5 Reaction time as a function of illuminance

[ Old 17.2.8 has moved to 17.2.3 xxx]

The subject of reaction time relative to illuminance will not be explored in detail here. The field involves many performance parameters related to the motor system as well as the visual system. To acquire data on other animals, it frequently requires considerable species-specific training. Lit, Young & Shaffer have provided some data on humans as a function of the color of the stimulus220. Other data is provided in Chapter 12 and Section 17.6.4.

17.3 The Chrominance Characteristic of the human eye

The following material will provide a theoretical foundation for the currently used measures of chromatic visual performance. Contrary to the conventional wisdom dating from Thomas Young, this section will demonstrate that the human visual system is fundamentally tetrachromatic. The fact that the human retina is tetrachromatic while the complete eye is largely trichromatic influenced the development of the theoretical foundation. It was necessary to accommodate the tetrachromatic properties of the human visual system in the overall framework.

218Dartnall, H. (1962) The photobiology of visual processes In Davson, H. ed. The Eye, Volume 2; The Visual Process. NY: Academic Press pp 323-365 219Burns, S. & Elsner, A. (1985) Color matching at high illuminances: the color-match-area effect and photopigment bleaching J Opt Soc Am A vol 2, pp 698-704 220Litt, M. Young, R. & Schaffer (1971) Simple time reaction as a function of luminance for various wavelengths Percep Psychophysics vol. 10, no. 6, pg 371+. Also in Uttal, W. (1981) pg 487 Performance Descriptors 17- 197

Simultaneously, it was desirable to provide a link with the available database that was assembled based on the trichromatic assumption.

Contrary to the baseline assumed by the CIE, and derived from Young, the visual system is not based on additive color. While the actual chromatic processing in vision is closer to the subtractive color suggested by Hering, the subtractive color concept does not provide an adequate baseline either. Chromatic processing in biological vision is based on a slightly more complex method that can be described most simply as differential color where differential is used in the algebraic sense of a difference between two quantities. A more complete label would be multichannel, orthogonal differential color. The system takes the difference in signal intensity between pairs of chrominance channels determined by the spectral absorption of the chromophores. It then processes these differences as if they were orthogonal to each other. In interpreting the result, it defines white as the achromatic point where the signal value in all of these channels is zero. This interpretation results in a perception of color more similar to the opponent theory of color proposed by Hering than the additive approach proposed by Young.

To provide a proper theoretical foundation, it will be necessary to extend a number of current definitions to a higher level of specificity and to propose alternate explanations of a number of phenomena (such as color constancy).

The task is complicated by the need to define color with greater precision as well as develop the concepts of color contrast more clearly.

A– Based on this work, the definition of color will be clarified considerably. Specifically, it will be shown that color (or a synonym for color) IS a physical property of objects. For clarity, it may be necessary to separate the intrinsic color of an object from the “perceived” color of the same object perceived and reported by an individual. The semantic difficulty associated with the expression “reported by the individual” will be discussed. Since such a report is usually given in a specific language, the semantics used depends heavily on the training of the individual involved. As an example, which is truly red, an apple or a ? If you said apple, which variety of apple is synonymous with red? What is actually needed is a mathematically precise method of specifying an absolute color. This section will provide such a method for the first time.

B– The problem of defining the color of an object has recently become more significant with the wider use of image recording devices that display their record in real time next to the actual object of the recording. This problem is an old one. It was first encountered in the early days of color television development when it was found the perceived image of a monitor was different than the perceived image of the actual scene regardless of the linearity of the television channel used. If the reproduced scene had a different luminous intensity than the initial scene, the human observer saw a differently colored image on the monitor. The industry determined it was more important to present a pleasing picture to the audience viewing the monitor than it was to maintain “color constancy” between the scene and the image.

C– This problem of reproducing an accurate or a pleasing rendition of a scene is shared in the graphics industry in general. The limitations of the common 4-color subtractive color process used in printing is well known. It is so serious in the current day that is now promoting a 6-color subtractive printing process (the Hexachrome process) as more compatible with the requirements of the printer’s customers.

D– The problem of rendering a chromaticity diagram of acceptable precision is the same as that in rendering high quality printing. Pending the development of a rendering of the New Chromaticity Diagram for Research using a more precise subtractive color process, the Diagram proposed by this work will be presented in additive color on a monitor with the most important colors specified by the number assigned according to the Munsell renotation system.

When discussing color monitors and their use in psychophysical research, it is important to note that monitors differ significantly in their spectral characteristics. Sproson has addressed this 198 Processes in Biological Vision

problem obliquely when discussing color television221. He emphasizes that the European (PAL) and United States (NTSC) systems do not call for the use of the same ideal phosphors, and that the actual systems offered by manufacturers in these two areas use different phosphors. Although he has called for world wide standardization, this is unlikely to occur. Non television monitors often use different phosphors as well. It is important that a researcher be much more specific about the chromatic content of his test stimuli. Giving a brand name for the overall monitor does not describe the characteristics of the cathode ray tube enclosed.

E– Providing clear definitions regarding color contrast is more difficult than for color itself because of the impact of both spatial and temporal factors. Graham & Brown have provided several definitions to clarify this problem.222 “Simultaneous color contrast involves a change in the hue, saturation and brightness of a test light owing to the influence of a nearby inducing color.” “Color adaptation is manifested by changes in hue, saturation, and brightness that occur during exposure to a given light; these changes may influence the perceived color of a succeeding light.” However, even these definitions do not separate brightness variations from color variations. This additional separation will be observed here. They also focus on the concepts of hue and saturation that are not intrinsic to the visual system as discussed below.

It should become evident that the current debate in philosophical circles is complicated by their reliance upon an inadequate model of the biological (and particularly the human) visual system as well as its interaction with the physical world223. It appears this community continues to rely primarily upon the additive assumption concerning the sensing of spectral light in the determination of color (although they also struggle with the Hering model which is incomplete), has relied upon an incorrect proposition related to the peak spectral wavelengths of absorption by the photoreceptors of the biological eye (particularly the long wavelength photoreceptor), and has not interpreted the color constancy effect properly. This leaves them at a great disadvantage when attempting to ascertain the truth with regard to almost any aspect of color. However, these problems do not discourage the debate among dedicated philosophers from continuing224. These discussions make interesting reading except for a fact noted by one of their own, “Teller sees only a tedious squabble about words.” This work will show that the physical color provided by the real world can be traced through the neural system until it results in the generation of three analog signal amplitudes that represent any color perceived by the organism. How the organism describes this perception to another organism is primarily a question of semantics.

The three analog values representing the perception of color related to an element of the scene can be stored in the volume of three small neurons. This is why the source of this register has not been found within the billions of neurons within the CNS. If the saliency map within a brain can be located, it will then be possible to locate the neurons storing the perceived color of any currently imaged scene element. It does not appear likely that the saliency map stores perceived color information in long term memory with any degree of precision.

The philosophical community does not have the information required to discuss color constancy with any degree of precision. The tone of their discussions suggest they are only talking about the first order perception of color while operating within the photopic region of vision. They appear to overlook the second order changes in color

221Sproson, W. (1983) Colour Science in Television and Display Systems. Bristol: Adam Hilger Ltd. pp 25- 115 222Graham, C. et. al. (1965) Vision and Visual Perception. NY: John Wiley & Sons pg 452 223Byrne, A. & Hilbert, D. (2003) Color Realism and color science Behavior Brain Sci vol. 26, no. 1, pp 3- 64. Continues in vol. 26, pp 52-63 (2003)

224Byrne, A. & Hilbert, D. (07 May 2004) Continuing commentary on “Color Realism and Color Science" http://web.mit.edu/abyrne/www/colorrealismrevisited.html Performance Descriptors 17- 199 introduced when an object is viewed using one source of light and then viewed using a second light source of significantly different spectral distribution, even within the photopic region. When comparing daylight to incandescent light, they do not recognize the significantly different perception related to the loss of signal under incandescent illumination related to the 400–437 nm region of the spectrum. 17.3.1 Historical background & the definition of color

The literature of the chrominance characteristics of human vision is so extensive as to be described as humongous. However, it is frequently contradictory, contains large amounts of anecdotal and unsubstantiated general material, and lacks a strong scientific base. The literature also exhibits two other prominent characteristics. It is the most prominent example in science of reliance upon semantics in the absence of a theoretically based numerically oriented description of a phenomena or system. It is fundamentally in error since it does not recognize the inherent tetrachromatic capability of the human visual system. McCamy characterized the situation with regard to one system of color descriptors as: “Unfortunately, the five principle hues of the Munsell hue circle do not relate in any way to any previous theory of color vision nor to the application of trichromacy to color reproduction.225” This is because every scientific epoch in vision has assumed a different number of critical pigments or lights. The first began with Young using three. Then Hering focused on four (or six). Munsell then introduced the idea of five. It will become clear later that Munsell’s choice was fortuitous in an unusual aspect.

As McCamy points out, the problem is further complicated by a lack of precise definition of the word color. There are a variety of specialized definitions of color, most of which are found in the creative and graphic arts, not the sciences. MacAdam recently addressed this problem just within the scientific community226. Section 17.3.1.4.1 and the glossary of this work provides eight specialized definitions of the term color. This work will focus on color as the perception reported by the human in response to an external electromagnetic stimulus. This perception can be associated with a perceptual space that is closely correlated with the electrical signals in the S-Plane of the retina.

Another complication is the frequently heard assertion that the human eye can discriminate as many as several million colors from each other. These types of statements are semantically sloppy. The human eye has no absolute chromatic sensitivity. It operates on chromatic (and luminous) differences. In most color oriented laboratory experiments, the eye is used as a null detector or to arrange a set of samples in a orderly sequence. The eye is not able to estimate the chromatic difference between two samples unless it views them simultaneously.

As an example, show a subject two in a time sequence separated by three seconds. Then ask him/her to tell you which one was closer to green and specifically how much closer to green it was (in terms of resolvable steps).

As a second example, ask a subject to view three similar color samples in time sequence, two of which are metameres. After two or three seconds, ask the subject to tell you which two of the three were metameres and how they differed chromatically from the third sample. Then ask the subject about the difference between the metameres. It matters little in the above experiments whether the subject knows in advance what questions he will be asked. It also matters little what the ambient light conditions are. The subject is hard pressed to assign an absolute color to any color sample.

In everyday usage, a subject is limited in absolute color discrimination to about twenty colors. The basic colors typically consist of the number of named radials in the Munsell Color Space consisting of about six clearly different colors and the colors intermediate between these colors. Beyond this dozen colors, the ability of two subjects to provide the same names to samples presented in a double blind experiment becomes very small.

225McCamy, C. (1993) The Primary hue circle. Color Res. & Appl., vol. 18, no. 1, pp. 3-10 226MacAdam, D. (1985) The physical basis of color specification, in Color Measurement: Theme & Variation, NY: Springer-Verlag, pp 1-25. 200 Processes in Biological Vision

To achieve, maximum discrimination (under controlled lighting conditions to assure repeatability) sample pairs should be of finite size (to be determined) and uniform surface reflectance. They should also be in juxtaposition with each other with the part line falling on the fovea and possibly be limited to part lines falling on the foveola. Although authors frequently describe either the C.I.E. and the Munsell systems of color notation as predating and leading to the other, they are inherently different. They indicate the significant problem of interpreting empirical data in the absence of an adequate theoretical model. The description of the human color capability based on a circle is a very ancient methodology. Birren provides an interesting summary of some of the variants encountered over time227. One of these, due to John Ruskin, equates the color circle with the twelve signs of the zodiac. The color names John used are, if nothing else, lovely. More recently, Fehrman & Fehrman have re-visited this ground from a current artistic and architectural perspective228. The inadequacy of the C.I.E system has been summarized very succinctly by Venkataraman; “the CIE system does not provide a satisfactory specification of color for two reasons: (a) the variability of chromaticity coordinates with colorant concentration, and (b) the non-uniformity of the color space with respect to visual perception.”229 This work will correct the above problems. It will provide a definition of the word color as it applies to a number of situations. It will also provide a theoretical foundation for both the Munsell Color System and, to the extent possible, the C.I.E Chromaticity System.

---- The development of our understanding of color as a science has occurred during a series of epochs. These began with the early “philosophical” scientists, was followed by the empirical “physicists” and has recently culminated with the efforts of the psychophysicists.

17.3.1.1 Early philosophical models; Young, Maxwell, Hering & Kries

Thomas Young is generally credited with being first to concentrate his efforts on the science of color in 1802-03. However, Newton preceded Young by at least 130 years.

Newton included a in his 1666 Opticks that was later also developed by Hering and perfected by Munsell.

Young’s steps were quite tentative. Young espoused a three node color space that was initially described by the colors red, green and blue. A year later he wrote in terms of red, green and violet without giving a clear reason for the change. Maxwell followed Young by a half a century and stayed with the red, green & violet triad. Late in the 19th Century, Hering espoused his system based on a quadrate consisting of two pairs of colors. His color pairs were red & green and blue & yellow. Kries introduced a different mathematical arrangement based on Hering230. In the red-green pairing, he specified perceived red as resulting from stimulation of both the S– and L– spectral channels. In is blue-yellow pairing, he specified yellow as resulting from stimulation of both the M– and L– spectral channels.These writers based there choices primarily on their own observations. Any further justification was largely philosophical (in the current usage of the word). Silvestrini and Fischer have provided an extensive history of the various theories of color (59 by their count) from Young’s time forward231. Each of the color spaces described by the above investigators can be rationalized with the more fundamental color space of this work. The key is to recognize that perception involves color differencing in an orthogonal color space. In this interpretation, white is represented by a null condition in each of two channels. Based on the

227Birren, F. (1966) Color: a survey in words and pictures. New Hyde Park, NY: University Books, Inc. pg. 145 228Fehrman, K. & Fehrman, C. (2000) Color: the secret influence. NY: Prentice-Hall 229Venkataraman, K. (1977) The anaylytical chemistry of synthetic dyes. NY: John Wiley & Sons. 230Werner, J. (1998) Aging through the eyes of Monet. Chapter 1 in Backhaus, W. Kliegl, R. & Werner, J. Color Vision: perspectives from different disciplines. Berlin: W. de Gruyter pp 24-26 & 35-38 231Silvestrini, N. & Fischer, E. (2003) Color order systems in art and science http://www.colorsystem.com/index.htm Performance Descriptors 17- 201

proposed fundamental color space, both the Hering and the Kries color spaces involve color differences in the presence of a specific spectral bias. While the Young and the Maxwell conceptions of perceived color can be understood, as due to the summation of spectral signals involved, the underlying situation is quite different. The descriptive words of Werner regarding Monet’s visual condition and artistic accomplishments late in life are very useful (pp 35-38). However, the words lack scientific credence based on our current knowledge of the visual process and the additional capabilities of the aphakic eye to see colors (in the 342 nm to 400 nm region) not otherwise seen or named by humans and to impact the perception of colors in the 400 nm to 437 nm region) See subsequent sections below. As a preview, Figure 17.3.1-1 shows how the theoretical model of this work provides a foundation for both Newton’s original color wheel and the Young equilateral color space. While Young’s color space was equilateral, based on his reading of the laws of colored light summation in object space, it is easily transformed to a right triangle in perceptual space and overlaid on the New Perceptual Chromaticity Diagram. The diagram assumes equal photon flux per unit wavelength for all stimuli and a fully dark adapted eye (or equivalent). While this triangle transformation can be considered conformal, it is not rectilinear. The result is a “white” that appears near the hypotenuse of the triangle shown by the dashed line at 45 degrees. With the transformation, the white point is at 40% of the length of the two legs of the triangle from the right angle. Newton’s color wheel was perceptual in character and merely needs to be rotated 135 degrees to overlay the New Perceptual Chromaticity Diagram as shown by the dashed circle. The circle is annotated with labels corresponding to Munsell’s color space.

The triangular overlay demonstrates the broad area of color space (the magenta’s) not addressed adequately by Young’s color space. This is the region that cannot be matched to additive combinations of three narrow band primaries of red, green and blue in photometry (colorimetry). Such matching requires a green component be added to the test sample to bring it within the confines of the right triangle. Newton’s color space, as definitized by Munsell, includes all of the color space of human vision. 202 Processes in Biological Vision

Figure 17.3.1-1 A foundation for both Newton’s and Young’s conception of color space. Only simple transforms are required to overlay them onto the New Perceptual Chromaticity Diagram

None of these early investigators were aware of the ultraviolet sensitive spectral channel of the human retina. They typically ignored the color space represented by spectral wavelengths shorter than 437 nm. 17.3.1.2 Early empirical model of Munsell and the C.I.E.

In the early 20th Century, two efforts were made to quantify the color space. Munsell provided a largely philosophical color space, based on his work as an artist, but one quantified so that he could use it to specify the colors needed to prepare different paints232. He offered no theoretical foundation for his choice of a five node system based on red, yellow, green, blue and . The C.I.E took a different approach based largely on the blossoming needs of industry to quantify what people could see within the color space. While basing their approach on the trichromatic hypothesis of Young-Maxwell, quantifying their results with a precision of about five nm, and presenting their color space using cartesian coordinates, the C.I.E. approach lacks any theoretical foundation. Fairman, et. al. have provided a recent narrative

232Long, J. (2011) The New Munsell Student Color Set: 3rd Edition NY: Bloomsbury Academic ISBN-13: 9781609011567 Performance Descriptors 17- 203 describing the development of the C.I.E color-matching functions233. Their conclusions were two. First, the procedure followed was logical based on the formulating principles adopted. Second, they concluded “We have shown that likely none of these formulating principles would be adopted if the system were formulated from a fresh start today.” Neither Munsell or the investigators associated with the C.I.E. were aware of the ultraviolet sensitive spectral channel of the human retina. 17.3.1.2.1 The Munsell perspective

McCamy has provided a good review of the background of the Munsell Color System, including the left-handedness of the Munsell system notation. He also provides a proposed modification to the Renotated Munsell Color System of 1967. Unfortunately, his paper does not contain any substantive theoretical model supporting his proposal nor specific wavelengths for the variety of colors he deals with. Although he bemoaned the lack of a theoretical foundation in the work of others as noted above, his new proposal remains based on semantics and empirical data. While the problem he desires to correct is well known, the more rigorous statistical approach of Indow & Aoki234 is more appropriate but remains based on empirical data, not a theoretical base. Lacking a theoretical base, it is useless to discuss which of the Munsell labels blue-violet, blue, and violet-blue better describe the semantic blue described by McCamy. Fehrman & Fehrman have provided a detailed list of Munsell’s conception of the original space235. Guth has introduced a largely conceptual model of the visual system (not related to physiology) and raised several problems with the Munsell Color Space236. These concerns are at a very precise level. Similar concerns have also surfaced in the development of this work. However, Guth continues to assume a color space based on radials that do not change hue with radius.

Boker237 has introduced a level of mathematical theory not commonly found elsewhere in the visual sciences. He outlines the steps required to show that what he calls the perceptual color space is in fact continuous from a mathematical perspective. This condition is satisfied if the coefficients of the terms in the functions defining the color space are continuous and well behaved. This condition is necessary if the color space is to be amenable to routine mathematical description. Unfortunately, Boker’s approach cannot be used to demonstrate his thesis that the color space has a metric (is in some mathematical sense continuous) without knowledge of the underlying mathematical functions that describe that color space. His lack of an adequate theoretical model of the visual system is indicated by the empty section of his paper labeled “Neurophysical models.” Using the models of this work, equations will be presented below that demonstrate that the visual color space does exhibit a “metric” since the functions creating that space are mathematically well behaved both individually and as a group. In fact, the color space conforms to the so-called local Euclidean metric. This is the type of color space sought by the C.I.E. in moving toward, but not achieving, a uniform color scale in their more recent Chromaticity Diagrams.

Relying on the literature, Boker describes the nature of the signaling transforms present in the visual system as a truly tangled mapping which is both many-to-one and simultaneously one-to-many. This work attempts to provide significant clarification in this area. It shows that the “many-to-one and simultaneously one-to-many situations he describes are in fact entirely determinate. One must merely use a different transformation to obtain an orderly mapping through the system. The question of mapping entails several levels of encoding, some of which are reversible and some are not. It concludes the system only involves feedforward signal processing at the signal path level and that the fundamental many-to-one nature of the system is the result of a simple integration over the spectral interval of each photoreceptor cell. For purposes of signal projection, an additional many-to-one encoding scheme is used that is completely and unambiguously reversible within the cortex if required. The redefinition of the Munsell Color Circle by McCamy relies upon a mixture of the color names commonly associated with both additive and subtractive without defining these colors scientifically. This is unfortunate, because these names are associated with spectral characteristics that are not mutually exclusive. This

233Fairman, H. Brill, M. & Hemmendinger, H. (1997) How the CIE 1931 color-matching functions were derived from Wright-Guild data. Color Res. Appl. vol. 22, no. 1, pp 11-23 234Indow, T. & Aoki, N. (1983) Multidimensional mapping of 178 Munsell colors. Color Res. & Appl., vol 8, pp. 145-152 235Fehrman, K. & Fehrman, C. (2000) Op. Cit. pp. 202-203 236Guth, S. (1991) Model of color vision and light adaptation J. Opt. Soc. Am. A. vol. 8, no. 6, pp 976-993 237Boker, S. (1995) The representation of color metrics and mappings in perceptual color space. www.nd.edu/~sboker/ColorVision2/ColorVision2.html 204 Processes in Biological Vision

work will replace the term cyan (a name associated with a broad spectral band in printing) with (defined as associated with a narrow spectral band centered on 494 nm) when discussing a hue circle to avoid this problem. A similar problem is associated with the term yellow which is used widely in applications involving both additive and subtractive color. It would be best if this term could be divided into two semantically acceptable terms where yellow was defined as referring to a narrow spectral region centered on 572 nm. In this case, an alternate term, like canary, would define a color with a broader spectral absorption described below that was still centered near 572 nm. Unfortunately, the Y in yellow is used as part of the description of the CMYK, subtractive, color system of printing. This application oriented designation is not likely to change within the popular press in the foreseeable future. Within the process color community, the alternative label, CMCK is frequently encountered. The letters stand for “Cyan,” “Magenta,” “Canary,” and “Black” respectively. Canary, not yellow, is used to label the broadband spectral pigment. The New Chromaticity Diagram for Research presented in this Section should accomplish three goals. It should alleviate, and/or quantify, the concerns of McCamy over the accuracy of the renotated Munsell Color System. It should also provide the theory required to precisely define the mathematical characteristics of the radials of the Munsell Color System (and if desired both the McCamy suggested modifications to that system and the C.I.E. (1976) Chromaticity Diagram ). It also provides a method of determining how well the available empirical Munsell data has been matched to a quasi-theoretical framework ala Indow & Aoki and how close the C.I.E. (1976) Diagram has come to an undistorted Euclidean color space. This work does not support the embarrassment expressed by McCamy concerning the location of semantic labels on the chromatic planes of the Munsell Color System. It does provide a theoretical framework with which to judge the assertions by both Judd and Nickerson and by the ISCC- NBS regarding the semantic labels (in English) to be assigned to the radials of Munsell.

The 2-dimensional color space of the New Chromaticity Diagram, in agreement with the Munsell book of Colors, IS NOT circular. It is both rectangular and rectalinear. The axes are orthogonal. Any use of a color circle is merely a limited representation, for pedagogical purposes, of the rectilinear color space in circular coordinates.

Kuehni asserted in 2002, “A Euclidian uniform psychological or psychophysical color space appears to be impossible238.” While he did not provide a detailed proof of this assertion, it is clear that he was not considering an adequate physiological model of the visual system. He does note the need to define the term uniform precisely. “Here, uniform has the meaning of equal relative increments in unique hue and in blackness/whiteness based on defined starting and end points.” He did not include saturation. He discounts the Munsell Color Space as not being a meaningful psychological space as its chromatic axes are not defined. Sections 17.3.4 & 17.3.5 provide a resolution to this shortcoming. He concludes his limited discussion as follows. “Much fundamental work needs to be done.”

The color space developed by Munsell relied upon the concept that the sensation of hue did not change with saturation. As a result, the color space exhibited cylindrical symmetry about the white point. Wyszecki & Stiles note that this symmetry is not perfect and the observed hue rotated with illuminance239. By overlaying the Munsell Color Space on the New Chromaticity Diagram for Research, an additional complication is recognized. The skewing recognized by Wyszecki & Stiles is not uniform with hue angle. They made the empirically based observation that there was no skew associated with the 10Y radial and a second radial between 5P and 7.5P. Based strictly on theoretical considerations, only the 10PB, 10Y, 5R and 5BG radials should be straight lines in the New Chromaticity Space. Stated differently, there is no skew associated with the Hering axes of the Munsell Space, only for off-axis radials. The skewing is due to the fact that the underlying color space is rectilinear (based on P and Q values) and not radially symmetrical. When expressing the New Chromaticity Diagram for Research using a radial coordinate system, hue is not constant along a given radial. Sproson has plotted the radials of the Munsell Color Space on the CIE UCS (u’, v’) color space to illustrate the curvatures between the two240. Unfortunately, the 1976 modification of the 1960 CIE UCS space is still not orthogonal. It would be useful to see the same data, as well as the UCS coordinates plotted on the New Chromaticity Diagram for Research. . 17.3.1.2.2 Hue and Saturation are not intrinsic

A number of systems have been defined to illustrate the chromatic properties of vision based on a cylindrical

238Kuehni, R. (2002) Color: what could it be? SPIE Proc vol 4421 pp 642-645 239Wyszecki, G. & Stiles, W. (1982) Op. Cit. pg 509 240Sproson, W. (1983) Colour Science in Television and Display Systems. Bristol: Adam Hilger Ltd. pg 152 Performance Descriptors 17- 205 coordinate system. However, there is no indication that the visual system can process the transcendental functions required to support a cylindrical (or spherical) coordinate system. While presenting chromatic information in a rho,theta format is useful pedagogically, this presentation mode can not be related to the mechanisms of vision. The visual system employs a cartesian coordinate system. The quantities actually utilized in the visual system correspond to rho tan theta and rho cotan theta.

17.3.1.3 The C.I.E. (1931 & 1964) concept of color space is invalid for research

A brief description of the C.I.E color spaces surfaces some of the critical factors underlying their representations. 1. Grassman hypothesized a set of "matches,” not mathematical equations. 2. During the 1920-30's, the community interpreted Grassman's matches as algebraic laws applicable to light in object space. The CIE 1931 and 1964 chromaticity diagrams were based on the assumed additivity law and applied to a stimulus-based model in object space. Because of inconsistencies in this approach (RGB had to be replaced by XYZ), a "Standard Observer" was defined that was consistent with the XYZ system. 3. A well known problem in applying the stimulus-based approach was the failures of a real human observer to match colors in a bipartite color matching experiment in accordance with the standard observer.

4. Beginning in the 1960's, the CIE addressed the problem of developing a perception-based framework. The CIE Lab & Luv spaces were perception-based and their equations involved differences instead of Grassman's additions (see equations for L*a*b* & L*u*v*in the attachment).

5. The latest L*a*b* color space is approaching and very near my theoretical Chromaticity Diagram for Research (as cited earlier) if the a* and b* axes are rotated about 20 degrees. The L*a*b* space is also in agreement with Munsell's Color Space and compatible with Hering's axes in color space.

Grassman's Matches apply in additive form to the stimulus-based CIE 1931 & 1964 Chromaticity Space and the artificial "standard observer." Luminosity is always an additive process. Chromaticity is always a subtractive process. Chromaticity also involves two orthogonal axes (three for any wavelengths shorter than 437 nm) and vectorial subtraction. Grassman's Matches in subtractive form apply to the perception-based L*u*v* and L*a*b* uniform color spaces and the human or "real observer" (along with Herings's hypothesis, Munsell's empirical Color Space, and my theoretical Color Space). Bipartite color matching conforms to the subtractive form of Grassman's Matches as easily demonstrated using these latter Color Spaces.

- - - - -

The C.I.E developed a color space based largely on the blossoming needs of industry to quantify what people could see within the color space. The result was a first order, application oriented, description of color vision. Their approach was based on the trichromatic hypothesis of Young-Maxwell. However, the approach lacked any rigorous theoretical foundation. It is a description of color in object space and does not claim to represent the human perception of color. It is not compatible with the larger context of tetrachromatic vision relevant to the research environment. A critical problem with the C.I.E. concept of color space is its intrinsic assumption that the human visual system is linear and a linear transform can be created between the perceived response functions, R(λ), G(λ) & B(λ) and the C.I.E. object space functions x(λ), y(λ) & z(λ)241. Unfortunately, this assumption is known to be, and is demonstrably, false, thus undermining the entire C.I.E. color space concept. This is a major problem in the study of vision. Using linear matrix algebra to convert between the parameters of object space and perceptual space specified by the C.I.E. is not viable. Bird & Jones discuss the fact that at least three different methods exist for representing the fundamental response functions. They also discuss the fact that if the response functions are not linear representations of the C.I.E. 1931 color mixture functions, “it is not possible to define the corresponding primaries on the C.I.E.-1931 chromaticity diagram.” The Perception-based Chromaticity Diagram of this work and the Object-space Chromaticity Diagram of the C.I.E

241Bird, G. & Jones, R. (1965) estimation of the spectral response functions of the human cone pigments J Opt Soc Am vol 55(12), pp 1686-1691 206 Processes in Biological Vision are not contradictory. They are complementary. The research oriented Perceptual Chromaticity Diagram provides more details that can be applied to the object oriented C.I.E. Chromaticity Diagram. The perceptual diagram is particularly useful in illuminating the spatial non-linearities of the C.I.E. Chromaticity Diagram (Section 17.3.5.3). It is also important to note the C.I.E concept of color space relies on a single zone model. It assumes the signals from the various photoreceptors are linearly summed to provide the brightness signal and that other groupings of signals are linearly summed to provide the chrominance signal(s). These assumptions are demonstrably false based on electrophysiological measurements made as early as the 1950's by Svaetichin and by Tomita (Section 17.3.1.4). The human visual system involves a multi-zone architecture that is incompatible with the C.I.E. concept of color. 17.3.1.3.1 Analyses by other investigators

[xxx need to rewrite showing that one cannot match a purple with red green and blue ] Rubin & Walls242 provide a good review of the development of the CIE Chromaticity Diagram. A more comprehensive review including the 1976 modifications can be found in Miller243. Unfortunately Miller published in a trade journal not widely indexed. The progression from the 1924 diagram to the 1931, and then the 1960 which was “rapidly” replaced by the 1976 version, indicates the problems with the underlying concept (Section 17.2.xxx).

Basically, the diagram is derived from two linear equations:

C = xR + yG + zB where C is the “total color” and x, y & z are in percent

x + y + z = 100

The terms R, G, & B are assumed to be real functions representing the spectral absorption of the individual photosensitive channels of animal (in this case human) vision. Real is used here in the mathematical sense. The coefficients of these terms are assumed to be positive. Based on these two equation, both of which are linear, the description of a color is specified by plotting x and y with z known implicitly from the second equation. It is conventional to plot x and y along orthogonal axes in a Euclidean space. As pointed out by Rubin & Walls; “If three distinct primaries (red, blue, and green) are carefully chosen and standardized, all colors can be denoted as containing a certain proportion (i.e. percentage) of each of the primaries in the mixture.” They go on: “If we take only the colors in the spectrum, all the colors which correspond to the monochromatic radiations in this spectrum can be plotted on a curved line called the ‘spectrum locus’. The end points of this curve are joined by a straight line called the ‘purple line’.” They then proceeded to define how these primaries are chosen. Their two paragraphs are quoted in their entirety below.

“By far the most satisfactory method of colorimetry [to date] is one which is actually a process of tricolorimetry but employs an imaginary tricolorimeter, three imaginary primary lights, and an imaginary observer. This is the modus operandi of the CIE system of color specification. The raw datum required is simply the spectroradiometric curve of the sample--drawn automatically ‘while you wait’ by such an instrument as General Electric’s recording photoelectric spectrophotometer. From this curve, three others are derived, each of which shows for each wavelength the amount of one CIE primary light required to help afford a tricolorimetric match for the sample’s energy at that wavelength. The integrals of these three curves are thus the total amounts of the three CIE primaries which, mixed, would form an equivalent stimulus. The CIE primaries themselves are hypothetical lights whose colors are supersaturated--made so quite simply with pencil and paper since they represent perfectly legitimate ‘homogeneous linear transformations’ of the real color- mixture data of a group of real human observers. The average of these real observers constitutes the hypothetical CIE ‘standard observer,’ mixing the hypothetical primaries in a nonexistent instrument to make a visual match for the sample. Any way you slice it, the colorimetrist has a nerve if he claims he is measuring anything about the sample he is ‘specifying’!” The last sentence is quite compelling from recognized leaders in the field.

242Rubin, M. & Walls, G. (1969) Fundamentals of visual science. Springfield, IL: Charles C. Thomas, pp. 251-268 243Miller, K. (1985) Call to the colors. Photonics Spectra, February, pp. 75-82 Performance Descriptors 17- 207

These are only a few of the comments by many authors calling for a new Chromaticity Diagram for scientific purposes. It is granted that the 1931 Diagram is widely used in commerce where precision and correctness takes a back seat to consistency and stability. Furthermore, adding pigments in the commercial world is an inherently linear process. However, science should not be trapped into a situation where the locus of the spectral wavelengths are arbitrarily and erroneously specified as in the 1931 Diagram. For an interesting defense of the current standard, see the Science of Color244. Hunt added the observation245 that “It is also very important to remember that chromaticity diagrams are maps of relationships between colour stimuli, not between colour perceptions.” This statement appears too strong and a bit bizarre since these diagrams have all relied upon psychophysical data which by definition involves perceptions. However, Hunt’s position can be accepted to the extent the data was collected using the visual system as a null detector (a small signal technique). 17.3.1.3.2 Analyses based on this work

In visual research, a basic difficulty is that the CIE “color-mixture data of a group of real human observers” was assumed to involve linear visual processes. Furthermore, the G light was specified as the Photopic Luminosity Curve adopted by the CIE in 1924. Because of these assumptions, the pencil and paper transformations invariably required a secondary peak in the response of the red receptor; this secondary peak is 35% as high as the long wavelength peak and is located near 0.45:246. More seriously, this secondary peak is in the negative direction. No spectrographic recording has ever shown such a negative peak in the absorption characteristic of the long wavelength visual channel of any animal. Such a negative peak is not explainable theoretically.

The linear assumption simply cannot be supported under large signal conditions. Normal daylight vision involves large signal conditions. The color constancy phenomenon of vision is specifically designed to eliminate any misleading color shifts under large signal conditions. Vision is fundamentally logarithmic and involves a variety of highly nonlinear process. The scientists247 developing the adopted 1931 standard implicitly recognized the non- linearity involved. To avoid them, they presented the Tristimulus Computation Data with values ranging from 1 to 100,000, i.e., their methodology collapsed if they encountered values less than 1.0. Such values would involve negative logarithms. The same restriction was encountered in Chapter 13 when developing the equations relating to the non-algebraic addition encountered in animal vision.

In addition, defining the G light of the CIE tristimulus concept, which naturally becomes associated with the mid- wavelength spectral channel, as identical to the photopic luminosity function is not supportable. If true, this assumption would preclude the observation of brightness changes associated with the long wavelength or short wavelength spectral channel. While the Boynton school has attempted to eliminate the short wavelength spectral channel from the perceived luminance response, the difficulty with even this thesis will be analyzed in Section 17.3.1.5.

It is also worth noting the color mixture data developed for humans in the 1950’s by the National Television Standards Committee (NTSC) for color television. It showed clearly that humans did not require equal luminosities in each “color channel” of a color reproduction system for the human to experience a white sensation. The equations adopted involved about 15% for B and R with the remainder in the G light. These are similar to the percentages presented in Chapter 13 under Photopic conditions. Based on these studies, it is clear that the methodology, used by the C.I.E. is quite suspect. Equal weighting of the terms in the equation, x + y + z = 100 is not appropriate. An even more basic difficulty is the assumption that the visual system is based on the principle of “additive color” in object space. This thesis is strongly objected to by the Hering school. By totally separating the discussion of the luminance and chrominance capabilities of vision, a more realistic model of vision can be obtained. This model will demonstrate that, while the luminance aspects of vision rely upon additive processes, the chromatic aspects rely upon a spectral differencing technique. Another significant problem with the diagram is its treatment of “white” as a function of color temperature. The diagram is usually displayed as having a band of “white” that parallels the “Planckian radiator line.” This display

244Comm. on Colorimetry, ibid, pg 242-245 245Hunt, R. (1991) Measuring colour, 2nd ed. NY: Ellis Horwood, pg. 56 246Comm. on Colorimetry of Optical Society of America (1963) The Science of Color. Washington, DC: Optical Society of America pg. 265 247Comm. on Colorimetry, ibid, pg 264-267 208 Processes in Biological Vision

gives an erroneous impression and raises a question about how widely Hunt’s statement is observed. Depending on how it is observed, the conventional figure gives the impression that either the color stimuli along this band remains white continually, or the perceived color along this band remains white continually. However, neither of these situations is tenable. It is difficult to believe, the “color stimuli” can remain white over such a range of content based on additive color principles. The perceived color across the face of the chart varies considerably as a function of color temperature. At a color temperature near 6500 Kelvin, the “white” zone is an elliptical area near x=0.32, y=0.32 and the area near x=0.42, y=0.45 is yellowish-orange. At 2856 Kelvin, the situation is reversed, the first area is greenish-blue and the second area is “white.” This is apparently the reason the CIE never sanctioned a colorized CIE Chromaticity Diagram. The perceived colors are not stable when referred to the coordinate system in this figure . As presented, the white band of the CIE Diagram is more accurately defined as an envelope that contains the instantaneous area perceived as “white” without properly representing the instantaneous perception of color in this area. A more realistic representation of the correlated color temperature of a source is presented in Fehrman & Fehrman and credited to Bright Ideas248. The presentation in color plate 4 & 5 of Nassau249, and credited to Minolta, are believed to more properly represent both the 1931 Chromaticity Diagram and the 1976 u,v diagram. However, it is important to note that these figures are reproduced using a very limited capability 4-color subtractive color system as used in commercial printing. The list of theoretical difficulties with the C.I.E. (1931) Chromaticity Diagram can continue ad nauseum. The most serious objection is that it does not represent the actual color performance of any real individual. The Standard Observer is an entirely artificial object. The revised (1976) Diagram attempted to at least linearize the color space it attempted to represent. The success of this process can be gauged from [Figure 17.3.3-10] below. This figure shows the axes of the theoretical color space developed in this work to the color space of the C.I.E (1960) Uniform Color Space based on the work of Farnsworth. A goal of any new chart should be a rectilinear chromaticity presentation and/or a Spectrum Locus that display equal wavelength increments in equal distance increments. In such a chart, it would be possible to properly illustrate the actual spectral response of the eye in a proportional manner. Showing clearly its total would also be possible, although the printing process might fail to reproduce it completely. It would also be possible either to eliminate or give more meaning to the Purple Line.

Until a new CIE Chromaticity Diagram is adopted, any researcher should use great caution when invoking the 1931 through 1976 Diagrams as a foundation for, as a tool in or as corroboration of his work. 17.3.1.3.3 The C.I.E. color space is nonconformal

The C.I.E. 1931 color space has been known to be nonconformal for a very long time. Farnsworth first provided a quantitative discussion of this subject. A wide variety of studies have been made over the years attempting to define various empirical formulas to define the human color space250. These empirical studies resulted in the arbitrary changes in the CIE color space of 1960, and then in 1976. The change between the 1960 and the 1976 Diagrams was an arbitrary change in the v* scale of 1.5:1. It is unfortunate that the CIE chose to call the new color spaces as “Uniform Color Spaces.” These spaces remain nonconformal as reported in the general literature.

Krauskopf, Williams & Heeley have attempted to define the cardinal directions of color space using psychophysical measurements plotted on the nonconformal C.I.E. (1931) Chromaticity Diagram251. As demonstrated in Section 3.5.3, the obvious problem was there assumption that tangents generated in a local area of the Diagram could be extended as straight lines to their intersection with the spectral locus. These intersection are occasionally defined using the term copunctal points. Their terminology employed reddish, greenish, bluish and yellowish instead of more precise terms. Their discussion summarizes the limited utility of their proposed axes. 17.3.1.3.4 The interpretation of the C.I.E (x,y) Chromaticity Diagram

The C.I.E. Chromaticity Diagram (x,y) is known to be highly distorted in its presentation (See Section 17.3.5.3). It

248Fehrman, K. & Fehrman, C. (2000) Color; the Secret Influence. Upper Saddle River, NJ: Prentice-Hall, figure C-7 249Nassau, K. ed. (1998) Color for science, art and technology. NY: Elsevier 250Wyszecki, G. & Stiles, W. (1982) Op. Cit. pp 825-830 251Krauskopf, J. Williams, D. & Heeley, D. (1982) Cardinal Directions of color space. Vision Res. vol. 22, pp 1123-1131 Performance Descriptors 17- 209

also exhibits characteristics that are hard to define. The “purple line” is one of these characteristics. It has no theoretical foundation and merely connects two arbitrary points on the spectral locus as calculated in r,g and hence x,y space. These points are usually taken as 380 and 700 nm. The spectral locus is also based on less than a strong theoretical foundation. There is a triangular sector bounded by “a white” point and the two end points of the spectral locus. This area is frequently labeled the area of non-spectral colors for non-obvious reasons. The underlying reason relates to the methodology of “one-wavelength colorimetry.” This methodology is based on the principle of additive color and says that any color should be obtainable by mixing a white light with a second monochromatic light. It is obviously impossible to achieve this result along radials from the white point that do not intersect the spectral locus. Thus colors in this region are labeled non-spectral even though they are easily obtained by merely mixing two spectral lights. Smith & Pokorny discuss a variety of other problems with the above diagram252. Some of these have been discussed elsewhere in this document. A very important point is that the C.I.E. Chromaticity Diagram relates to “matches” made in object space under nominal but undefined or poorly defined conditions. As an example, the viewer should be fixated on the center of a bipartite field of unspecified diameter. Furthrmore, for similar matches to be achieved by two different observers, both observers must be pre-adapted to the same unspecified illumination prior to the matching. To avoid the effects of color constancy due to adaptation, it is necessary that an individual match be made during a short time interval.

Long ago, a spectral locus was calculated for the C.I.E. (1931) Chromaticity Diagram. This locus is generally shown as a single valued function in x,y coordinates. However, Brindley has shown that this is not the case in the spectral region beyond 645.2 nm253. Beyond this value the function is dual valued. This fact is recognized in the 1964 Supplement to the original diagram.

As a result of this work, figures have been drawn illustrating the nonconformality of the CIE (1931) Chromaticity Diagram. See Sections 17.3.5 for a detailed discussion and Section 18.1.5 with regard to an application. Similar analyses are available showing the nonconformality of the the CIE 1960 and 1976 Chromaticity Diagrams. 17.3.1.3.5 An interpretation of the Planckian Locus on the CIE Diagram

In 1963, Kelly computed a Planckian Locus for application to the C.I.E. (1931) Chromaticity Diagram254. He continued the assumption that the Chromaticity Diagram applied to object space and that all of the coefficients in the defining equations related to vision were constant. The discussion in Wyszecki and Stiles provides the background for these highly abstract and empirical calculations255.

The formulation of Kelly was based on fixed coefficients and additive color processing. It exhibits a minimal correlation with actual vision. The results of the calculations are not compatible with any change in the gain of the adaptation amplifiers of the photoreceptor cells that normally result in the phenomena of color constancy. As a result, the description of the Planckian Locus on the CIE Chromaticity Diagram is limited to an object space that is observed by a man-made colorimeter employing constant gain coefficients in its signal processing circuits. It does not represent any perception of color by any biological visual system.

A human observer viewing a scene illuminated by a Planckian radiator does not perceive any change in the scene as long as the illumination level is compatible with the photopic illumination range of the eyes (all adaptation amplifiers are within their operating range). Under these conditions, the gain of the individual spectral sensing channels change gain inversely with the magnitude of the stimulus. To the extent the adaptation amplifiers are able to maintain constant signal levels at the pedicles of the photoreceptor cells, the white point of a scene does not change as a function of color temperature and the Planckian Locus is perceived as a single white point located at P=0, Q = 0 in the coordinates of the New Chromaticity Diagram or approximately x = 0.33 and y = 0.33 in the CIE

252Smith, V. & Pokorny, J. (1975) Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm. Vision res. vol. 15, pp. 16-171 253Brindley, G. (1955) The color of light of very long wavelength J. Physiol. vol. 130, pp. 35-44 and later writings. 254Kelly, K. (1963) Lines of constant correlated color temperature based on MacAdam’s (u,v) uniform chromaticity transformation of the CIE diagram J. Opt. Soc. Am. vol. 53, pp 999- 255Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons, pp. 133- 146 & 224- 228 210 Processes in Biological Vision

Chromaticity Diagram. It is only when the illumination intensity falls below the level needed to maintain photopic operation that the perceived Planckian Locus begins to move. This can occur in two different ways. In the first, the light level can be reduced while maintaining a fixed color temperature. Under this condition, the perceived white point will vary depending on which spectral channel first deviates from maintaining a nominal signal amplitude at its pedicle. Describing the result of this event is complex because of the possibility that the long-wavelength spectral channel may go into square-law operation independent of the actual adaptation amplifier performances (another characteristic of the mesotopic illumination range). In the second case, the light intensity can be maintained constant in some radiometric sense while only the color temperature of that source is reduced. This condition is also complex since how the radiometric intensity is to be maintained is not obvious. Artists have adopted different approaches to illustrating the Planckian Locus on a colorized CIE Chromaticity Diagram based on the assumption of constant coefficients and Kelly’s calculations. The most common approach has been to show the “white area of the diagram as including the majority of the Planckian Locus between 2400 and 10,000 Kelvin. This has resulted in a hot dog shaped white area. However, this is in conflict with reality. The “white” area remains a nearly circular ellipse with a ratio of less than 1.5:1 between major and minor axes regardless of color temperature. When viewed by a man-made colorimeter, the center of the white area would move along the Planckian Locus. When viewed by a human, the white point would remain fixed until the photopic range of the eyes is no longer maintained. There is no problem in representing the white point in the perceived color space of the New Chromaticity Diagram. It remains fixed at P = 0, Q = 0 while the perceivable range of color space moves in toward the white point at reduced color temperatures or reduced incident intensity. 17.3.1.3.6 The interpretation of the C.I.E (a*,b*) or CIELAB Chromaticity Diagram

Nassau has also provided color plate 6 attempting to provide a visualization of the CIELAB Diagram overlayed with a Munsell Color Space, also credited to Minolta Corporation. Here again, the limitations of the 4-color subtractive color process used in commercial printing must be emphasized. Furthermore, the artist is attempting to show the color rendition at a much higher luminosity than he shows the central null area. The caption makes it clear that the CIELAB nomenclature is meant to be a scaled version of the Munsell renotated Color Space. What is not shown is the fact that the Munsell Color Space is not circular. The Munsell space is distinctly non-circular and the neutral point is not at the geometric center of Munsell space. The CIELAB presentation appears to remain an approximation to accommodate the empirically derived mathematical approximations used rather than represent any theoretical description or empirical measurements. The actual, and relatively bazaar, forms of the CIELAB and CIELUV color spaces are shown in detail in Wyszecki & Stiles256. The last line of the caption of each of these presentations is interesting if not confusing. 17.3.1.4 The early electrophysiological measurements; Svaetichin and Tomita

Beginning in the early 1950's, Svaetichin began exploring the retina using electrical probes257. He was followed closely by Tomita in the 1960's258,259. They were the first to record electrical signals from the retina with respect to the spectral wavelength of the excitation source. They published a variety of their results but were unable to provide a complete interpretation of them. Such an interpretation required a theoretical model that was more sophisticated than those available based on either Young-Maxwell or Hering, or the single zone model adopted by the C.I.E.. 17.3.1.5 More recent psychophysical models 17.3.1.5.1 Recent psychophysical model of McLeod & Boynton

During the latter part of the 20th Century, a new set of color spaces were presented based loosely on a trichromatic hypothesis with respect to photoreceptors but the Hering hypothesis with regard to color perception. These spaces

256Wyszecki, G & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons pp. 166-167 257Svaetichin, G. (1953) The cone action potential Acta Physiol Scand vol 29, Suppl 106, pp 565-600 258Tomita, T. (1965) Electrophysiological study of the mechanisms subserving color coding in the fish retina In Cold Spring Harbor Symposia on Quantitative Biology, Volume XXX. Long Island, NY: Cold Spring Harbor Laboratory pp 559-566 259Tomita, T. Kaneko, A.Murakami, M. Pautler, E. (1967) Spectral response curves of single cones in the carp Vision Res vol 7(7), pp 519-31 Performance Descriptors 17- 211 were based primarily on psychophysical measurements and presented in a totally uncalibrated context. MacLeod & Boynton recognized the nonconformality of the C.I.E. Chromaticity Diagram and sought a better color space260. They proposed a new projection space, that remained based on additive color principles, by postulating “no contribution to luminance by B cones.” Their claim was that this projection “directly represents the excitation of each cone type without the use of oblique coordinates.” It exhibited the unusual feature that a bright blue light did not exhibit any luminance because of the definition, luminance = R + G. Their postulate that B cones do not participate in perceived luminance is a strange one. They reference Smith & Pokorny as the first source of this position261. However, fig. 3 of that paper clearly shows the shoulder near 437 nm that represents the contribution of the blue spectral channel to the formation of what is clearly a photopic luminous response. Smith & Pokorny do not address directly the subject of B cone participation in the overall luminous response. Their second source is two papers by Tansley et. al. in 1978. Tansley & Glushko stipulate that they carefully selected protanopes missing a red cone and deutranopes missing a green cone262. Yet, their photopic luminous efficiency functions for these individuals matched each other as well as that of a normal trichromat. Tansley & Boynton make a more defendable observation with regard to the dependence of matching colors across the transition line of a bipartite field under minimally distinct border (MDB) conditions263. They conclude that “the B cones make little or no contribution to the perception of borders at the MDB point.” This appears to have more to do with the bandpass of the P-channel ( as noted in the NTSC, see Section 17.3.3.2.8 xxx) than it does with the participation of the S-channel in the luminous efficiency function. Neither of these papers offered any model of the visual system they were attempting to evaluate.

In 1983, Drum re-examined the subject of S–channel signals contributing to the “achromatic sensitivity function.”264 His graphics show a considerable contribution from the short wavelength photoreceptors in the luminous efficiency function, reminiscent of the Judd discussions of the 1950's. Even while using 3400 K light and an equal energy assumption, he concluded that the premise that b-cones did not contribute to the luminosity function should be re- considered.

MacLeod & Boynton stress the lack of conformality in their figure without using the term. They perform elaborate calculation that relate back to the underlying C.I.E. dataset to describe distances that are apparently equal in their figure. They note the variation in threshold with position in their figure. No experimental verification of their color space was provided in their paper.

All of the scales used in the M-B color space were relative scales. However, they did plot a spectral locus on the graph with absolute wavelengths shown. The vertical, b, scale was defined as b = B/(R + G). The horizontal scale was defined by R + G = 1. These scales do not relate to any electrical or physiological model of the visual system. 17.3.1.5.2 The DKL model of Derrington, et. al. based on electrophysiology

Derrington, Krauskopf & Lennie have made measurements at the LGN of a group of macaque monkeys265. Their basic assumption was that the signals they recorded at that location were linearly related to the intensity of the stimuli provided. The so-called DKL color space was an outgrowth of the McLeod-Boynton approach. They used a spherical coordinate system that was largely conceptual. Their detailing of this system appears ambiguous. They claim they the luminance scale reflected the contribution of all three spectral channels proportionally. However, they later speak of luminance cells that responded only to the sum of the R and G components of the stimulus. They said the two axes in the chrominance plane intersected at the white point. However, they did not indicate the significance of negative values of B along the constant R & G axis. Most of their discussion involve measurements on cells exhibiting a difference signal, i. e, R-G or B-(R&G) or their negatives. They did not define the mathematical

260MacLeod, D. & Boynton, R. (1979) Chromaticity diagram showing cone excitation by stimuli of equal luminance. J. Opt. Soc. Am. vol. 69, no. 8, pp 1183-1186 261Smith, V. & Pokorny, J. (1975) Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm. Vision Res. vol. 15, pp 161-171 262Tansley, B. & Glushko, R. (1978) Spectral sensitivity of long-wavelength-sensitive photoreceptors in dichromats determined by elimination of border percepts. Vision Res. vol. 18, pp 699-706 263Tansley, B. & Boynton, R. (1978) Chromatic border perception: the role of red- and green-sensitive cones. Vision Res. vol. 18, pp 683-697 264Drum, B. (1983) Short-wavelength cones contribute to achromatic sensitivity. Vision Res. vol. 23, no. 12, pp 1433-1439 265Derrington, A. Krauskopf, J. & Lennie, P. (1984) Chromatic mechanisms in lateral geniculate nucleus of macaque. J. Physiol. Vol. 357, pp 241-265 212 Processes in Biological Vision relationship expressed by R&G. However, it is defined in a preceding companion paper266. The symbology R&G is used to describe “some combined signal from red-sensitive (R) and green-sensitive (G) cones.” They also assumed that the frequency of the action potentials represented a vector that was directly proportional to the modulation of the signal at the point of measurement. This vector could be resolved into a component related to the modulation of each of the three classes of cones (assumed vector addition). Based on their analysis, they offered two estimates of the wavelengths associated with two specific colors These wavelengths were determined using an approach similar to Krauskopf, Williams & Heeley discussed above. As will be seen below, the two estimates offered by DKL differed from the values proposed here by only a few nanometers. This was primarily due to their assumption that the C.I.E. 1931 Chromaticity Diagram was conformal (See [Figure 17.3.5-8]). No unit vectors were defined for the DKL color space. The axes were only defined conceptually. 17.3.1.5.3 The Chatterjee & Callaway data based on electrophysiology

Chatterjee & Callaway have recently reviewed the participation of S-channel photoreceptors in macaque monkeys267,268. Their experiments were based on a tri-color monitor as a light source. Although they performed extensive calibrations to maintain stability within their experimental data, they did not describe the effective color temperature of their monitor. Modern monitors have a typical color temperature exceeding 5000 K. Sperling & Harwerth have shown that the spectral performance of macaque monkeys and humans is virtually identical (Section 12.2.2). Chatterjee & Callaway showed the S–channel photoreceptors contributed 9% to the overall photopic spectral response of their subjects. This value was based on the additive assumption concerning the contribution of individual spectral channels to the total response rather than the more appropriate logarithmic assumption used in this work. Their value was determined from electrophysiological response as a function of contrast based on normally adapted and spectrally adapted eyes. In either case, it is clear that the S–channel photoreceptors play a significant role in the photopic luminosity function of mammalian eyes. 17.3.1.6 Recent measurements in the mesotopic region

Walkey, et. al. have recently presented some measurements269. Unfortunately, they used photometric units to determine stimulation levels on a tricolor monitor. It would have been preferred if they had calculated the amount of stimulation on a spectral channel of vision basis. They originally determined their data points in CIE (1931) x, y space and then transformed them to CIE (1976) u’,v’ space. Most of their work was within a relatively narrow chromatic range of the CIE color space. Their data appears to highlight two conditions, the continued nonconformality of the CIE scotopic color space and the greater loss of chromatic performance of the eye along the red-green axis. They noted on page S41; “The nonuniformity of the u’, v’ color space is well known, . . .” They also noted that the asymmetry in their ellipses varies with stimulation level. The cause of this will be developed theoretically in Section 17.3.3.6.

17.3.1.7 Continuing difficulties in empirical experiment design

17.3.1.7.1 The persistent introduction of pigment triangles and tetrahedrons

Many investigators have attempted to represent the color space of the trichromat, and more recently the tetrachromat, using equilateral geometric figures. As discussed in Section 16.1.3, these color spaces are highly nonconformal. Their value is limited almost entirely to introductory level pedagogy. They are unable to represent the full

266Derrington, A. & Lennie, P. (1984) Spatial and temporal contrast sensitivities of neurons in lateral geniculate nucleus of macaque. J. Physiol. vol. 357, pp. 219-240 267Chatterjee, S. & Callaway, E. (2002) S cone contributions to the magnocellular visual pathway in macaque monkey Neuron vol. 35, pp 1135-1146 268Chatterjee, S. & Callaway, E. (2003) Parallel colour-opponent pathways to primary visual cortex Nature vol. 426, pp 668-671 269Walkey, H. Barbur, J. Harlow, J. & Makous, W. (2001) Measurements of chromatic sensitivity in the mesopic range Color Res. Appl. suppl vol 26,pp S36-S42 Performance Descriptors 17- 213 perceptual range of color. Goldsmith used these forms in a recent review270. In an unusual twist, he used the terms S, M & L as relative terms in his figure 23. The lower left of his triangles are both marked S but they refer to different wavelengths in the blue or ultraviolet. Neumeyer and others have generally used the terms UV, S, M & L as absolute terms271. Since these color spaces are nonconformal, they have little utility in research. The various inconsistent figures in the literature attempting to plot the spectral locus within such a space illustrates the difficulties involved. 17.3.1.7.2 A critical problem with CIE conforming color measurements

The CIE has settled on the use of 10 degree and 2 degree fields for the collection of visual data over a period of years. When collecting data using the smaller field, it is quite common to use a bipartite field of this size surrounded by a larger field, typically of degrees. The bipartite field is frequently split by a horizontal line. Figure 17.3.1-2 shows that this is an inherently poor choice. The figure is reproduced from a plate in Davson based on an original by W. S. Stiles272. The original plate should be viewed to better interpret the following remarks. In each panel of the figure, the field is quite uniform, indicating an excellent match during chromatic discrimination studies, except for the central region along the line of fixation. In these studies, the results become quite different when the area within the 2 degree field surrounding the line of fixation is studied. There is a small area of about 1.2 degrees that is representative of the foveola of the retina. However, in the transition between this area and the surround, the measurements show two lips. These lips exhibit a smooth variation in chromatic discrimination capability with distance from the point of fixation, due to averaging of the signal illuminated by the test source.

Measurements within the 1.2 degree area representing the foveola are relatively uniform, except for a sharp division between the upper and lower lips. This division appears to be due to the method of chromatic discrimination within the higher neural centers of the brain. The area above and below the horizontal meridian are processed by separate regions of the brain and then merged. It appears the merging is not done well. In practice, the visual system does not rely upon chromatic discrimination in this region. The system is known to be largely insensitive to spatially fine changes in color within this area. It appears to rely upon the average value of the surrounding colored region to define the perceived color of material within the area of the foveola. 17.3.1.8 A new conformal color space based on electrophysiology is required

There is an obvious need for a truly conformal color space adequate for research purposes. Such a space would replace the earlier attempts at such a space discussed above. It would necessarily be a tetrachromatic color space to accommodate the generic visual system. Finally, it would recognize the electrophysiological architecture of the visual system. This architecture is based on multiple signaling channels employing differences in scalar voltages. It would not be based on the concept of additive color. Such a color space is presented in Section 17.3.3. Figure 17.3.1-2 The appearance of 10 degree fields arranged for metameric matches with different combinations of spectral lights. A 2 degree circle has 17.3.2 The chromatic discrimination been superimposed on each field. See the higher quality plate referenced. The outer parts of the field give a function, C(8,F) perfect match, but the central part, “Maxwell’s spot,” does not. The effect varies considerably in different 17.3.2.1 Background observers. The numbers at the sides give the wavelengths in nm mixed in each half of the matching field. From a There is good wavelength discrimination data for the plate in Davson, 1962 redrawn from an original by Stiles.

270Goldsmith, T. (1990) Optimization, constraint, and history in the evolution of eyes. Quart. Rev. Biol. vol. 65, no. 3, pp 281-322 271Neumeyer, C. & Arnold, K. (1989) Tetrachromatic colour vision in goldfish and turtle. XXX pp 617-631 272Davson, H. ed. (1962) The Eye, Volume 2: The Visual Process. NY: Academic Press, opposite pg 234 214 Processes in Biological Vision human eye in the literature. Wyszecki & Stiles273 provide a good review as of 1982, although individual cited papers must be examined on questions of experimental procedures. Of particular importance was the energy distribution of the illumination source used, the band edge characteristics of the filters used, and the statistical variation in the recorded data. As Wyszecki & Stiles noted, “Wavelength discrimination depends on the luminance level, surround, field size, portion of the retina used...as well as the technique of observation (strict fixation or scanning).” As they noted using the data of Willmer & Wright, under strict conditions of fixation, the wavelength discrimination was greatly reduced. In fact, based on this work, it should disappear in the absence of temporal changes in the scene associated with presenting the test imagery. Willmer & Wright’s data shows a better sensitivity in the 532 nm. to 625 nm. region than at shorter wavelengths under fixation conditions. However, this work would suggest that part of their increased sensitivity may be due to the flicker rate used in their experiments. The square-law response of the L- channel appears to contribute to this change in sensitivity. The data from Wright & Pitt (1934) for a two degree diameter bifurcated field is very similar to the 1958 data of Bedford & Wyszecki except in the 400-430 nm. Region where it appears Wright & Pitt were probably instrumentation limited. Whereas Wright & Pitt reported data at 70 Trolands, Bedford & Wyszecki reported for 100, 500, & 2000 Trolands while using different and smaller field sizes. The variation in discrimination capability with respect to illumination level does not appear systematic in the latter data, probably because of limited repetition of the experiments and no statistical averaging. MacAdam has provided very precise data274. McCree has provided data at 0.85 and 150 Trolands275. No significant discussion of the theoretical wavelength discrimination capability for human, or animal, vision could be found in the literature. The only discussion was based on a mathematical calculation based on a “line model” of the visual detection process. The recent experimental data of Griswold & Stark concerning aphakic human eyes in the ultraviolet is relevant and reviewed in Section 17.2.5. It strongly suggests the short wavelength limits on the chromatic discrimination function is due largely to the absorption of the lens. 17.3.2.2 Theoretical capability

As in the case of the new Chromaticity Diagram, it is expedient to consider the signaling situation at the input to the midget ganglion cells. This allows deferral of discussion about the signaling characteristics between the ganglion cells and higher cognitive centers, e.g. using the pulse techniques associated with projection neurons. The nominal situation is shown in Figure 17.3.2-1 for any chordate, including humans. While the spectral absorption band of the UV–channel is truncated in the humans, and other large chordates, by the absorption of the lens (see Section 2.4.2), there is data showing the UV–channel photoreceptors are functional in these retinas. Data was reviewed in Section 17.2.5 that supports the conclusion that this is true even in adult humans.

273Wyszecki, G. & Stiles, W. (1982) Color Science, 2nd ed. NY: John Wiley & Sons pp. 570- 274MacAdam, D. (1942) Visual sensitivities to color differences in daylight J. Opt. Soc. Am. vol. 32, no. 5, pp 247-273 275McCree, K. (1960) Colour confusion and voluntary fixation Opta Acta, vol. 7, pp 281 and 317-323. Also in Crone R. (1999) A history of color Boston, MA: Kluwer Academic Publishers pg. 197 Performance Descriptors 17- 215

Figure 17.3.2-1 The signal flow schematic used for calculating the chromatic discrimination function of human vision (and other chordate vision). The details of spatial encoding are ignored in this figure. Photoreceptor cells in foveola (also) connect directly to individual bipolar and parasol ganglion cells projecting directly to the Pretectum. While the UV–spectral channel is truncated in large chordates, it still plays a significant role in chromatic vision.

Because of limited data to aid in determining whether the relevant lateral cells are associated with the Inner or Outer Plexiform Layers, only the designation lateral cells will be used. Each transducer element (Trans) contains the appropriate chromophore. Each element labeled G may be either a photoreceptor cell or a combination of a photoreceptor cell and a bipolar cell. During the discussion of chromaticity, the only condition on these amplifiers are that they exhibit a stable gain condition during experimental procedures. This requirement is compatible with the small signal tests anticipated. It is also compatible with the operation of the adaptation amplifiers within the photopic operating region. It is desired to determine the nature of the signal applied to each channel represented by a midget ganglion cell (MG). What is at the moment unspecified is the order of subtraction in the lateral cells (triangular symbols) and the difference in gain between the lateral cell inputs, if any. 17.3.2.2.1 Simplified calculation of the amplitude portion of the C(8,F) To simplify the mathematical manipulations required in this discussion, this section will ignore the contribution of the UV–channel photoreceptors. The methodology can be expanded by the reader if desired. The contribution of the UV–channel will be considered in the overall performance provided by the chromatic threshold function. Assuming the lateral cells have a linear transfer characteristic, the output of each cell as a function of the amplitude of the inputs should be a straight diagonal line. The major question is whether, the input presented to the lateral cells 216 Processes in Biological Vision is a current directly associated with the signal current or a voltage representing the logarithm of the signal current. Both assumptions were examined in the development of the following scenario. It was found that only the logarithmic assumption conformed to the measured data. Thus the input to the lateral cells will be taken as the voltage at the output node of the amplifiers, typically the pedicle of the photoreceptor cells. The signals at the output of the lateral amplifiers is then given by:

C = ±(ln A - ln B) and G = ±(ln D - ln E)

where A, B, D & E may have different peak amplitudes. The sensitivity to each of these channels to variations in the input is generally found by taking the derivative of the signal C or G and comparing it to some threshold value, either a fixed threshold level or possibly a statistical noise level. This is a trivial step until the actual input as a function of wavelength is specified. Under the specified conditions of stable small signal gain, the input as a function of spectral wavelength for each channel is described by a gain term multiplied by the absorption characteristic of the individual chromophoric transducer. Considering all of the gain terms to be equal to a constant for the moment and setting that constant to unity, Figure 17.3.2-2 (a) and (b) show the resulting output signals and their derivatives using the parameters of the Standardized Human Eye found in this work. These curves are shown on the assumption of a constant photon flux per unit spectral bandwidth across the spectrum and recognize the square-law characteristic of the L-channel. They also make the assumption that C is given by the form A - B, or the S-channel minus the M-channel signal. In the second case, G is given by the form D - E, or the M-channel minus the square of the L-channel signal.

The solid line in (a) represents the transfer characteristic at the output (C) of the short wavelength differencing circuit. Note the change in the character of the function at the extremes. The function is monotonic. This differencing circuit provides excellent performance between 400 and about 560 nm. with a nominal midpoint at 486 nm. It provides no sensitivity to wavelengths outside of this range. The dotted line represents s similar fictitious situation for a long wavelength differencing circuit wherein the L- channel transducer was linear. It is also monotonic and provides excellent but unrealizable performance. The dashed line represents the output (G) of the long wavelength differencing circuit for the real situation with the L-channel de-excitation process creating a square-law type signal. The linearity of the output signal is not as good as for the short wavelength case. In addition, the curve is not monotonic, showing a reversal in slope beyond 655 nm. However, it is adequate within the region it is normally used as seen below. Yang, et. al. have provided data for the goldfish that closely tracks the theoretical short wavelength

Figure 17.3.2-2 (a)The transfer function between the logarithm of the input illumination and the output of the lateral cells of the chrominance channels. (b) The derivative of the of the transfer function. Solid line; short wavelength chrominance channel. Dotted line; long wavelength channel assuming linearity. Dashed line; long wavelength channel assuming L-channel follows a square- law relationship. Performance Descriptors 17- 217

discrimination function presented in (a)276 Pane (b) of the figure presents the derivatives of the functions in (a). The solid line represents the short wavelength circuit and the dashed line represents the actual long wavelength circuit. The dotted line is shown only for reference and assumes a linear L-channel response to photoexcitation. The solid line actually presents a better fit to the data points of Trezona (for observer PMG labeled Y(588 nm)) than does her proposed best fit277. Similarly, the theoretical dotted line fits her data for B(468nm) quite well after factoring in the absorption of the lens at wavelengths shorter than 400 nm. 17.3.2.2.2 Calculation of the complete chromatic threshold function

If the merging of the information from the individual chrominance channels is as suggested in the previous paragraph is correct, the theoretical composite chrominance amplitude function becomes quite similar to that shown in [Figure 17.3.2-2], a nearly straight line with a constant slope across most of the visual spectrum from the 400 nm limit due to the lens out to about 600 nm.. The derivative of such a line is a constant. This derivative would define the change in composite chrominance signal amplitude as a function of wavelength interval. Investigations supporting this work have generally described the dominant noise (or threshold) factor in the visual system under photopic conditions to reside in the stellate cells of the CNS. If this is correct, the theoretical composite chrominance threshold would be related to the absolute amplitude of these thresholds in the individual chrominance channels. If these threshold were equal, the theoretical composite chrominance threshold function would then be a constant signal amplitude as a function of wavelength interval divided by a constant threshold value. Under these conditions, the theoretical function would be essentially a constant truncated by the overall absorption envelope of the visual system.

[Figure 17.3.2-2(a)] suggests that the performance of the human visual system need not employ the UV–channel photoreceptors of its retina. Alternately, [Figure 17.3.3-2 ] suggests that it may. The few documented reports available for both normal and aphakic humans suggest they perceive a very de-saturated color when exposed to narrowband light at 400 nm. These observations would indicate the O–channel is fully functional and controlling the perceived chrominance in humans. The perceived color is labeled in this work. The consequences of this finding will be explored in Section 17.3.3.2. 17.3.2.2.3 Apparent equal participation of the spectral channels in forming C(8,F) While the form of the luminance threshold function, T( λ,F), suggests the dominance of the M–channel in the perception of luminance, this does not appear to be the case with respect to the perception of chrominance. As a result, the question raised in the theoretical formulation of the luminance threshold function can also be addressed here. The amplitude of the chrominance threshold function across the visual spectral band appears nearly constant (truncated primarily by the absorption associated with the lens and the long wavelength skirt of the L–channel spectrum). This suggests that the contributions of the individual spectral channels to the chrominance threshold function are nearly equal. If true, this would suggest that the density of the spectrally selective photoreceptors were nearly uniform in the retina of Chordata throughout their lifetime. 17.3.2.2.4 C(λ,F) under mesotopic conditions

The chromatic threshold function is a clear example of a function defined in terms of signalto noise ratios at a point(s) within the CNS. The noise threshold within the CNS remains essentially constant. Similarly, the signal amplitude is also held constant within the photopic operating range. However, the signal and the resultant signal to noise ratio begin to fall as the system enters the mesotopic operating region. Because of this, the chromatic threshold function, frequently expressed in terms of a just noticable spectral difference (JND) as a function of wavelength, begins to take on a more complex shape than within the photopic region. While the function generally shows a reduced JND across the spectrum as a function of light level, the effect is more pronounced in the Q–channel region of the spectrum because of the square-law character of the L–channel signal

276 Yang, X-L. Tauchi, M & Kaneko, A. (1983) Convergence of signals from red-sensitive and green- sensitive cones onto L-type external horizontal cells of the goldfish retina. Vision Res. vol. 23, no. 4, pp. 371-380 277Trezona, P. (1976) Aspects of peripheral colour vision, in Modern Problems in Ophthalmology, Streiff, E. ed. vol 27, pp 52-70 218 Processes in Biological Vision and the resultant Q–channel signal. The evaluation of the function is also compounded by the fact that the intrinsic signal to noise ratio of the signal due to quantum fluctuations in the photon flux must also be considered. Because of the complexity of the mathematical manipulations involved, the complete function will not be evaluated here. Instead, data from the literature will be presented as the baseline. 17.3.2.3 Comparison with the literature

Figure 17.3.2-3 presents a comparison of the theoretical and measured chromatic threshold function under photopic conditions. In this case, the noise level is dominated by the noise of the stellate cells of the CNS. Frame (a) is drawn on the assumption that the higher cognitive center eventually receiving the two chromatic difference signals from the midget ganglion cells is able to select the channel that gives the best spectral wavelength discrimination signal. Thus, at wavelengths shorter than a nominal 500 nm., the short wavelength difference signal will be used. At longer wavelengths, the long wavelength difference signal will be relied upon. The resulting wavelength discrimination function is calculated using the input from only three photoreceptors, one chromophoric photoreceptor of each type. Figure 17.3.2-3(b) presents the wavelength discrimination function from data of Bedford and Wyszecki, for observer G.W. The presentation is a bit complex because of the test conditions used. Several variables were varied at one time. The solid curve represents a horizontally bifurcated visual field of one degree and a nominal illumination level of 100 Trolands. The dashed curve represents two 2.0 minute diameter visual fields with centers separated by 24 minutes of angle. The test fields are illuminated at a nominal 500 Trolands. The dash-dot curve is for two 1.5 minute fields separated by 40 minutes and illuminated at 2,000 Trolands. The horizontal scales of (a) and (b) are different. The “projected wavelength diff.” scale in (a) is completely arbitrary and is added only to aid in the comparison. The scale value of 6 was aligned with the transition point near 625 nm. The scale raises many questions which deserve experimental attention. It would be useful to determine the relationship between the minimum detectable color difference and the associated signal to threshold ratio within the cognitive center. Data from several investigators over a more limited spectral range is summarized in Uttal278. The empirical law of his figure does not conform to the actual situation in the region of 400 to 450 nm.

278Uttal, W. (1981) A taxonomy of visual processes. Hillsdale, NJ: Lawrence Erlbaum Associates, pg 422 Performance Descriptors 17- 219

The agreement between the proposed theoretical wavelength discrimination function and the measured data is remarkable. The agreement is exceptional even without taking into account the quality of the filters used in the laboratory experiments or other experimental considerations discussed earlier (such as the large spacing between the test fields at high luminance levels). It should be noted that the primary competing model in this area, the Stiles line element model279, does not indicate any minor maximum in the region of 440-460 nm. at all. There have been a number of “line element” models. They all involve a number of assumptions and approximations not supported by the actual measured data. The line element model of Stiles and the related test data of both MacAdam280 and Wyszecki & Fiedler all have presented a series of discrimination ellipses that are similar and point generally to the actual peak chromophoric absorption wavelengths proposed in this work, 437,532 and 625 nm. The discrimination sensitivity figures are ellipses because the coordinate system used was not a conformal one. When plotted on the various C.I.E. chromaticity diagrams, they generate graceful arcs terminating at the above wavelengths. The basic data needs to be re-plotted in a conformal space such as the proposed New Chromaticity Diagram for Research. See Section 17.3.3. Figure 17.3.2-3 The proposed wavelength discrimination function for human vision and relevant supporting data. The transfer functions between the logarithm of the (a) The theoretical function. (b) Measured data input illumination and the output of the lateral cells of describing the same function based on a three light levels the chrominance channels, shown in [Figure 17.3.2- and visual field sizes. See text. From Bedford & 2(a) can be compared with the valence functions Wyszecki (1958) defined by Hurvich & Jameson281, and frequently reproduced. While they are conceptually similar, they are quite different in detail.

The valence functions of Hurvich & Jameson are entirely postulated based on heuristic assumptions drawn from psychophysical experiments, and relate to the Hering school. Furthermore, their experimental design did not call for “double blind” procedures. In fact, they used data based on their personal visual performance. The failure to use double blind procedures has been a frequent expedient and common problem in visual research. They were the leading and outspoken exponents of the Hering Theory in their time. This apparently shaped how they interpreted and presented their data.

At the extremes in wavelength, their functions appear to go to zero because of a loss in brightness sensitivity not a loss in chromatic response. It appears their valence functions are related to the product of chromatic sensitivity and brightness sensitivity. Between the extremes, their valence functions are biphasic or even triphasic. Their chromatic valence versus wavelength function for the short wavelength difference, labeled blue-yellow, is appropriately positioned but trails off inappropriately at the extremes and appears mis-assigned with respect to the proposed source. Their long wavelength difference function also appears poorly positioned and shows a reversal below 530 nm. which is not found in the actual situation (See Section 17.3.2.4). The first order nature of their proposition does not predict the necessary deviations in these functions. These deviations are necessary to provide the appropriate derivatives that are actually employed in the wavelength discrimination process.

279Wyszecki & Stiles, op. cit, pg. 665 280Pg. 308 281Hurvich, L. & Jameson, D. (1955) Some quantitative aspects of an opponent-colors theory. J. Opt. Soc. Am. vol. 45, pg.602 220 Processes in Biological Vision

A surprising fact is that the theoretical long wavelength differential is in excellent agreement with the measured data. The slope of the putative long wavelength function based on the square-law characteristic of the L-channel predicts a perceived hue reversal for wavelengths beyond 655 nm. This is almost exactly what is reported by Stiles & Burch as shown in Figure 17.3.2-4.

The figure is taken from Wyszecki & Stiles, page 425. They have made slight changes in the interpretation that should be reviewed. The data points labeled Brindley Isochromes are actual data for a four degree field. The curves are from the C.I.E. (1964) large-field chromaticity coordinates for a ten degree field. The data appears to show, and the curves do show by definition, a crossover point at precisely 645.2 nm. However, the curves are abstract in that they were

computed in the tristimulus context. The r10 (λ) value was not zero at this wavelength, only omitted as a convenience. Furthermore the C.I.E. curves do not track the points of Brindley, especially beyond 700 nm.

The difference between a predicted cross-over wavelength for hue reversal of 655 nm. and the Standardized value of 645.2 nm. is not large, 1.5%. This is undoubtedly smaller than the experimental error Figure 17.3.2-4 Observations of hue reversal in the deep in any individual data acquisition cycle. However, it is red. From Stiles & Burch, 1955. troubling. A preliminary perturbation analysis was performed on the model. It was found that the relative amplitudes of the perceived illumination and the specific ½ amplitude wavelengths of the chromophore did not significantly effect the predicted crossover at 655 nm. However, it was found that the color temperature of the input radiation played a major role. As the color temperature was reduced below the equal flux condition, the cross-over wavelength and the amplitude of the hue reversal both decreased. There was no hue reversal at the equal energy condition, and of course, no cross-over. These results suggest one of two things. There may have been absorptive materials in the optical path, either biological or man-made, that were not characterized or controlled. The optics of the eye are generally not color selective in this spectral range. Alternately, the color temperature of the luminance viewed by the test subject and used to acquire the data, standardized in the C.I.E. (1964) large-field chromaticity coordinates for a ten degree field, was not adequately controlled. It was apparently over-rich in the shorter wavelengths. This could have been due to a number of conditions in the test set, including the use of coated optics that were optimized for shorter wavelengths. It is important that any revised standard quantify the intensity and color spectrum of the radiation used to collect the data. The exact adaptation state of the subject should also be specified.

All of the data presently available in the literature regarding wavelength discrimination, and particularly that cited above must be considered exploratory in terms of experiment design. This is because each experiment had at least three independent variables that were not effectively separated and/or controlled. These include, the illumination level, the precise illumination color temperature, the illumination duration, the fixation level, spatial integration within the retina and spatial sharpening within the retina, particularly affecting small scenes. Consideration of these factors would normally result in the smoothing of the theoretical function. This smoothed result would generally result in even better agreement with the data. Figure 17.3.2-5 shows a different graphic of the fold back of perceived color in human vision developed by Lewis282. He notes, in agreement with the above prediction of this work, “This leads to an interesting prediction about changes of hue in the far red. If two visual pigments, with different values of λ0, have equal gradients at some wavelength in the red their gradients should diverge again at still longer wavelengths, the pigment with its maximum further towards the red having the steeper gradient. In other words, if the ratio of 'red' to 'green' sensation rises with increasing wavelength to an apparently constant value, that value must be a maximum, and the ratio should begin to decrease again at sufficiently long wavelengths. This prediction has been strikingly confirmed by the observations of –1 Brindley (1955).” Lewis uses 526.3 nm (1/19,000 cm )as λ0 in his calculations. It is proposed he could have used

282Lewis, P. (1955) A theoretical interpretation of spectral Sensitivity curves at long wavelengths J Physiol vol 130, pp 45-52 Performance Descriptors 17- 221

–1 1/18798 cm just as well, giving 532 nm for his λ0. .

Figure 17.3.2-5 Plot of equivalent wavelengths- Wyszecki & Stiles indicated there were significant wavelengths giving the same colour sensation in the far signatures in the data of Wright & Pitt and Bedford and red. The circles are experimental values obtained by Wyszecki. Table 17.3.2-1 summarizes their remarks Brindley (1955) and the crosses are theoretical values and compares them to those suggested by this work. calculated as described in the paper by Lewis. From Lewis, 1955.

TABLE 17.3.2-1 Spectral Signatures in Wavelength Discrimination

Wyszecki & Stiles This Theory Relative maxima ~460 nm. 485 ~530 500 & 546 combined

625 (inflection point at L-channel peak)

Relative minima ~440 413 ~490 485 ~590 574

The maxima and minima are obviously related to the orientation of the graph. The designations by Wyszecki & Stiles appear to be more influenced by the work of Wright & Pitt than by that of Bedford & Wyszecki. Wright & Pitt were probably limited by their instrumentation in the short wave region. Whereas the former work shows a maxima at ~460 nm., the latter work would suggest a lower number in line with the theoretical value. The suggested value of ~530 nm. appears to correlate well with a smoothed curve based on the theoretical 500 & 546 nm. The theoretical feature at 500 nm. may not be as sharp as shown in the figure. It represents the transition point used by the higher computational center. At shorter wavelengths, maximum discrimination capability is achieved using the S- minus M- difference. At longer wavelengths, the M- minus L2- difference is more precise. The inflection point near 625 nm. was not mentioned but it appears in the data of Bedford & Wyszecki. The suggested relative minimum at 440 is clearly closer to the theoretical value in Bedford & Wyszecki. The 490 nm. minimum is in good agreement with the proposed theoretical value of 485 nm. The suggested minimum near 590 nm. Is clearly closer to the proposed theoretical value of 574 nm. in Bedford & Wyszecki. Although less than obvious, the impact of the individual chromophoric channels can be seen in the proposed 222 Processes in Biological Vision

wavelength discrimination function. They are represented by the relatively flat areas between 413 & 485 nm., between 485 & 546 nm., and the inflection point at 625 nm. Wyszecki & Stiles introduce the subject of fixation during experiments to determine the wavelength discrimination function. They show an early discrimination curve attributed to Willmer & Wright (1945). The curve shows very poor discrimination in the 420-520 nm. region compared to the 520-620 nm. region. Their explanation that this is due to the essentially tritanopic nature of the fovea under small field viewing conditions seems inadequate. The discrimination was quite good in the 520-620 nm. region. A different explanation can be drawn from the fact that the refractive Wright colorimeter at Imperial College used a 2848 Kelvin light source as a standard. Such a standard has very little energy in the shorter wavelengths of the visual spectrum283. Hurevich & Jameson collected considerable data (1° field and 37° white surround) using similar techniques. That work has been reported widely and summarized frequently (Wyszecki & Stiles, pp 454-458). Romney284 has prepared a composite of the data presented in Trezona285 and the theoretical curves of this work. The Trezona data (based on a 2° field) is reproduced in Figure 17.3.2-6. The averaged crossovers of Trezona and the theoretical crossovers are quite similar. at 487.8/494 nm and 579.7/572 nm respectively, and well within experimental error at this time. Boynton reproduced a curve from Wright (1946) that shows the short wavelength crossover at 494 nm. He also explained the protocol (such as the 10° field) used in obtaining the Wright data. The major disparity in these experimental works appears associated with the measured red line in the vicinity of 500 nm (which also appears in Wright). It probably results from the linear assumption of signal addition commonly found in the early literature.

Neumeyer has collected information on the spectral sensitivity of goldfish286. There is considerable agreement between figure 4 of her 1984 paper and the theoretical waveform of [Figure 17.3.2-3] if a few points are noted. She used an inverted ordinate and truncated the measurements at 400 and 725 nm. A question can also be raised concerning the measurements at 725 nm with respect to the actual intensity of the test source at this wavelength. The sensitivity between 510 and 560 nm is difficult to resolve with filters of 8-14 nm width (as in the case of similar data for humans from Bedford & Wyszecki). Within these considerations, her peaks at 470 nm, 530- 540, and 660 nm are comparable. As seen in the analysis of this work, these peaks are due to a difference between the response of the individual Figure 17.3.2-6 Wavelength discrimination as a function chromophores and have no direct relationship to the of wavelength. Blue lines; a composite of the theoretical spectral peaks of the underlying chromophores at 437, discrimination functions of vision without any allowance 532 & 625 nm (or as listed in that paper, 450, 530 & for averaging between signal paths. Red lines; 625 nm). empirically measured discrimination functions from Trezona. Figure prepared by Romney, 2005. 17.3.2.3.1 Discrimination versus fixation If one separates the question of field size from illumination intensity and from the degree of fixation in the experiments of Willmer & Wright, a more appropriate explanation is available. Recall that the degree of fixation we are discussing here is related to the control of the so- called tremor of the eye, not the gross motions associated with tracking or scanning. This work has reviewed the data in the literature that confirms that the visual mechanism in animals requires a change in signal level at the photoreceptor for detection. More precisely, a change is required that is adequate to exceed the discrimination threshold in the higher cognitive centers. The change may be generated temporally or spatially through relative motion between the line of sight of the photoreceptor and the object field. Because of the square-law nature of the

283Thomson, L. (1949) Intensity discrimination of the central fovea measured with small fields. J. Physiol. (London) vol. 108, pp. 78-91 284Romney, A. (2005) personal communication. 285Trezona, P. (1987) Individual observer data for the 1955 Stiles-Burch 2O pilot investigation J Opt Soc Am A vol 4, pp 769-782 286Neumeyer, C. (1984) On spectral sensitivity in the goldfish. Vision Res. vol. 24, pp 1223-1231 Performance Descriptors 17- 223

L-channel response, the changes in response applied to the long wavelength discrimination circuits are larger than those applied to the short wavelength discrimination circuits for the same degree of temporal or spatial change. Normally, the tremor of the eye is approximately one pixel in amplitude. This amplitude is large enough to cause an adequate signal for most scenes. However, as the scene detail is reduced, the tremor is not adequate and the signals generated fail to exceed the threshold level required by the brain. The experiments of Willmer & Wright were performed in the 1940's and used “strict fixation,” a less than precise term. However, the degree of fixation was large enough to cause the average wavelength discrimination capability in the short wavelength region to fall to 50 nm. while the long wavelength average remained below 5 nm. Clearly, these experiments had nothing to do with a tritanopic condition in the fovea. As seen elsewhere in this work, if the degree of artificial spatial fixation had been 100%, the only wavelength discrimination capability of the human eye would have been due to temporal transients. The word “null” at the top of the y-axis in the figure is to denote a meaningless value for the wavelength discrimination capability at zero angular motion of the line of sight with respect to the object, e.g. zero tremor or 100% tremor compensation in the test equipment. Before reaching the null condition, both the short wavelength and long wavelength discrimination capability will approach 100 nm., their nominal maximum condition due to the width of their differencing range. The short wavelength discrimination capability will approach this limit faster than will the long wavelength capability due to its inherent square-law capability as indicated earlier. The curves labeled 1, 2 & 3 illustrate these conditions. 17.3.2.3.2 Discrimination versus Illumination

The gross characteristics of the wavelength discrimination performance of the human eye can be predicted based exclusively on the model. Assuming that the theoretical discrimination function of Figure 17.3.2-3 represents the photopic performance of the eye, the performance under mesotopic and scotopic conditions can be estimated. Figure 17.3.2-7 contains measured wavelength discrimination function at two illumination levels and a predicted wavelength discrimination function as a function of illumination. The upper half of the figure is from McCree. The lower half of the picture shows the predicted performance of the eye based on this work.

At lower light levels, only a straight line segment is used. Initially, as the illumination level is reduced, the adaptation amplifier gain in each photodetection channel will attempt to rise in order to maintain a relatively constant signal amplitude at the input to the differencing circuits. As long as this signal level can be maintained in each channel, the function will resemble the theoretical curve, 5. As the illumination is reduced farther, the performance capability associated with the long wavelength discrimination capability will fall faster than its short wave equivalent due to the square-law nature of the L-channel, 4. This performance can be associated with the mesotopic range of vision and will continue up through 3. As the illumination level is still farther reduced, the signal level in the L-channel becomes too low for effective operation and the Scotopic region is reached, 2. In this region, the long wavelength discrimination condition is Figure 17.3.2-7 Measured and predicted values of the null and the short wavelength discrimination capability wavelength discrimination function in humans. The lower is quite low if not null. At this illumination level, figure shows the predicted function for six different vision is essentially achromatic. At lower light levels, illumination levels at a color temperature of 7053 Kelvin. both channels are at null, 1, and vision is The upper figure is for two illumination intensities. The monochromatic. color temperature of the source was not given. From McCree (1960). 224 Processes in Biological Vision

Purdy has provided data related to this figure that has been interpreted by Wyszecki & Stiles287. They interpret the data for a three degree field split field with intensities of 100 Td and 1000 Td, to be a Bezold-Brucke hue shift with changes in retinal illuminance. Based on the model, this should be interpreted as a change in hue sensitivity between these two levels. Because of the large change in illumination intensity, part of this sensitivity shift may be due to a change in the adaptation level of the chromatic photodetection channels also. By subtracting these two functions, a hue shift can be defined. However, this shift is not due to a change in mechanism leading to a hue shift, only to a change in sensitivity. Vos and Walraven have also provided calculated wavelength discrimination functions for three different illumination levels based on a line element (geometric) model of the visual process288.

17.3.2.3.3 Discrimination versus spatial integration

The order of spatial integration appears to vary with location within the retina. Only a few data were found in the literature describing the effect of spatial integration on chromatic discrimination. Most only reflected differences as a function of circular test field size (presumably in the region of the fixation point). Figure 17.3.2-8, from Weale289 shows the data of Forshaw for one degree, 27 minute, and 14 minute field diameters. These field sizes are considerably above the size of individual pixels in the field. They suggest a significant discontinuity in the 460 nm. region for very small field sizes. Nothing has appeared in the development of the model to account for this discontinuity. A similar discontinuity, involving tritanopes, has been discussed by Walraven290.

17.3.2.3.4 Color discrimination in cases of anomalous color vision

The data of Section 16.3.4.5.5 suggests that the simplified analysis of color discrimination based only on the P– and Q–channels may not tell the complete story for human vision. Wright noted that in the absence of proper operation of the P–channel, the subjects still showed “very keen wavelength discrimination in the far violet.” That data strongly suggests that the O–channel plays a significant role in human color discrimination in the 400-437 nm region. Figure 17.3.2-8 Wavelength discrimination functions for If true, the curve in [Figure 17.3.2-6] is the result of various tests field sizes. From Weale, 1960. merging all three chrominance channels with the O–channel dominating below 437 nm, the P–channel dominating from 437 to 532 nm and the Q–channel dominating at wavelengths beyond 532 nm. 17.3.2.3.5 Discrimination versus other independent variables

On first review of Figure 17.3.2-3, it is surprising to see the wavelength discrimination of the human eye becomes better at lower illumination levels. Further review shows that this is only because of the difference in test image size used. The immensely larger test field size used at the 100 Troland level impacts the interpretation of the results. It is reasonable to assume this is due to spatial integration among the illuminated photoreceptors. It may also be that the narrow gap between the two halves of the test field provide additional signal enhancement involving spatial differencing. Such differencing may be designed to “sharpen” the edge response of the channels due to the scanning motion of the photoreceptors, in response to tremor, and their finite size. If more extensive data were available regarding wavelength discrimination as a function of illumination that was not polluted by variations in test field size, it would be possible to select an appropriate illumination level and perform a series of tests involving only the size of the test field, or only the spacing of the test and reference fields. The

287Wyszecki, G. & Stiles, W. (1982) Color Science. 2nd. Ed. NY: John Wiley & Sons. pg. 422 288Vos, J. & Walraven, P. (1972) An analytical description of the line element in the zone fulctuation model of colour vision. Vision Res. vol. 12, pp. 1327-1365 289Weale, R. (1960) The eye and its function. London: Hatton Press. Pg. 127 290Walraven, P. (1962) On the mechanisms of colour vision. Soesterberg, Netherlands: Thesis, Institute for Perception pg. 63 Performance Descriptors 17- 225

information gained could provide significant information concerning the role of spatial signal enhancement in wavelength discrimination performance. 17.3.2.4 Comparison of the C(λ,F), T( λ,F) and V(λ) functions

Figure 17.3.2-9 compares the photopic Chrominance discrimination and the luminance discrimination functions plotted with respect to wavelength and normalized to a common value. Both the empirical luminosity function, CIE Standard V(λ), and the theoretical luminance threshold function, T(λ,F), are shown. The critical feature to note is the much flatter and broader character of the measured chrominance discrimination function. It closely matches the proposed chrominance threshold function, C(λ,F) for F near 100 Trolands. The horizontal dash-dot line is the theoretical chrominance threshold function without incorporating any loss in sensitivity at the edges of the spectral band of the S– or L–spectral channels. It is the derivative of the chrominance discrimination function of [Figure 17.3.3-2]. The chrominance discrimination function remains nearly two orders of magnitude higher at 437 nm than the empirical luminous efficiency function, and about one order higher than the theoretical luminance threshold function. The situation is similar, but not as prominent near 625 nm. This difference highlights the uniquely separate signal processing paths proposed in the fundamental block diagrams of the visual system presented in Section 17.1.4. It also confirms that the gain coefficients used to compute the performance descriptor of the luminance channel, T(λ,F), are different from the coefficients used to define the performance descriptor of the composite chrominance channel, C(8,F). No data is currently available for the change in the theoretical chrominance threshold function, C(8,F), as a function if the intensity level. 17.3.2.5 Features of the new function

Besides providing a road map for the identification of features in future wavelength discrimination experiments, the proposed wavelength discrimination function places a clear limit on the capability of the human eye to discriminate colors. There is a very well defined zero in this capability at wavelengths below 380 nm. There is also a long wavelength limit. Further analysis and/or experiment may be needed to determine if it is at 655 (the point of polarity reversal) or 696 nm. It is also clear that wavelength discrimination degrades in an orderly manner with illumination level. It degrades more rapidly in the long wavelength portion of the spectrum. The degradation continues in both the long and short wavelength channels until it has a magnitude on the order of 100 nm. as limited by the maximum amplitude excursions of the differencing circuits, as a function of wavelength. At still lower illumination levels, no wavelength discrimination is reported by the animal. Whether the cessation of color discrimination is related to the analog circuitry of the retina or the circuitry related to higher computational centers is unresolved. 226 Processes in Biological Vision

Figure 17.3.2-9 Comparison of the chromatic and luminous discrimination functions. Solid line, Bedford & Wyszecki, 1958. Long dashed line, CIE (1924) visibility function, i. e., a negotiated Standard based on an unrealizable (ficticious) Standard Observer. Short dashed line, theoretical luminous threshold sensitivity function of this work in the absence of filtering. Dash-dot line, the theoretical composite chrominance threshold function as suggested by this work (ignoring truncation due to the absorption spectrum of the visual system).

The function could easily be expanded to include the effect of spatial integration with image field size if more data were available. 17.3.3 Definition of a “New” Chromaticity Diagram

This section will employ a variety of color graphics to illustrate the concepts involved in a new chromaticity diagram. However, it must be noted that neither the available printing techniques nor the available trichromatic monitors are able faithfully to reproduce the colors associated with the different wavelengths of light. (See Section 17.3.3.3.8). The human visual system has a color palette broader than any of these systems.

Currently the hue, saturation and luminance palettes of computer programs have not evolved to an industry standard. As they are currently, these palettes are designed to only encompass the three primaries defined in terms of additive color by the conventional wisdom. They are unable to address the perceived fully saturated color capabilities of the human eye at 415 nm (saturated purple), the limit of short wavelength vision near 395 nm and the nominal limit of long wavelength vision near 655 nm. Because of these limitations, the actual color related to a given wavelength of light is best determined by observing the atomic spectral lines of radiating gases. Only approximate colors can be presented using any other techniques. When observing such a line, recall that the human visual system is not able to memorize a specific color. It is designed to perceive instantaneous differences in color over small spatial distances. The recognition that the human visual system, along with that of most other chordates (if not all animals), is tetrachromatic requires development of a New Chromaticity Diagram for Research. The new Diagram must be based on real color-mixture data using the proper transformations (which are not homogeneous or linear). Such a diagram can be based on a variety of foundations; biophysical, electrophysical, psychophysical or other. Performance Descriptors 17- 227

While Griswold & Stark have shown that the aphakic human eye is tetrachromatic, there are still questions concerning whether the O–chrominance channel is fully functional. While Stark has described his color sensations in part of the 300-400 nm region, the description is not comprehensive. He has remarked that he perceives a blue fading to white-blue as the wavelength becomes shorter. This would be expected based on this theory. The question remains: what does he perceive at wavelengths significantly shorter than 395 nm. A distinct color may be perceived in that region. If so, its perception is shared only between aphakic humans and the other animals sensitive to this spectral region. The results of this work suggest that an electophysical color space can be defined that is compatible with recently defined psychophysical color spaces. This type of color space will be taken as the baseline. As shown in [Figure 17.1.4-1], all three of the chrominance channels associated with a tetrachromat (O–, P– and Q– ) must be represented in the new color space. To accommodate the tetrachromatic nature of the visual process, it is necessary to define a three dimensional color space for the new Diagram. To maintain conformality in this space, it will be based on a right parallelepiped. Several simplified variants of the complete New Chromaticity Diagram will be defined for pedagogical purposes. The basic form of these diagrams was developed in Section 16.1.3. In this Section, appreciating that only the chromatic channels of the visual process are being considered is important. It is postulated that the luminance channel is entirely separate from the chrominance channels. Avoiding thinking in terms of a total visual experience where the luminance and chrominance information is mixed may be difficult for some readers (as in the conceptual foundation of the current C.I.E. Chromaticity Diagram). Possible presentations combining both the luminance and chrominance descriptors will be discussed in Section 17.4.

It is also important to differentiate between the various illumination levels, defined here as the hypertopic, photopic, mesotopic and scotopic levels. It is shown that when defining a more fundamental chromaticity diagram, the diagram depends on the above illumination levels. This is true for all long wave trichromats and all tetrachromats. The hypertopic and photopic diagrams are stable with illumination. The scotopic diagram is also stable but different. Recognizing the dynamic nature of the New Chromaticity Diagram for Research at the Mesotopic Level is important. 228 Processes in Biological Vision

Recalling that the charge, or current, at the input to the adaptation amplifier of each photoreceptor cell is a linear function of the input photon flux to the respective channels is important. An exception is the L-channel where the charge is related to the square of the input photon flux. In both of these situations, there is also a potential non- linearity due to saturation in the level of excitons in the disks. This potential situation is of little consequence at illumination levels at least as high as the photopic range. At photopic and hypertopic illumination levels, the adaptation amplifiers in the photoreceptors operate at less than maximum gain. Their actual gain is controlled by the avalanche breakdown phenomena. The result is a large amount of negative internal feedback in each individual photodetection channel. This results in a constant (average) output current level at the pedicles of all photodetection channels, at least in a given region of the retina, over a very wide range of photon flux intensities. The resulting overall gain is determined individually for each photodetection channel. The instantaneous dynamic range of each channel remains on the order of 100:1. This phenomenon essentially eliminates the difference in the output characteristic of the L-channel, as compared with the other channels, within the hypertopic and photopic illumination ranges. When the illumination level falls into the mesotopic range, the charge or current delivered to the input of the adaptation amplifiers is so small that avalanche breakdown is still significant. However, the effect of negative feedback is no longer a significant factor. Under this condition, all of the adaptation amplifiers are operating at full gain and the square-law characteristic of the L-channel is faithfully reproduced at the pedicle in that channel.

Recalling that the signals represented symbolically by the letters UV, S, M, and L are scalar amplitudes of the current at the pedicles of the photoreceptors is important. These scalar values are obtained by the integration of the product of the incident flux and the spectral absorption associated with each photodetection channel, both as a function of wavelength. The same scalar value can be obtained in a given channel by employing either a monochromatic light source or a broader band light source of lower peak intensity. Before the invention of the laser, using a relatively wide spectral bandwidth test signal in psychophysics was normal. The cost of an incandescent source was less. It will be seen that these wider bandwidth test sources can introduce several problems into good experiment design with which investigators must deal. One of the problems is that the P and Q signals are generally not independent. They are obtained by taking the difference between the UV, S, M and/or L channel signals resulting from test sources that excite more than one channel at a time. It is quite possible, and probable, that an investigator can obtain different, even diametrically opposite, results from his experiments depending on the energy distribution within the specific spectral bandwidth of his test source(s).

The signal paths through the visual system of the retina are directly coupled. This condition makes the mathematical description of each stage difficult. It is possible to represent each processing stage in multiple ways depending on what properties are associated with the previous and following stages. This would be an almost intractable problem if the signal paths were all interconnected on a current basis. However, as shown earlier, the current at the output of each photoreceptor is passed through a diode. The resulting voltage across the diode is the voltage of the pedicle with respect to the surrounding inter-neural matrix (INM). It is this voltage that is sensed by later stages using a high impedance connection. The impedance of this connection is sufficiently high that even a large number of parallel connections do not change either the signal or resting potential component of the total voltage. The signal voltage at each pedicle is proportional to the natural logarithm of the current through the diode. 17.3.3.1 Conceptual framework for the new chromaticity diagrams

At the current time, defining four distinct types of chromaticity diagrams is important. The first would be a complete diagram suitable for describing tetrachromatic vision. This is the default diagram that can be used to describe the color vision of any animal. A simpler diagram is only appropriate if it is shown that the animal lacks one or more of the four chromophores of vision. The second would be a diagram suitable for describing the short wavelength trichromat (as typically associated with Arthropoda). Members of Arthropoda are generally believed to lack the L- channel chromophore. However, this has not been proved conclusively. Most of the experimental work in this area has been psychophysical in nature. The third would be a diagram describing the long wavelength trichromat (as typified by the human and other large animals based on the conventional wisdom). This diagram would be appropriate if the O-chrominance channel has completely atrophied. The final form would represent the large animals, including humans, who exhibit tetrachromatic vision that is significantly blocked in the ultraviolet by the absorption of its own lens. Before proceeding, it is important to stress this work does not support the so-called “color equation” defined as the linear vectorial sum of three spectral colors, R, G & B. Neither does it support the belief that the color performance of the visual system is derived from a factoring (in some unknown manner) of this equation. This work relies upon the architecture of the visual Performance Descriptors 17- 229

system to define the equations relative to the color signaling performance of that system. These equations are not directly related to the perception of luminance by the system. 17.3.3.1.1 Background

Several investigating teams have attempted to define a chromaticity diagram compatible with tetrachromatic vision. These have generally employed an equilateral tetrahedron and made the assumption that the color information is summed linearly in the visual process. These approaches have not progressed to the point of providing absolute scales to the figures or concerning themselves with conformality in the color space. See Section 16.1.3.1-2. No attempts were found in the literature to extend the C.I.E. Chromaticity Diagram into the ultraviolet. Boynton291 has written on attempts to rationalize a chromaticity diagram based on his psychophysical background. Unfortunately, the work is all based on the principle of additivity, an interpretation of the color equation in linear space, and a trilateral graphic presentation. In some cases, he has suggested portions of his work are only appropriate for pedagogical purposes. Dow292 addressed the psychophysics of vision and suggested that the luminance component of vision is based on the summation of photoreceptor signals while the chrominance component uses signal subtraction. He lists the 12 possible subtractive permutations of signals from three photoreceptor types. This is followed by a brief discussion of the ambiguities still present in the Hering model of the visual system. No conclusions were drawn but many references were provided.

Adopting the foundation developed in this work, the new chromaticity diagram should be independent of the luminance of the signal. The luminance should be treated exclusively in the Luminance Response Diagram. To accommodate tetrachromatic animals, the chromaticity diagram should include three orthogonal axes. The peak wavelengths associated with the absorption of each chromophore of vision should be located along these axes. The scale along each axis relates to the difference signal created from the signal amplitudes of the respective chromophore channels. Since the visual system involves a number of non-linearities, defining the specific location in the visual system represented by the new chromaticity diagram is also necessary. The temptation is to define it at the output of the perceptual system. This location is represented by the response of the animal to interrogation about what he thinks he sees. The response is frequently hindered by the perceived luminance information. 17.3.3.1.2 The morphological location supporting the New Diagram

[Figure 17.2.5-12] has provided the overall signal processing architecture of the tetrachromatic visual system. It shows clearly that the chrominance signals are formed in Stage 2. Signals associated with each chrominance signal are available in analog form at the output of the differencing amplifiers (generally labeled horizontal cells). Encoded versions of these signals are available in pulse form at the output of the ganglion cells of Stage 3. Recovered versions of these signals are found at the output of the stellate cells of Stage 3.

Two questions need to be answered. First, where can the desired signals be most easily measured by electrical probe? Second, where is the quality of the signals best? Many investigators would prefer to probe for pulse signals primarily because they do not understand the role of analog signals in the retina. These investigators prefer to probe the outputs of the ganglion cells. However, they do not know the encoding algorithms used to convert the analog signals into those pulse signals. Therefore their data is at best exploratory. Svaetichin and Tomita probed for analog signals in the retina and defined what became known as the S-plane. This plane is essentially the location of the axons of the horizontal and bipolar cells (probably the area now known as the inner plexiform layer). They recorded both chrominance (difference) and luminance (summation) types of signals at this location. While not precisely defined in their day, this is the earliest physical location that these types of signals exist within the visual system. The S-plane will be taken as the physical location associated with the New Diagram. It is important to note that the performance of the visual system at the S-plane is subject to differential adaptation. This adaptation may be induced by the normal operation of the photoreceptor cells. It is also important to note that the psychophysical responses of subjects may differ from the electrophysical data associated with this plane due to nonlinearities and asymmetries in the subsequent signal processing. However, these deviations seem small and associated primarily with temporal mechanisms that introduce transient effects.

291Boynton, R. Op. Cit. Pp. 128-144 292Dow, B. (1991) Colour Vision, in The Neural Basis of Visual Function, Leventhal, A. ed. as volume 4 of Vision and Vision Dysfunction, Cronly-Dillon, J. general ed. Boca Raton, FL: CRC Press. Pg. 318 230 Processes in Biological Vision

17.3.3.1.3 Development of fundamental chrominance signals

The signals produced at the S-plane have been developed in detail in Chapter 16. Only the symbolic forms of these equations will be used in this section. The chrominance signals were shown to be given by one of two sets of equations depending on the operational status of the adaptation amplifiers in the L photodetection channels. For hypertopic and photopic conditions, they are given in symbolic form as: O = LnUV - LnS Eq. 17.3.3-5 P = LnS - LnM Eq. 17.3.3-6 Q = LnL - LnM Eq. 17.3.3-7 Under the less favorable mesotopic conditions, the last equation changes to:

Q =LnL2 - LnM Eq. 17.3.3-8

Whereas the symbols S, M & L represent integrated values corresponding to actual currents in the axons of the photoreceptors, the logarithms of these terms represent the voltages measured at the pedicles of the respective photoreceptor cells in the retina.

Look first at equations 5, 6 & 7. As shown in [Section 16.3.4] the values of O, P and Q are nearly linear functions of spectral wavelength. However, they are also functions of the irradiance level. As the radiation level is reduced, the signals approach the threshold level of the circuits associated with the stellate cells monotonically. As this occurs, the perception of color is lost gradually beginning with the colors nearest the null axes of 494 and 572 nm. Eventually all sensation of chromaticity in the scene is lost. Now look at equation 8. Because of the square associated with the L signal, the voltage associated with this channel decreases even faster than those associated with the other channels. This causes an additional loss in the perception of the reds. In practice, the subject typically sees the saturation of all colors decreasing as the radiation level falls. While he fails to perceive low saturation colors first, he retains some chromatic perception of high saturation colors near 437 and 532 nm even after the loss of all perception of the reds. Finally, the observer becomes achromatic. This condition is encountered although all of the photoreceptors are still operating at maximum sensitivity and gain. This process was illustrated in [Figure 17.1.1-2]. 17.3.3.2 Defining the tetrachromatic chromaticity diagram

The Science of Color293, written by the Committee of Colorimetry of the Optical Society of America, presents a discussion of the complex parameters involved in the perception of color (without any recognition of the tetrachromatic sensitivity of the human eyes). The discussion struggles to separate the chromatic parameters from the luminance parameters while attempting to continue to use the common semantics of the English language. Their conceptual discussion centers on the use of cylindrical coordinates. The term hue is used to define the color of the scene on their chromaticity diagram and the term saturation is used to describe the intensity of that color relative to white. The form of the above equations does not involve trigonometric functions. No substantive report could be found in the electrophysiological literature where neurons performed transcendental calculations. Although using analogies to hue and saturation in art and pedagogy may be convenient, it is best to avoid cylindrical and spherical coordinates in research. The mathematical analogies to the actual process rely upon the simple logarithmic functions presented above. [Figure 11.6.4-2] presented the architecture of the visual system related to signal formation in the retina. This figure shows a distinct separation of the signaling paths into three chrominance channels (O–, P– and Q–) and one luminance channel (R–). Each of these channels generates a scalar signal based on the scalar potentials at the pedicles of the photoreceptor cells. It is most likely that the brain uses the actual values of O, P & Q recovered from Stage 3 (signal projection) to perceive the chromatic characteristics of the individual locations in a scene. It would do this by comparing these values, stored in a saliency map, to a “lookup table.”

293Science of Color (1963) Jones, L., chairman of the committee NY: Optical Society of America pp. 34-83 including color plates Performance Descriptors 17- 231

The scalar values of O, P & Q are essentially independent of each other. How they are presented graphically is largely a matter of preference if certain conditions are observed. The goal would be a simple presentation that is easily interpreted, uses absolute scales and is conformal. Conformality insures proper portrayal of relationships between the quantities. The easiest way to achieve these goals is to employ a three-dimensional color space conformally transferred onto a Cartesian coordinate system. Since it has been shown that O, P & Q are nearly linear with respect to wavelength, it is intriguing to attempt to use a spectral locus conformally transformed onto such a Cartesian system. Section 16.1.3.3 has shown that this can be done through the introduction of only two arbitrary features. These are the wavelengths at which the spectral locus is folded. These points have been chosen to coincide with the nominal peak absorption of the two chromophores, Rhodonine(7) and Rhodonine(9). These chromophores have peak absorption wavelengths of 532 nm and 437 nm respectively. The only available justification for these choices is found in Section 17.3.2. It is shown there that a transfer occurs within the brain between relying on the P-channel value and the Q-channel value to determine the “color” of the scene element. This transfer occurs at a wavelength very close to 532 nm for one of the transitions. It will be assumed similar experiments in the future will confirm a similar transition between the O– and P–channels at a wavelength near 437 nm. The only data relevant to this choice appears to be from Tan294. It is quite exploratory in character. Future laboratory work may optimize the above choices. Based on these choices, Figure 17.3.3-1 illustrates the resulting totally conformal three-dimensional color space. Note that the spectral locus is continuous. The orientation with 300 nm at the extreme upper corner was chosen arbitrarily. This choice gives a New Chromaticity Diagram that is compatible with much of the recent psychophysical literature.

Note that there is a null in each of the three chrominance equations. The location of this null in object space is a function of the state of adaptation of the eye. When transferring the chrominance equations to this color space under dark adapted conditions, the null in the equation for Q occurs at 572 nm. The null in the equation for P occurs at 494 nm and that for O occurs near 395 nm. These values are shown by the long dashed lines.

When O = P = Q = 0, there are no chrominance signals to transfer from the retina to the brain. However, there is still luminance information being transferred. The above equation defines the “white point,” W. Based on the above determinations, the “white point” for a tetrachromat occurs at the intersection of 395, 494 and Figure 17.3.3-1 (Color ) The foundation for the 572 nm using the folded spectrum locus as a scale. chromaticity diagram of tetrachromatic vision. W marks Note that this point is not described by the sum of any the location of “white” in the diagram. W’ shows the signals. It is described by the condition where the location of “white” for a long wavelength trichromat. W” three difference equations are all equal to zero. This shows the location of “white” for a short wavelength color space differs fundamentally from the trichromat. conventional assumption of additive color. Additive color assumes that white is described by the sum of the intensities associated with a group of spectral terms. Since O, P & Q are nearly linearly related to wavelength and all are equal to zero at the intersection W, considering this point a displaced zero within the conformal space is convenient. As a result, any color can be uniquely described in terms of its O, P & Q coordinate values. 17.3.3.2.1 What colors does a tetrachromat perceive?

There has long been a question concerning what do bees, and other animals sensitive to the ultraviolet spectrum, perceive when viewing ultraviolet light. Recently it has been shown that the aphakic human perceives ultraviolet light. The precisely measured spectral efficiency functions of Tan and of Griswold & Stark show that the human

294Tan, K. (1971) Vision in the ultraviolet, PhD Thesis, Utrecht, available in Univ. of Missouri Library, cal QP481.T16 232 Processes in Biological Vision

luminance channel is described precisely by the proposed spectral efficiency of this work. The congruence of the predicted and independently measured composite spectral response is strong support for the validity of the model. However, a question remains to be answered. Is the third chrominance channel (the O-channel) of tetrachromatic vision fully functional in the human? This section will show the answer is Yes! The English language has a profusion of words to describe colors dominated by radiation at very short wavelengths, less than 437 nm. This condition might suggest active mechanisms associated with short wavelength vision that are not well understood. The model of this work would suggest that the human retina can perceive colors in the region of 300 nm to 437 nm. To do this, the O–channel must be functional. The model also suggests a null in the O- channel response near 395 nm. It would exhibit the same characteristics as the nulls in the P- and Q-channels. If the above is true, the question focuses on what colors does the aphakic eye see in the region of 395 to 437 nm and in the region of 300 to 395 nm? Tan, Stark & Tan, Griswold & Stark, Chen & Stark and Stark (in a personal communication) have described what the aphakic perceives in these regions. Some of these papers either relied on the conventional wisdom or did not control all of the pertinent variables. Tan presented a PhD dissertation in 1971. The work investigated both the spectral efficiency function and color matching focused on the ultraviolet capability of aphakic humans. He used lights at 444.4, 526.3 and 645.2 nm as sources of comparison. The discussion of his work that is most widely available is by Wolbarsht295. Much of the broader discussion in Wolbarsht is not supported by this work. There is also some discussion of it in a review by Stark & Tan (apparently written largely by Stark)296. Unfortunately, these two papers provide differing versions of the same figure from Tan297. Although both are labeled chromaticity diagrams, they are based on graphs of anomaloscope readings (note the negative values along both scales in these figures). Both graphs show a bending and intersection of a locus with itself. This feature suggests the inadequacy of the anomaloscope configuration used. The configuration only allowed matches using mixtures of blue, green and red lights. Wolbarsht noted that “If the lens is removed, the sensitivity in the ultraviolet will be such as to produce color confusion. Monochromatic light within the ultraviolet spectrum appears to be matched by something other than blue.” He noted in his caption to figure 9 that “it would be necessary to substitute a wavelength in the ultraviolet for the blue at 444.4 nm in the anomaloscope to make a real match. An aphakic individual cannot match ultraviolet light shorter than 340 nm with any visible wavelength between 400 and 700 nm.”

Stark & Tan summarized their work through 1982 in the above review. Unfortunately, their descriptions are heavily flavored by several apriori assumptions. They encountered difficulty relying on the trichromatic assumption. They also had difficulty in settling on the precise mechanisms supporting absorption in the ultraviolet. After noting a peak in the ultraviolet absorption of the aphakic eye near 350 nm, they attributed it to the “cis-peak of rhodopsin.” This was presumably the putative achromatic rod chromophore. They also assume the spectral characteristics of the short wavelength chromophore extend into the ultraviolet farther than previously assumed. They also assume the total ultraviolet sensitivity to be the summation of the β-peaks in the response of the S, M and L channels. This is based on their assumption that the β-peak in the absorption of retinoids in dilute solution is significant in vision. Finally, they interpreted their findings using a unique chromaticity diagram as discussed above.

The Stark school was ambivalent concerning the nature of the ultraviolet absorption as late as 1994. In Stark, Wagner & Gillespie, the absorption in humans is presumed to involve a summation of β-peaks associated with the S, M and L chromophores. However, they confirmed Tan’s earlier findings. They said “data for sensitivity mediated by the short-, and perhaps the long-, wavelength cones suggest UV sensitivities beyond those expected from the cone rhodopsin’s cis peak. . . . ” In Chen & Stark, the ultraviolet absorption in goldfish is attributed to a distinct ultraviolet photoreceptor (referred to as a “cone”). These ideas suggest a convergence toward the model of this work. Tan developed part of a color space based on the above assumptions, use of a 58 minute diameter stimulus and bipartite color matching. It is noteworthy that he used 494 nm and 582.5 nm as normalizing wavelengths in these experiments. These are the null wavelengths of the P– and Q– chrominance channels proposed in this work. The figure of Tan reproduced in Stark & Tan is the result of a complex de-convolution using a technique first used by Wright. It should not be accepted as factual without understanding the mathematics involved.

295Wolbarsht, M. (1976) The function of intraocular color filters. Fed. Proc. vol. 35, no. 1, pp 44-50 296Stark, W. & Tan, K. (1982) Ultraviolet light: photosensitivity and other effects on the visual system, Photochem. Photobiol. vol. 36, pp 371-380 297Tan, K. (1971) Op. Cit. Performance Descriptors 17- 233

Stark & Tan contributed the following. “For aphakic observers, monochromatic UV looks violet or blue, though somewhat whitish (unsaturated). These stimuli trace a loop extending into the near the blue-violet (400-450 nm) portion of the triangle’s perimeter.” If this statement is reworded to suggest saturation decreases as the wavelength approaches 400 nm, it would be precisely as expected by this theory. This appears to be the case based on subsequent discussion with one of their subjects (twenty years later). A question remains about what color is perceived on the short wavelength side of the null point near 395-400 nm. Gaydon298 stated that the color appeared blue, not violet, as quoted on page 116 of Wyszecki & Stiles. Until the question of what color is perceived for narrowband stimuli between 300- and 395 nm under photopic conditions is answered more definitively( See [Figure 17.1.4-1]), the perceived color of light at 342 nm will be defined as Monet (in honor of the famous painter who became aphakic while still painting). Purple will be reserved for a spectral color near 410 nm (on the long wavelength side of the null at 395 nm). In April, 2008, I encountered a subject exhibiting at least partial UV vision due to a malformed lens at birth. She reported ultraviolet light generated either a lilac or pinkish-purple due to UV light. Richard Hammond presented a TV program over the BBC on 23 March, 2010 involving a man with his biological lenses removed who discusses his resulting UV vision299. The program should be available in the USA on the Discovery Channel in the near future. He claimed that after the operation he started to see bright purplish and blue light emitting from scanners used to scan currency notes. He also said that rainbows had far more color in them now than he had seen before. This is completely expected. No information was provided on the types of replacement lenses he was using. He did not demonstrate his ability to see at wavelengths shorter than 400 nm.

In summary, the human visual system is fundamentally tetrachromatic. In the absence of the lens, the luminance channel of the system exhibits a spectral sensitivity that is considerable between 300 and 700 nm. The system exhibits three fully functional chrominance channels. These channels broaden the Hering concept to include three opponent color axes,

+ the aqua-red axis passing through 494 nm, + the yellow-violet axis passing through 572 nm and + an axis passing through 395 nm (lilac) whose other terminus is not labeled at this time.

Derrington, Krauskopf & Lennie determined axes very close to two of the above three axes in 1984300. They specified one axis as 492 ± 3 nm and the second axis as 558 ± 4 nm. In referring to the Derrington et al. material, the psychologists Abramov & Gordon301 introduce the color name “” to describe 492 nm. Similarly, they used the color name “” when describing 558 nm. They describe the complement of teal as “cherry” and the complement of chartreuse as violet. These designations are compatible with this work although it may be useful to consider a different name for a color at 572 nm which would be more yellow than 558 nm.

For purposes of discussion, the aphakic eye perceives a color near 300 nm that will be labeled hyacinth and a color at 342 nm that will be labeled Monet. A very unsaturated color is perceived at 395 nm (a null point) that will be labeled lilac. For the aphakic human eye, white is an indication of a null in all three chrominance channels.

The experiments of Tan on aphakic humans are worthy of repetition using a source wavelength near 300 nm if anomaloscope matches are to be obtained for monochromatic lights in the region of 300 to 395 nm. The ultraviolet photoreceptors and signaling channel of normal humans are active, although significantly blocked by the absorption of the lens. A source of radiation near 400 nm must be used if precise anomaloscope matches are to be obtained for humans when they are presented with monochromatic radiation in the region of 400 to 450 nms. [xxx too much duplication regarding the term and physiology of “aphakic” here and in 17.1 and 17.2 to 17.4.

298Gaydon, A. (1938) Colour sensations produced by ultraviolet light Proc Physiol Soc (London) vol 50, pp 714-720 299http://www.bbc.co.uk/iplayer/episode/b00rqgh4/Richard_Hammonds_Invisib le_Worlds_Out_of_Sight/ 300Derrington, A. Krauskopf, J. & Lennie, P. (1984) Op. Cit. 301Abramov, I. & Gordon, J. (1994) Color appearance: on seeing red–or yellow, or green, or blue Ann Rev Psychol vol 45, pp 451-485 234 Processes in Biological Vision

17.3.3.2.2 What colors does a human perceive?

Based on the knowledge that the human visual system is fundamentally tetrachromatic, defining what a human perceives in detail is possible. A human uses four quantum-sensitive spectral channels with peak sensitivities at 342, 437, 532 and 625 nm. Theoretically, it can determine the mean wavelength of any stimulus between 300 and 655 nm. Practically, it can determine the mean wavelength of any stimulus within this range limited primarily by the absorption of its own lens, the color temperature of the radiation source and the reflectance of the scene in object space. This restricts its chromatic discrimination range to 395 nm to 655 nm under suitable photopic illumination conditions. The theoretical color discrimination range of the human visual system is shown in Figure 17.3.3-2. In this figure, the mean wavelength of the radiation from a scene element is computed as an integral. It is the integral of the product of the spectral properties of the radiant source, the reflectance of the scene element and the absorption of the individual chromophore to that irradiation. Thus, a given scene element may stimulate more than one chromatic channel if the reflectance of the element is sufficiently broad. As a result, the scene may be represented in chrominance space by a point that is not on the spectral locus.

For scene elements with a mean wavelength shorter than 437 nm, the location in human chrominance space is determined by signals acquired by both the UV-- and the S-- spectral channels. These signals will be reported via the O--chrominance channel as shown by the solid line in the figure.

Without a functional O--channel, the data in the 400-437 nm region would be reported via the P--channel. There would be no transition in signal processing between the O-- and P-- channels. Performance Descriptors 17- 235

Figure 17.3.3-2 Theoretical composite human color discrimination function under high contrast photopic conditions. The individual discrimination functions are aligned to show their individual ranges and their composite range (solid line portion of each function). Cross over between functions occurs at 437 and 532 nm. Scene elements with a mean spectral wavelength of less than 437 nm are reported by the O-channel. Scene elements with a mean spectral wavelength of between 437 and 532 nm are reported via the P-channel. Scene elements with a mean spectral wavelength of greater than 532 nm are reported via the Q-channel. See text.

Whether the UV-channel participates in signal generation is highly dependent on the color temperature and hence the spectral content (on a quantum flux basis) of the radiant source. Both the UV– and S–channels are excited by signals in the 395 to 437 nm range. Figure 17.3.3-3 illustrates the significance of the color temperature of the source and the limitation introduced by the absorption of the lens. The excitation is relative to the input to the neural portion of the photoreceptor cells (before the adaptation amplifiers). While the adaptation amplifiers can compensate for the reduced excitation if it is part of the background, such compensation reduces the extent of the photopic operating range of the visual system significantly. This compensation will adversely affect the incremental signal gain relative to the other spectral channels. The overall effect is to reduce the apparent contrast in this region. 236 Processes in Biological Vision

Figure 17.3.3-3 Effect of source color temperature on the color discrimination capability of the human eye. The three curves were normalized with respect to 700 nm. The precipitous drop in excitation near 400 nm is due to the absorption of the human lens. Note the substantial reduction in excitation of the photoreceptor cells in the wavelength region between 395 and 437 nm using 2856 Kelvin illumination, (illuminant A).

It can be concluded that the ultraviolet spectral channel of human vision is important in perceiving colors in the spectral range of 395 nm to 437 nm. The ultraviolet channel is crucial to the fidelity of the perception process when the source of illumination is of adequate color temperature. If the source temperature is not adequate, perception of , and near 437 nm will be hampered. 17.3.3.2.3 A simplified three-dimensional framework for true trichromats

While a three dimensional Cartesian coordinate system is easy to visualize, working with it on paper is difficult. Figure 17.3.3-4 illustrates a simplified coordinate system that remains conformal. Its derivation is discussed in Section 16.1.3.3. The figure is obtained by splitting the figure along the vertical axis and rotating the UV-S-M surface around that axis until it is in the same plane of the S-M-L surface. The coordinate space on either side of the vertical axis remains conformal. However, the two sides are not connected conformally and certain colors cannot be represented properly. The criteria for the perception of “white” remains the same. The values of O, P and Q must all be equal to zero. For a short wavelength trichromat, a complete chromatic space can be created based on the left half of the figure. This assumes the Q–channel is absent or dysfunctional. For a true long wavelength trichromat, a similar chromatic space can be created based on the right half of the figure. Here, it is assumed the O–channel is Performance Descriptors 17- 237 absent or dysfunctional. Recently, it has been determined that the human visual system is tetrachromatic at the S-plane of the retina and the O-channel is fully functional. However, the excitation of the O-channel is very limited by the absorption of the lens at wavelengths between 310 and 395 nm. Furthermore, very few artificial light sources emit radiation in the 300 to 310-nm region. As a result, the total figure can be used to represent normal human vision by ignoring the region between 300 and 395 nm. Under conditions where sufficient ultraviolet irradiance reaches the retina, the entire figure can be used to define human color vision. However, such high levels of ultraviolet irradiance could be medically damaging to phakic eyes. As noted below, the line connecting 437 and 532 nm is the spectral line and not a Hering axis. The chromatic Figure 17.3.3-4 (Color) A simplified foundation for a space between the 437-532 nm line and the 395 nm three- dimensional color space. Each side of the figure line is not represented correctly in previous remains conformal. However the two sides are not chromaticity diagrams. It is out of the plane of the connected conformally. The human visual space can be typical x,y chromaticity diagram. The region centered represented by the space to the right of the 395 nm line. on 415 nm is labeled purple in this work. The region of 420-425 nm is labeled . A mixture of either of these colors and a spectral yellow or red cannot be represented in this figure. 17.3.3.3 A New Chromaticity Diagram for human vision

As discussed in Section 17.3.3.2.2, the human cannot be defined as a trichromat for research purposes. Humans are tetrachromats suffering from a physiological blockage of light in the region of 310 to 395 nm. However, his/her UV sensitivity is significant in determining the chromatic perception of the overall system. Therefore, humans are best described as blocked tetrachromats.

For clarity, this section refers to the perceptual space of the human visual system as represented at the S-plane of the retina under dark adapted conditions. It should be noted, there is no direct relationship between any component of the chrominance space and the perceived illumination of the scene. This perceptual quality is determined completely independently in the R-channel of the system. This is one area where the C.I.E. Diagram, which defines the amplitude of the M-channel signal as equivalent to the perceived brightness of the scene illumination. The chromatic signal channels do not relate to luminance intensity in any simple direct way. In this presentation and in reality, the signal information in the luminance and chrominance channels are calculated completely independently from the information presented by the photodetection channels. See Section 17.1.4.

Creating a two-dimensional color space for human vision similar to that described above is possible. This opportunity arises from two conditions. The first is the frequent relative lack of irradiance from a scene in the 395 to 437-nm region. The second is the relative unimportance of mixtures of two or more lights where one light contains a significant number of quanta in the 395 to 437-nm region. Under these conditions (typical of artificial illumination), the utility of the UV– and O– channels are limited. It is also indicative of why artists and museums attempt to achieve a higher color temperature illumination in their exhibition spaces. Movie theaters also use higher color temperature sources so that purples can be reproduces more effectively. 17.3.3.3.1 A chromaticity diagram under optimal illumination

Consider the three-dimensional color space of a tetrachromat as a hollow cardboard box instead of a solid cube. For convenience, assume that the Q axis only extends to 655 nm. Cut the box in a plane containing the 395 nm line and parallel to the S-M-L plane. Now unfold the four panels that are perpendicular to the S-M-L plane to form only one plane. Figure 17.3.3-5 shows two variants of the resulting two-dimensional color space. 238 Processes in Biological Vision

Figure 17.3.3-5 A complete color space for blocked tetrachromats (including humans). Left; the proposed space with locations described by wavelengths. Right; the proposed space with locations described by named colors. The third Hering chromatic axis, passing through 395 nm (Lilac) is defined as the null value of the O-channel. It circles the figure. This representation shows all three pseudo-white points individually.

The curved lines in the figure are to indicate the identity between the two points at the ends of each arc. The scale for the O-channel is shown along a radial. It applies equally to both the horizontal and vertical representations of the O-channel.

Both variants illustrate the three pseudo-white points that represent the individual conditions where two out of the three chromatic signals have null values. W’ represents the white of conventional wisdom. This is a location along the two conventional Hering chromatic axes represented mathematically by P = Q = 0.00. W” represents the similar condition where O = P = 0.00. W”’ represents the condition where O = Q = 0.00. W” and W”’ are each shown at two locations representing the same axes for different values of the unspecified third parameter. The frames also illustrate a collection of unique colors to be defined below.

This diagram provides the answer to the question, what color does a bee see in place of white? White! In this conceptual chromaticity diagram, white is perceived as the absence of signals in all available chrominance channels.

While not totally conformal, this figure is conformal within each area delineated by fold lines. Under conditions of artificial illumination, the values of the O–signal approach zero in each of the four foldout panels. Therefore, the perceived chromaticity diagram of the human under normal artificial illumination can be appropriately represented by the space within the rectangle bounded by 437, 532 and 655 nm. Under higher color temperature illumination or when using monochromatic sources in the laboratory, the presence of signals in the O–channel must be anticipated. Trimodal stimuli can only be interpreted in terms of the three- dimensional color space. However, because of the selection criteria used in the brain, many bimodal stimuli can be adequately represented in the above two-dimensional representation. The presence of signals in both the O– and Q–channels will elicit the perception of colors represented within the areas of the top and bottom foldouts. One interesting color is located at 655 nm and 415 nm. It is labeled mauve in this figure. While magenta is defined as a mixture of blue and red, mauve is a mixture of purple and red. It can be considered a “super magenta.” The definition agrees with that of the American Heritage Dictionary and is among those used to describe the same area in the Munsell Color Space. The presence of signals in both the O– and P–channels will elicit the perception of colors represented within the areas of the left and right foldouts. These colors are perceptually less distinct and will remain unnamed at this time. These spaces include combinations of colors, such as bluish-purple mixed with green, that are not found along the Performance Descriptors 17- 239

spectral locus. These are bimodal spectra. Bluish-purple mixed with green is distinctly different from the spectral color labeled aqua. Reproducing all of the colors perceived by the human under ideal illumination is virtually impossible. Neither printed media nor monitors are designed to faithfully or consistently reproduce such a range. The use of conventional trichromatic monitors in psychophysical experiments is a major impediment to research in color vision. Important colors will be defined explicitly as to spectral content in Section 17.3.4. 17.3.3.3.2 A chromaticity diagram under incandescent illumination

As noted in the equations of Chapter 16, the value of the O–signal approaches zero under two conditions. First, when there is low chromatic saturation in the UV– and S– portions of the object spectrum. Second, when the source radiance levels in both of these channels are low. Thus, for incandescent illumination, the value of the O–signal is usually insignificant and location W’ represents the actual perceived white. This point indicates the absence of chromatic signals in all of the chrominance channels. If the actual perceived white in a scene exhibits a bluish or purplish tinge, it is because the value of the O–signal is not identical to zero. Under conditions of normal artificial illumination (color temperatures below 3600 Kelvin), the values of the O–signal are negligible in each of the four foldout panels. Therefore, the perceived chromaticity diagram of the human under normal artificial illumination can be appropriately represented by the space within the rectangle bounded by 437, 532 and 655 nm. Since the signal in the O-chrominance channel is negligible, the selection rules used in the brain will always favor the chromatic discrimination function presented by the P-channel. Under this condition, the limit of color discrimination at short wavelengths is due to the limit in the P-channel discrimination function (nominally at 400 nm). 17.3.3.3.3 Fundamental, primary and cardinal axes in perceptual space

The complete equations for P and Q (Section 16.3.4) allow a chromaticity diagram to be constructed that employs linear scales in these two quantities. Using P and Q as the fundamental axes insures that the graph remains conformal with the dataset. [Figure 16.3.4-1] shows the nearly linear relationship between the value of P and Q and their respective wavelength regions. Therefore, a choice can be made between preparing the diagram based on using linear scales based on the scalar values of P and Q or on the associated wavelengths. Convenience is served by making the scales on the primary axes linear with wavelength and presenting a secondary set of scales for P and Q. The scales expressed in absolute wavelength will be considered the primary axes of this work. This approach introduces a slight distortion in the P and Q scales. Where maximum precision is required, and when the above figure has been confirmed by precise laboratory measurement, the actual P and Q secondary scale values corresponding to the primary scales can be plotted exactly.

These primary axes do not pass through any of the white points of the three-dimensional color space appropriate for displaying the color perception of the human. It is useful to define such a set of axes to maintain compatibility with the experimental, particularly the psychophysical, community. These axes can be defined as the cardinal axes and are best defined as parallel to the primary axes. When defined in this way, there are actually three cardinal axes as shown in [Figure 17.3.3-4 & 17.3.3-5]. The axes passing through the wavelengths of 494 nm and 572 nm are the classic axes of Hering. The third axis, passing through 395 nm, is a newly defined Hering axis compatible with the blocked tetrachromatic color space of the human. 17.3.3.3.4 Hue and saturation are not fundamental parameters

While many investigators have adopted polar coordinates in the display of their data, and polar coordinates play a useful role in pedagogy and the arts, the fundamental parameters associated with color vision are not polar in character. As discussed in [Section 17.3.3], a true perception of “white” involves the absence of signals in all of the operational chrominance channels. This condition requires that O = P = Q = 0.00 in the general tetrachromat and in the human (a blocked tetrachromat). This point can be rigorously defined in a three-dimensional color space, a color cube. If desired, polar coordinates can be used to describe a color relative to this white point. However, the angles (preferably measured relative to the Cardinal axes) and lengths of the vectors do not have any intrinsic relationship to the visual process. A true perceptual white cannot be rigorously defined by a single point in a two-dimensional color space. The point P = Q = 0.00 can be considered a true white point if no significant signal exists in the O-chrominance channel. This condition is often achieved in the psychophysics laboratory by employing a light source of limited color temperature. 240 Processes in Biological Vision

However, this condition seriously limits the perception of colors in the blue and purple region of the color space. Under the above conditions, the use of polar coordinates based on a “white point” within the S-M-L plane must be defined as a secondary set of parameters. Here again, polar coordinates can be used to describe a color relative to this white point. However, the angles (preferably measured relative to the Cardinal axes) and lengths of the vectors do not have any intrinsic relationship to the visual process. 17.3.3.3.5 The New (hypertopic & photopic) Chromaticity Diagram for Research

A New Chromaticity Diagram for Research can be prepared using absolute scales in a rectilinear two-dimensional graph space with minimum compromise. However, several caveats must be attached to the figure. First, the color space only applies to blocked tetrachromats (primarily chordates with ocular globes > 20 mm in diameter). Second, the color space is primarily used for stimuli with half-amplitude full spectral widths greater than 50 nm. If multi-modal, each mode of the stimuli will meet the above criteria. Third, when narrower band stimuli are used in the short wavelength regions, the impact of the O-chrominance channel must be recognized.

Fourth, if a color temperature of less than 3600 Kelvin is provided by the ultimate source, filters of any spectral width can be used with this diagram.

These caveats are designed to surface the fact that the perceived colors in the spectral region of 400 to 437 nm will differ depending on the test circumstance. They depend on the color temperature of the light source and the selection rules used by the brain. The second and fourth caveats insure that the subject will not perceive saturated purples at test wavelengths below 437 nm. In the absence of these two caveats, the subject may perceive saturated purples correctly.

With these caveats, the resulting complete graph of perceived color by humans is shown in Figure 17.3.3-6. The nominal color shown within each circular segment representing the maximum saturation color perceived at the coordinate value of the center of the segment. This method of presentation of the human color gamut does not require the introduction of a “purple line” and there are no “non-spectral colors.” Saturated magenta, for instance, is a bimodal color obtained by mixing 437 nm. radiation and 655 nm. radiation.

Note the word perceived in the above paragraph. This is a Diagram of the response of the human eye in perceptual space, not the nominal stimulus applied to the eye in object space as used to define the CIE Chromaticity Diagram. As presented, it is applicable to the nominal eye under dark adapted conditions. This state of adaptation is presumed to be the same as that achieved when viewing an equal quanta per unit wavelength source, e. g., a “daylight” source with a color temperature of 7053 Kelvin for the normal human eye.

Using this presentation format, the wavelength scales are linear and the field of the graph is conformal. A unique color can be defined precisely and unequivocally using only two wavelength numbers. Furthermore, the result of adding two lights of known spectral distribution can be determined using simple arithmetic and geometry. White is always perceived at one point, the point where the value of both P and Q are zero. A perception of pure white can be obtained by mixing only two monochromatic spectral wavelengths, 494 and 570 nm in object space under dark (and presumably equal flux) adaptation. A perception of white can also be obtained by mixing any two lights where the integrated product of the spectral characteristics of the individual lights and the photodetection channels of the eye result in a chrominance channel response given by P = Q = 0. Adjusting the spectral content of two lights to meet the above condition is essentially impossible without an adequate model of the eye. The C.I.E. Chromaticity Diagrams are misleading in this area because of their lack of conformality. Therefore, the conventional practice is to use three lights and vary their relative intensity levels until the condition P = Q = 0 is obtained empirically. The above procedure is the key to the perception of white under nominal variations in the weighted average spectral content of the nominal scene. The individual adaptation amplifiers of each photoreceptor in the eye share a common metabolic energy source. This source has a common source impedance for all of the photoreceptors in a given region of the retina. Therefore, the amplifier gain of these individual photoreceptors tend to respond as a group in order to maintain a constant signal level at their output terminals. The result is the well-known fact that after a short Performance Descriptors 17- 241 interval, the individual exposed to such atypical scene irradiance will not perceive it as atypical. This is the phenomenon of color constancy. It will be developed further in Section 17.3.6. 242 Processes in Biological Vision

Figure 17.3.3-6 [Color] A physiology-based Chromaticity Diagram for Humans applicable to the Hypertopic and Photopic regions. The colors shown are only for discussion purposes. Monitors and “North American” process cannot reproduce the correct colors for wavelengths below 447nm. At least some “European” process color printing can reproduce the purples between 400 & 430 nm but at the expense of the blues between 440- & 470 nm. The figure is conformal and shows the limits of chromatic discrimination in the O, P and Q chrominance channels. This theoretical figure is based on a uniform photon flux per unit bandwidth source. A blackbody at a color temperature of 7053 Kelvin is the closest equivalent. Such a source is equivalent to nominal daylight and is very similar to a D65 source. In the region beyond 655 nm, the perceived color of an object is no longer monotonic. The perception of color in the region between 400 and 437 nm is restricted when using normal incandescent illumination. The purples will appear as blues. Performance Descriptors 17- 243

In brief, if the scene in object space exhibits an excess of radiation in one region of the spectrum, assume red for the moment, the adaptation amplifiers associated with the L-channel will reduce their gain parameter automatically. This is due to the higher current attempting to pass through them in the presence of the internal feedback mechanism. The result is the phenomena of color constancy in perceptual space. The integrated product of the spectral characteristics of the scene in object space and the gain characteristic of the individual photodetection channels will remain essentially constant in the face of slow variations in the average spectral content of the scene. The perceived value for white in perceptual space remains at the point P = Q = 0. However, the actual coordinates of the same point reflected into object space may be quite different from this value. This is due to changes in adaptation by the photoreceptor cells. In object space, the white point is always described by a specific set of coordinates. However, defining these coordinates precisely under clinical conditions is difficult. The clinician will normally define a circular area (typically elliptical on a C.I.E. Diagram) including the white point as the locus of white. This circular locus can move about as the spectral content of the object space radiation changes. The fact that the white locus remains a small ellipse while it moves about, due to changes in color temperature of the source, is not illustrated correctly in the normal C.I.E. Chromaticity Diagram presentation. The edges shown at 400 nm and at 655 nm are drawn to describe the limit of color discrimination as a function of wavelength for the P and Q channels. The area beyond 655 nm is perceived as a slightly less saturated Red than the region near 655 nm. This phenomenon is discussed elsewhere in this work.

The colors shown in [Figure 17.3.3-7 xxx ]can be specified much more precisely mathematically than they can be illustrated in printed pictures. Colors, with their nominal English names, are defined by their P and Q values as shown in Table 17.3.3-1 244 Processes in Biological Vision

TABLE 17.3.3-1 Mathematical Definition of Principal Colors in the New Chromaticity Diagram for Research for the Hypertopic & Photopic Condition

Color name P value Q value Radial Comment Coordinates Rel to H. Red @ Saturation Red, Hering 0 Ln[1 + Lx/K] 0 494,655 Violet Ln[1 + S/K] 0 90 437,572 Aqua 0 --Ln[1 + M/K] 180 494,532 Green --Ln[1 + M/K] = --Ln[1 + M/K] 225 Values are negative and equal 532,532 Yellow --Ln[(1 + M/K] 0 270 532,572

Orange --Ln[1 + M/K] Ln[1 + Lx/K] --- L2 must be greater than M see defin [1 + M/K]

Magenta Ln[1 + S/K] Ln[1 + Lx/K] 45 Angle for small L, where Lx. S see defin Cyan Ln[1 + S/K] --Ln[1 + M/K] 135 Angle for S = M see defin

* The bold numbers correspond to the single wavelength commonly associated with this color.

The first point to note is that the three “primaries,” red, green and blue, are not equally spaced in angle around the white point. This asymmetry has lead to the definition of “Hering” color pairs. Using the above definition, Hering Red is complementary to Aqua (not green) and Violet is complementary to Yellow. The terms black and white play no formal role in this New Chromaticity Diagram for Research. White, in the context of chromaticity is a null condition. It can represent any point along the black-white continuum.

The second point to note is that the power, x, associated with the L-signal is equal to 1.0 within the photopic range due to the adaptation process related to the L-spectral channel. The value of x is 2.0 within the mesotopic range (See Section 17.3.3.6).

Livingstone & Hubel made a particularly significant comment concerning their experiments involving color in 1984302. “In typical experiments the object viewed is a small test spot of light on a dark or diffusely lit white background. The results can be deeply counterintuitive—that monochromatic light seen as “blue” added in the right amount to monochromatic light that we call “yellow” produces the sensation of “white,” a sensation also evoked by light containing all wavelengths; that cyan (blue-green) plus red similarly produces white; that red plus green gives yellow.” These are exactly the results predicted by this theory and illustrated by the New physiologically-based Chromaticity Diagram. Their use of the term counterintuitive appears based more on their prior training than on their observations. Pridmore has recently completed an extensive set of experiments expanding on those of Purdy (1937). The labels of some of the features of the spectra are different. However, the result confirm many of the wavelengths defined in the above table to at least +/–5 nm and some to an accuracy better than +/–2 nm303. His reported effect of color temperature on perceived wavelengths is quite interesting (pg 3903). It shows the performance loss when the photon flux in the short wavelength region is reduces disproportionately. Unfortunately, his “extended spectrum” is entirely

302Livingstone, M. & Hubel, D. (1984) Anatomy and Physiology of a color system in the primate visual cortex J Neurosci vol 4(1), pp 309-356 303Pridmore, R. (1999) Unique and binary hues as functions of luminance and illuminant color temperature, and relations with invariant hues Vision Res vol 39, pp 3892-3908 Performance Descriptors 17- 245 empirical and based largely on freehand graphic curve drawing304. 17.3.3.4 Limitations on the presentation of the New Chromaticity Diagram

The presentation of the New Chromaticity Diagram for Research in full color is difficult. The art of color reproduction (as opposed to the creation of original art) does not employ a continuous pallette of colors. The brain relies upon the computational powers of the retina to develop sets of parametric values, O, P and Q that it perceives as specific colors. For primarily economic reasons, both the printing and display industries have settled on the use of three fixed chromaticity colors near the edges of the human color space that can be mixed by adjusting their intensities. The mixing is accomplished within a pixel size that is below the resolution capability of the observing system. The result can be a very satisfactory rendition of the original object for colors within this color gamut. However, such systems cannot reproduce, or present “colors” outside the selected color gamut. Such systems cannot create an O–, P– or Q– value exceeding that of the selected pigment or phosphor. To adequately reproduce the New Chromaticity Diagram for Research, it is important that the three pigments or phosphors be carefully chosen. Ideally they should be located on the spectral locus. The mean wavelength of the middle component should be located near 532 nm. The mean wavelength of the long wavelength component should be at or beyond 655 nm. The mean wavelength of the short wavelength component should be as near 400 nm as possible. This is necessary to adequately stimulate the O–channel and reproduce the purples properly. If this component has a mean wavelength near 437 nm, colors found in the 400-437 nm region of actual human vision will not be reproduced. 17.3.3.4.1 Broad versus narrow irradiances in the laboratory

Because of the significant overlap in the absorption spectra of the Rhodonines when configured for vision, the spectral width of the irradiance used to probe the color space of vision is important. The mean wavelength of the irradiance is always the critical parameter. However, the deviation about the mean has a significant impact on the excitation of the spectrally adjacent absorbers. As a result, using narrowband irradiance sources when attempting to qualify the New Chromaticity Diagram for Research is important. A bandwidth of less than 5 nm is expected at this time. These same specifications apply when one is using two separate sources simultaneously to reproduce irradiances applicable to the interior of either the 2-D or 3-D color space.

17.3.3.4.2 Capability of displays

Before making a comparison of chromaticity diagrams, discussing the capability of the various display methods used to present them and the performance of the eye observing the diagrams is important.

All conventional display systems are based on the linear processing of either active sources (lights) or passive materials (pigments). The interplay of active sources is described mathematically by addition. The similar interplay of passive materials removes spectral content from the original illumination. The resultant change in illumination is best described by subtraction.

The various display methods are invariably based on linear summation of chromatic information. In fact, since it is a transmission and reproduction medium, color television has taken great pains to maintain a linear relationship between the reproduced image and the source image. To insure this feature, a term known as gamma in the graphic arts is used. Gamma is the exponent of the transfer coefficient between the output and input signals. The gamma is typically not 1.0 in cathode ray tubes and additional circuitry is needed to compensate for this fact. The photographic arts industry is also an image reproduction medium. However, it both suffers from and frequently uses to its advantage variations in the gamma on a spectral channel by channel basis. The animal (and human) eye is not based on linear addition of chromatic information. In fact, it is much more complicated. It involves a variable gain mechanism in each spectral channel and exponential addition (and subtraction) of signals from each spectral channel. With the arrival of computer-supported publishing, both desktop and commercial, this subject has taken on greater interest and reached a higher level of understanding among the graphic arts community. Appreciation of the difference between additive color systems, as used in light generating systems such as computer displays and television monitors, and subtractive color systems, such as inks, paints and tinted materials, has become more

304Pridmore, R. (1993) Extension of dominant wavelength scale to the full hue cycle and evidence of fundamental color symmetry Color Res Appl vol 18(1), pp 47-57 246 Processes in Biological Vision

common. Each of these display methods has a proscribed range of color rendition, known as a gamut, determined by the phosphors or other light source used in additive systems, or the family of pigments used in subtractive systems. The gamut of the human eye is wider than the gamut of either of these systems. Usually, this is based on a commercial decision. There is no reason an additive or subtractive system cannot exceed the gamut of the human eye. Many additive systems do, particularly in the ultraviolet region, but the human is unable to perceive this fact. The subtractive color system used to print most books, called process color, has a gamut that is significantly smaller than the gamut of the human eye. Therefore, printing a Chromaticity Diagram representative of the capability of the human eye using process color is not possible. An alternative printing technique uses what is called “.” This system uses more specific inks for each color or group of colors but is more expensive commercially. The capability of most additive systems, including common computer monitors, is somewhat better in this respect but still not adequate for research purposes. For research in vision, the color gamut should extend from the short wavelength limit of human color discrimination, at 400 nm, to the long wavelength limit that is less precisely defined but is near 655 nm. This range excludes the perceived color reversal range beyond 655 nm. The source should be capable of generating narrow band intensities of constant flux per unit bandwidth. The only method of achieving this gamut currently is with a multi-channel narrow bandwidth colorimeter incorporating a 7053 K source. A black body source at this temperature that is not encumbered by a spectrally limiting envelope or optical system provides a uniform illuminant within +/-5.7% over the human visual spectrum. Table 1.3.3.4 provides quality factors for other common illuminants.

There is little correlation between the names and RGB values assigned to colors used in personal computer displays, and the color capability of the human eye. This is true for both Macintosh and Windows based systems. As illustrated below, the RGB computer values (now represented by multiple versions of what is described as sRGB encoding) are based on a three dimensional orthogonal color space, not the two dimensional color difference space of the neural system. Investigators are cautioned to avoid the introduction of uncontrolled variables in the use of such displays in psychophysical experiments. Windows has recognized that the terms dark green and light green are not appropriate. Dark and light are better reserved for discussions of intensity level. Microsoft has chosen to describe a fully saturated “green”, hexadecimal code 00FF00, as . This name is commonly associated with a color close to the Hering axis terminus at 572 nm. However, this location differs significantly from the corner of human color space near 532 nm. 17.3.3.4.3 Remaining functional complications

The possibility of cross-coupling of signal information within the retina before the chromatic signals are created must be addressed. There are two major possibilities, involving several possible configurations, with different consequences.

Spatial filtering in the process of chrominance signal formation

Many locations in the literature suggest cross-coupling between the output of horizontal cells and the pedicles of the photoreceptors. The output of the horizontal cells is usually associated with the outer plexiform layer. Since this coupling would feed color difference signals back to a spectrally pure output of a photoreceptor cell, it would constitute external feedback relative to that spectral channel. If the arborization of the horizontal cell was extensive, this mechanism would also introduce chromatic cross coupling between distant points in the field of view. The result would be that the perceived colors would be highly complex functions of the color of the surrounding scene. The perceived colors could even be functions of variations in the surround if the arborization of the horizontal cells introduced spatial filtering techniques to emphasize, or de-emphasize, certain spatial frequencies. Spatial processing between luminance channels There is also the possibility that the lateral neurons associated with the inner plexiform layer, frequently grouped under the name amercine cells, might introduce spatial cross-coupling between the luminance channel signals from the bipolar cells. This would be the case if the lateral cells of the inner plexiform layer introduced the results of their processing back into the dendrites of the bipolar cells in the inner nuclear layer. Depending on arborization of the amercine cells, spatial filtering of the luminance information relative to the surround would result. Spatial processing between chrominance channels

The possibility that amercine cells may manipulate the chrominance signals must be considered. They would obtain Performance Descriptors 17- 247 signals from the pedicles of either horizontal cells or intermediary bipolar cells. Again depending on arborization level, the output of these cells could be of endless variety. They could reflect center surround relationships or sensing of spatial patterns of a specific chromaticity. There can be little doubt that cross-coupling does occur between the luminance and chrominance signal paths. The literature is replete with many examples of the sensitivity of the psychophysical experiments in this area to both the color of the surround and the spatial extent of the test image and/or the surround. However, two points are important. Many of the observed cross-couplings are unimportant in the real world. No clear examples of external feedback of horizontal cells to the pedicles of photoreceptor cells have been recorded electrophysiologically. Furthermore, no requirement for such feedback exists in the proposed system. Bandlimiting of chromatic information The literature also includes a considerable amount of data on this subject compiled by the National Television Standards Committee, NTSC, in the 1950's. This data was compiled for two reasons. There was a need to determine the least amount of data required to be transmitted to satisfy the needs of the observer and to minimize the complexity of the electronic hardware involved. The latter were particularly important when combined with the mandate that the new color television system produce a color signal that could be received without distortion on a black and white receiver of the day. The resulting dot-sequential-color system took advantage of the limitation on the performance of the human eye to the greatest possible extent.

Two primary conclusions were developed by the NTSC305. The human eye could not determine the color of fine detail in a scene and the perception of color by the eye was bandwidth limited, particularly along the (S–), (L–) diagonal in a polar coordinate chromaticity diagram. A major criterion for the adoption of any axes was that the system could reproduce the skin tones of a Caucasian with maximum fidelity using the camera tubes and the display monitor phosphors available then. The system adopted, and is currently used around the world, transmitted the chrominance information in an asymmetrical bandwidth-limited channel separate from the luminance information. Two chrominance subchannels were defined within this channel. One channel transmitted a signal representing the information along a diagonal axis drawn generally through the white point and a point of high green saturation. The second channel transmitted a signal representing a diagonal through white and perpendicular to the above diagonal. The signal representing the diagonal including S and L (the Q channel of that system) was bandlimited more severely than the other (I) channel (400 kilocycles and 1.3 megacycles respectively in the NTSC system). The resulting NTSC axes are shown in [Figure 17.3.3-8].

Additional discussions of the temporal bandlimiting features of the chromaticity channels will be found in Section 17.6.3.

17.3.3.5 Auxiliary Constructs applied to the New Chromaticity Diagram

The orthogonal feature of the new Chromaticity Diagram for Research lends itself to many extensions. These extensions allow other data to be coordinated with the Diagram in order to make additional predictions and interpretations. The Diagram is a representation of the perceived color performance of the human eye as represented by the signals occurring in the plane of the lateral cell axons. It is possible to compare the object scene with this Diagram and make judgements about the operation of the photodetection and matrixing elements distal to this position. The obvious features that can be studied are: + the performance of these elements as a function of illumination level, + the performance of these elements as a function of the color temperature of the illuminance of the observed scene + both the gross and individual adaptation levels of the photodetection channels. Additional constructs include: + the pulse intervals of the action potentials related to the chrominance channels 17.3.3.5.1 Theoretically achievable chromatic discrimination capability

305Zworykin, V. & Morton, G. (1954) Television, 2nd ed. NY: John Wiley & Sons. 248 Processes in Biological Vision

In Figure 17.3.3-7, a new Chromaticity Diagram with an auxiliary construct is shown. This combination displays the ability of the human eye to discriminate hue under nominal conditions. An auxiliary set of axes has been aligned with the original axes. Both a theoretically ideal and the measured discrimination functions of [Figure 17.3.2-7] are shown. The two waveforms have been bisected to accommodate the conformal transformation used in the new Chromaticity Diagram. The y-axis of the auxiliary constructs specifies the hue discrimination capability, d.c., of the eye as it would be represented by a line parallel to the spectrum locus at that wavelength. Thus in the ideal situation, the d.c. would be a constant value of about 2 nm. This would be represented by a series of double ended arrows parallel to each axis and two nm. in length (The arrows are shown expanded 10:1 for clarity). At any location within the normal color space, the individual would be able to discriminate with an accuracy of 2 nm. parallel to either of the two spectrum loci. If the capability of the observer is taken as an RMS function, it is possible to combine these two values probabilistically. The result is a d.c. of 2 nm. in diameter at that point. This is the conceptual Figure 17.3.3-7 [Color] Illustration of extended new foundation for what are generally known as MacAdam Chromaticity Diagram to show ideal and theoretically ellipses, because of their appearance in the achievable chromatic discrimination capability under conventional C.I.E. color space. nominal conditions. Discrimination capability loci shown expanded 10:1 Looking at the achievable theoretical wavelength functions, it is seen that the achievable d.c. is not the same throughout color space. At a wavelength of 440 nm., the achievable d.c. is about 5 nm. This is shown as a double arrow parallel to the spectrum locus near 440 nm. On the y- axis. At 580 nm., the achievable value is about 2 nm. A double arrow is shown near 580 nm., as above. At the intersection of the 440 and 580 nm. lines in color space, the achievable d.c. is an ellipse with a vertical axis of 5 nm. and a horizontal axis of 2 nm. as shown. By repeating this procedure, the theoretical discrimination capability of the eye can be specified throughout the new Chromaticity Diagram for any set of assumed nominal conditions.

17.3.3.5.2 Achievable discrimination capability versus test field RESERVED

17.3.3.5.3 Achievable discrimination capability in color deficient subjects

It is quite possible to use the New Chromaticity Diagram to evaluate color deficient individuals, particularly those suffering from poor blue-yellow discrimination capability. There is a small difficulty in using the Diagram to evaluate those with a red-green deficiency caused by the conformal mapping used to bend the axes at 532 nm. Their discrimination capability along the red-green axis should extend “around the corner” on this Diagram. It would be better to use a slightly different diagram as will be developed in the next Chapter on abnormal vision.

17.3.3.5.4 Action potentials of the optic nerve vs illumination spectrum

Figure 17.3.3-8 provides the New Chromaticity Diagram extended to indicate the pulse interval and frequency of the action potentials produced by the midget ganglion cells of the chrominance channels in human. Both a frequency and a interpulse interval scale are shown along each axis for convenience. The exact location of W is not known at this time. However, the figure shows the best available estimate based on the neutral points reported by color deficient individuals. Protanomalous and deuteranomalous individuals report a neutral point at or near 494 nm. Similarly, tritanomalous and tetartanomalous individuals report a neutral point at or near 572 nm. Thus, W is shown as 570,494 on this spectrum locus. There is data (See Section 16.7.1) indicating that the nominal frequency of the continuous streams of pulses generated by ganglion cells in complete darkness is typically 30 pulses per second. This value will be taken as the nominal pulse rate for midget ganglion cells under null conditions. The arrows indicate the direction of increasing values based on available data from the NTSC committee, see Zworykin & Performance Descriptors 17- 249

Morton306. They did not discuss action potentials within the eye. They did indicate that humans were slower to perceive the colors exciting the short wavelength and long wavelength channels of vision. Therefore, as discussed in Chapter 14 and in Section 17.6, the tentative conclusion is drawn that the pulse frequency increases as the median spectral color in the P-channel approaches 532 nm. A tentative conclusion is also drawn that the pulse frequency increases as the median spectral color in the Q-channel approaches 532 nm. as well. Additional experiments will be required to determine the minimum and maximum frequency (pulse intervals) encountered in actual subjects.

17.3.3.5.5 Definition of Hue and Saturation

There has long been an interest in defining a color system based on radial coordinates that described the performance of the eye. It has been difficult because of the impact of color temperature on the perceived colors. Using the New Chromaticity Diagram for Research, this problem of definition is avoided. Furthermore, by transforming the coordinates of the New Diagram back to the old diagram and a specific color temperature, mathematically definable lines of constant hue and saturation can be plotted on the old diagram. Before performing such transformations, it is important to define hue and saturation precisely.

In the past, hue has generally been defined in terms of a radial angle relative to an arbitrary reference direction, generally using an artistic rendition of a “color wheel” but occasionally using the C.I.E. 1931 (x,y) Chromaticity Diagram. The definition based on Figure 17.3.3-8 [Color] New Chromaticity Diagram the (x,y) diagram is different when transferred to the extended to show the interpulse interval of the action C.I.E. (u,v) Chromaticity Diagrams. potentials of the chrominance channels, P and Q as a function of median spectral wavelength. The definition of saturation has been even more difficult. One generally used definition defines the saturation scale as a linear scale from a specific “white” point on the (x,y) diagram to the spectral locus or purple line. Such a representation involves two problems. The saturation scale is of variable length as a function of hue. In addition, the saturation scale loses credibility in the region near 500 nm. because of the recognized distortion of the chromatic scale in this region. This distortion was one of the main reasons the (u,v) diagram was adopted.

The availability of the two chrominance channel scalar values, P & Q, provides the opportunity to define saturation (and hue) more formally. Particularly in the case of P, these functions have well defined extreme values as shown in Figures 17.3.2-2. They exhibit distinct threshold levels as shown in 17.3.2-3. They also change in amplitude with respect to the illumination parameter in a monotonic manner as shown in Figure 17.3.3-2. Based on these facts, the fundamental definition of saturation involves the magnitude of the P and Q signals in relation to a threshold value. Although it is possible the relationship could involve a difference, it is more likely to be represented by a ratio. Making this basic assumption, the mathematical definition of saturation for a specific perceived color is given by the ratio of the absolute value of P or Q to a fixed threshold value. The maximum value of these ratios is set by the maximum value of the scalar values of P and Q. The above mathematical definition is completely compatible with Eq. 17.3.3-11 & 12 and their special cases to be examined below. It is immediately seen that the maximum saturation achievable at a given location in the spectral space of the New Chromaticity Diagram is given by two values, |P|/Thresh. and |Q|/Thresh. at that location. Within the hypertopic and photopic illumination regimes, these values are independent of the illumination level. The saturation level is essentially proportional to the rectilinear distances between the white point and the specific spectral location. Within the mesotopic regime, the P and Q values at a given spectral location decrease with illumination. As the P and Q values reach threshold level at a given spectral location, chromatic vision is lost at that location. Upon reaching scotopic levels, the saturation level falls below the threshold level at all spectral locations and only achromatic vision is possible. As indicated in Section 17.3.3.2, P & Q are not independent of each other for negative values. The M–channel

306Zworykin, V. & Morton, G. (1954) Television, 2nd ed. NY: John Wiley & Sons. pp. 817-825 250 Processes in Biological Vision input dominates both signals. In addition, after recovery of the P and Q signals in the brain, there appears to be a selection process where the more positive of P and Q is used to define the saturation level. This selection process avoids conflict in the perception of hue and also limits the maximum perceived saturation in the region between 494 and 570 nm. As in Section 17.3.3.2, the assumption will be made that this transition wavelength occurs at the center of the M-channel absorption spectrum, 532 nm. Because of this selection process, the absolute saturation level in the region between 494 and 570 nm. is never as high as in the regions of 400 nm. and 655 nm. The resultant map of absolute saturation level in P,Q space is the same as the map adopted for the New Chromaticity Diagram, a rectangular area which is asymmetrical with respect to the white point. Within this space is an additional square centered on white that defines a constant absolute saturation contour determined by a monochromatic source traversing the visual spectrum. This absolute level is equal to the maximum absolute saturation value achievable in the region of 532 nm. A second set of values corresponding to an absolute mathematical saturation of twice the unity value occur at wavelengths of 418 and 646 nm. for a monochromatic source. The highest achievable value of absolute mathematical saturation is between 2.2 and 2.5 based on this derivation. The definition of hue is much simpler using the New Diagram. The logical zero angle reference is the positive Q axis. This radial leads directly to a mathematically definable “red” that contains no “blue” or “green,” P = 0. Similarly, a mathematically definable “blue” that contains no “red” or green” is definable at the extreme positive value of P, Q = 0. Finally, a mathematically definable “green” that contains no blue or red is found at the extreme value of the radial at 225 degrees where P = Q. Note carefully that these three mathematically defined primaries are not equally spaced in angle. Figure 17.3.3-9 defines a the mathematical hue and absolute saturation space according to the above rationale. At wavelengths shorter than 400 nm., the saturation value remains constant at the level corresponding to 400 nm. At wavelengths beyond 655 nm., the saturation decreases slightly in consort with the hue reversal.

The space within the unity saturation square provides a mathematically defined and traceable “square” color wheel that is believed to be distortion free when based on the values of P and Q (See Section 17.3.3.5.1). It appears that this space covers most of the hue and saturation space used in normal practice, both artistic and commercial. If necessary a slightly rectangular and off-axis color wheel can be used based on the nominal maximum absorption point of the three chromophores, 437, 532, and 625 nm. This rectangle extends to a maximum absolute saturation of about 1.5 in P and Q. This degree of asymmetry is similar to that used in NTSC color television.

The derivation of a conventional artistic and commercially useful color wheel from the above mathematical color space would be desirable. However, there are three problems.

+As shown above the mathematical hue and saturation space is not symmetrical about the white point for absolute saturation values greater than unity.

+The details regarding the selection process involving the P and Q functions in the region between 494 and 570 nm. is not known precisely. +The two functions are not related by an equation of the form x2 + y2 = z2. Because of these problems, there is no simple way to transform the rectangular mathematical hue and saturation space into a conventional circular color wheel with the primaries separated by 120 degrees and a saturation vector of constant maximum value. By adopting a color wheel with the primaries spaced by 90 Figure 17.3.3-9 [Color] Hue and Saturation coordinates and 135 degrees, and adopting a relative saturation applied to the New Chromaticity Diagram. The square scale, a color wheel results that is only mildly box surrounding the white point and passing through 456, distorted. 532 and 608 nm. describes the highest absolute saturation that can be obtained for an arbitrary hue. The rectangle 17.3.3.6 Perception and display of color passing through 418, 532 and 646 nm. describes the locus of twice the absolute saturation that is only achievable for spaces wavelengths shorter than 456 nm. and greater than 608 nm. Performance Descriptors 17- 251 17.3.3.6.1 Comparing the new diagram with MacAdam, Farnsworth, etc.

D. L. MacAdam307 performed some meticulous experiments during the 1940's in an attempt to define the color discrimination capability of the human eye on a point by point basis in color space. He used the C.I.E. 1931 Chromaticity Diagram as a framework for his data. The resulting maps of sensitivity ellipses have been a subject of considerable discussion ever since. What has never been noted in the literature to the authors knowledge is the proclivity of the ellipses to point to the true peak spectral wavelengths of the visual chromophores, 437, 532 and 625 nm. Of course this phenomena is easier to recognize in hindsight. Farnsworth308 attempted to re-present the data of MacAdam using a color space topology that caused all of the ellipses to approximate circles. The results are quite enlightening. Although his border continued to consist of a spectrum line derived from the same fundamentals as the C.I.E. (1931) Chromaticity Diagram, the results bear a striking resemblance to the orthogonal coordinates of the new Chromaticity Diagram presented above. Figure 17.3.3-10 presents the data of Farnsworth with the two orthogonal axes of the new Diagram as an overlay. Recently, a diagram similar to that of Farnsworth but based on a modified Hering foundation has become popular. It also appears in the same orientation as the new diagram proposed here. However, it maintains the old spectral locus and purple line. Rodieck has provided a textbook version of this diagram but it does not incorporate any scales309. Greenstein, Zaidi, et. al310. have provided papers describing the derivation of this “S-cone system.” Associated with Rodieck’s version are some unique diagrams suggesting that the L and M chromophoric channels are not independent. The reproduction quality of that figure is quite limited due to the use of process color in the printing. The purples are not shown properly. See Section17.3.3.6.2.

MacAdam presented his data based on illuminant C as defined in the 1930's. This illuminant is located at x=0.315, y=0.315 on the C.I.E Diagram and approximates an equal energy source. An illuminant more closely approximating an equal flux source, a Planckian radiator near 8000 Kelvin would be at x=0.295, y=0.303. A new rectilinear coordinate system, compatible with this theory, can be overlaid on the data of Farnsworth. The white point at P = Q = 0, approximately (494, 570) in nm., can be overlaid on the equal flux point at x=0.295, y=0.303 and the axes rotated about this point to obtain a reasonable match. A reasonable match is primarily for artistic and pedagogical purposes since the spectrum line and the purple line are derived from a set of conceptual principles that are not traceable to the absorption characteristics of the animal eye.

Lacking new experimental data, the orientation of the overlay axes was chosen to conform approximately to the C.I.E. spectrum line and to include all of MacAdam’s data within the new spectral envelope.

As indicated above, no discussion is appropriate concerning the exact location of the “Spectrum Line” in these earlier diagrams since it is derived under less than ideal assumptions. However, it does exhibit a relatively linear scale between 530 and 620 nm. If the scale in the area of 530 to 570 was brought into alignment with the proposed axes, the ellipses could still be circular within the 10-20% error estimated for the data in Wyszecki & Stiles. Little data was taken by MacAdam in the far blue region of the spectrum because of instrumentation and subject performance difficulties. Therefore, the effect on the ellipses of adjusting the topology and linearizing the scale between 532 and 400 nm. can not be stated. A new re-presentation of the raw data is needed to answer this question.

Tansley & Boynton have provided an unusual variant of the C.I.E. (1960) UCS grid311. It uses a non orthogonal coordinate system with y plotted on a scale that appears to be double logarithmic.

307MacAdam, D. (1942) Visual sensitivities to color differences in daylight. J. Opt. Soc. Am. Vol. 32, pg. 247 308Farnsworth, D. (1944) The Farnsworth rectilinear uniform chromaticity scale diagram No 38. Memorandum Report # 44-1 New London CT: Med. Res. Lab. U.S. Submarine Base or Wyszecki & Stiles, 2nd Ed. pg. 311 309Rodieck, R. (1998) The first steps in seeing. Sutherland, MA: Sinauer Associates pg. 352 310Greenstein, V. Zaidi, Q, Hood, D. Spehar, B. Cideciyan, A. & Jacobson, S. (1996) The enhanced S cone syndrome: An analysis of receptoral and post-receptoral changes. Vision Res. Vol. 36, pp. 3711-3722 311Tansley, B. & Boynton, R. (1978) Chromatic border perception: the role of red- and green-sensitive cones. Vision Res. vol. 18, pp 683-697 252 Processes in Biological Vision

Figure 17.3.3-10 A re-plot of MacAdam ellipses compared to the new Chromaticity Diagram. MacAdam ellipses are plotted on a rectilinear coordinate system by Farnsworth, (1944). Note the x and y coordinate values of the C.I.E. Chromaticity Diagram shown as curved lines. The data is overlaid on the rectilinear coordinate system of the new Chromaticity Diagram.

Wyszecki & Stiles critiqued Farnsworth by pointing out the data points of Farnsworth were not as circular as the circles drawn over them suggested. This should have been expected. Farnsworth was performing an empirical manipulation of data of un-quantified precision. Stiles had previously analyzed methods of bringing his line element model of color discrimination into agreement with the data of MacAdam. Neither of these investigators employed an orthogonal chromaticity space as used in the New Chromaticity Diagram. Using the new Diagram and the extended scales of minimum wavelength discrimination capability of Section 17.3.3.3.2, it is clear that the raw data generating “MacAdam ellipses” should be ellipses even in an orthogonal color space. This is true without any manipulations of the data relative to tristimulus values or space. It is true for the theoretical case using equal photon Performance Descriptors 17- 253

flux illumination and it is certainly true at the color temperature of the luminance used by Bedford & Wyszecki. The ellipses will be even more elliptical at lower color temperatures.

17.3.3.6.2 Difficulty in documentation and display

An important subject is seldom addressed in the vision research literature but is important in the graphic arts. The gamut of colors perceived by the human is larger than that provided in a typical computer monitor or television display device. The visual gamut is considerably larger than that available in conventional color printing using what is known as “process color.” This situation makes it difficult to display the chromatic capability of the eye using conventional graphics. Zworykin & Morton have discussed this subject in some detail and provided composite Chromaticity Diagrams of the capabilities of various systems along with the technical performance characteristics of practical television display devices312. Adobe Systems Incorporated313 also discusses this subject in connection with their graphic arts software program, “Illustrator.” Ready & Warner314 discuss the situation from the context of the desk top computer. Their figure on page 283 shows the difficulty of reproducing a , from a monitor, on paper using process color. They also suggest alternate “special names” for some colors to provide a more understandable correlation between computer colors and graphic arts colors. These context specific names probably only confuse the issues raised in TABLE 17.3.3-1. Another problem in displaying an appropriate human color gamut is the difference between the inks commonly used in “North America” and “Europe.” A comparison of the widely reproduced spectra of Dowling illustrates the problem. In Gouras (printed to North American process color standards), the spectrum does not represent the region between 400-430 nm well. While it should appear purple, that region appears blue like the region from 440 to 460 nm. However, in the same figure printed in Backhaus, et. al.(printed to European process color standards), the spectrum reproduces the 400-430 nm region as a saturated purple315. However, the region 440-460 does not reproduce as a saturated blue. It is distinctly purplish. While it appears the two authors used separation negatives from the same source , the difference appears to be due to the use of a different magenta ink in the two color printing processes.

A more detailed explanation of this problem appears as question 236 on the website, www.askpantone.com.

The two main CMYK standards are SWOP and Euroscale. SWOP is an acronym that stands for Standard for Web Offset Publication, and is the North American standard. Euroscale, as the name implies, is used primarily in Europe. There is an actual difference in the Cyan and Magenta inks between SWOP and Euroscale, such that if the same set of CMYK values are used in the two standards, you would likely achieve two different results. Further, Euroscale inks are generally printed at a higher density than SWOP inks.

The difference in process color reproductions can be understood most clearly in the tetrachromatic context of [Figure 17.3.3-1] of Section 17.3.3.2. While the cyan and yellow inks have the same, or similar, spectral distributions in the two systems, the magenta is significantly different. The North American magenta has one spectral peak in the red and the second between 440 and 460 nm in the blue. The reproducible color gamut is in the plane defined by 437, 532 and 655 nm. Positive values cannot be generated in the O-channel of vision by this dye set. Hence, a purple, in the range of 400-430 nm cannot be reproduced by this system. The European magenta (at least that used to print Backhaus, et. al., has one spectral peak in the red and the second between 400 and 430 nm in the purple. The reproducible color gamut is now in a plane defined by a point between 400 & 430 nm, and 532 and 655 nm. While positive values can be generated in the O-channel of vision by this dye set, a high positive value cannot be generated in the P-channel. Hence, a blue, in the range of 440-460 nm cannot be reproduced by this system. The area expected to represent a saturated blue will appear as an unsaturated blend of purple and aqua The conclusion from reviewing the above material are several. The field is confusing because of the evolution of many systems for describing the chromatic capability of various presentation mediums and visual systems.

312Zworykin & Morton, Op. Cit. pp. 762-813 &912-915 313Adobe Illustrator 8.0: User Guide (1998) San Jose, CA: Adobe Systems Incorporated pp. 157-159 314Ready, K. & Warner, J. (1996) Hybrid HTML Design. Indianapolis, IN: New Rider Publishing pp.279- 285 315Backhaus, W. Kliegl, R. & Werner, J. (1998) Color Vision: Perspectives from different disciplines Berlin: W. de Gruyter, pg 11. The same background spectrum was used in many figures of this work. 254 Processes in Biological Vision

Both of the widely used additive and subtractive color systems, are based on the linear summation of individual colored lights or pigments. They both attempt to achieve control of both brightness, hue and saturation simultaneously. They both suffer significant limitations in the reproduction of the visual spectrum. The additive systems have been more successful in this regard when using only three lights, red, green and blue (RGB). The subtractive systems have generally found it unsatisfactory to use only three pigments. A four pigment system is usually employed based on cyan, magenta, yellow (canary is preferred) and black (CMYK). Even this four color system of subtractive color is quite limiting and the highest quality graphic arts material is manufactured using spot color, i.e., special dyes with greater spectral purity and saturation range than that in commercial process color reproduction. There can be significant differences in process color printing when magenta inks of different spectral characteristics are used to reproduce visual spectra. It is only possible to display the entire human visual color gamut using monitors and printed graphics by incuring higher than normal costs. The printed graphic must employ specially tailored dyes in what is known as “spot color” in the trade. Alternately, the new system known as “hexachrome™” printing, introduced by Pantone, can be used. It remains deficient in rendering purple when using SWOP inks.

Because of the above difficulties, it is important to provide a numerical value for the peak wavelength of the absorption or transmission spectrum of the light or pigment, as a minimum, when discussing the spectral elements of vision. Where possible, both the peak wavelength and some indication of the dispersion from that peak is desirable.

One should be particularly aware of the poor performance of the CMYK system with regard to high saturation yellow and blue.

One should also be aware that the specification of a numerical value for a color in computer code only specifies the relative intensity of the electrical signal applied to the presentation device, it does not necessarily relate to the actual color produced. The color produced depends on the specific phosphor, filter or other transducer used in the display device. 17.3.3.6.3 Typical achievable color spaces

As developed previously in this section, the maximum perceptible color gamut in animal vision is basically a conformal rectangle when presented in P, Q color space. The perceptible color gamut may be more limited at certain stimulus levels due to a variety of individual limiting mechanisms.

Although one is free to draw various triangles on the New Chromaticity Diagram by drawing lines connecting various colors along the periphery of the P,Q color space, such as red, green and blue, the perceptible colors of vision are not confined to the interior of such constructions. The human is able to perceive a distinct color for every combination of P and Q where P and Q may have positive or negative values. Using the wavelength scales, the total color space perceptible to humans is a rectangle enclosed by 400 nm to 530 nm. on the vertical scale and 530 to beyond 655 nm. on the horizontal scale. When examining the capability of broad spectral band sources to create perceivable colors, it is necessary to compute the P and/or Q values (p,q) caused by each source. This procedure is similar to the calculation of x,y values for the C.I.E. diagram. However, no imaginary absorption spectrums are used. The actual absorption spectrums of the animal chromophores are used. The calculations do involve the difference in logarithms where the logarithm arguments are integrals of products with respect to wavelength. If desired, the fundamental (p,q) values can be transformed directly into spectral values consisting of two wavelengths, one less and one more than 532 nm. As the model shows, the computation of a pair of P and a Q values involves the subtraction of pairs of values directly related to the spectral values at the pedicles of photoreceptor cells. While the auxiliary wavelength scales of the New Chromaticity Diagram show that any given color can be perceived based on stimulation by only two individual sources of appropriate mean wavelength, this is not the most convenient method. The general method is to use three sources, whose mean wavelengths are located near the corners of the New Chromaticity Diagram. By modulating the intensity of these three sources, any color included within the rectangle defined by these three sources can be perceived. Performance Descriptors 17- 255

In the case of active sources used to create trichromatic display devices, the spectrums of the individual sources is reasonably narrow and does not overlay more than one chromophoric absorption spectrum of vision. and the centroid of their radiant spectrum as a function of wavelength can be taken as their location on the New Chromaticity Diagram. Using these simplifying assumptions, the perceivable color gamut created by a typical trichromatic cathode ray display is also shown in Figure 17.3.3-11 . In the case of the process color method of color printing, the procedure is basically the same. The achievable color gamut is also shown in Figure 17.3.3-11. 17.3.3.7 The New Chromaticity Diagram for Research at Mesotopic levels

The performance of the visual system is distinctly different in the mesotopic region than it is in the photopic or scotopic regions. The individual spectral channels of the visual system are not operating in unison and color constancy, among other phenomena, is lost. However, human perception can still be described using a modified form of the New Chromaticity Diagram for Research. 17.3.3.7.1 Mesopic versus mesotopic vision

There is a terminology problem in this area similar to the one involving achromatopia and achromatopsia. In both cases, the shorter form is descriptive of a clinical condition known as a syndrome. In the case of achromatopia, it includes several independent diseases, one of which is a specifically defined condition called achromatopsia. The same situation applies here. Mesopia is the common term for a clinically recognized condition (syndrome), namely poor visual performance in the presence of limited light stimulation. The most obvious phenomenon occurring within the mesopic range is the operation of the iris. Figure 17.3.3-11 Realizable human color space using While not defined as closely with respect to the kinescope and printing techniques. The white wedge mesopic range as the next condition, the top of the shows colors not well represented in “North American” mesopic range is generally associated with the iris process color. Some “European” process color uses a beginning to open and allow more total flux to reach magenta containing a deeper purple instead of a blue. In the retina (See Section 2.4.3.1). The top of the this case, the purples are reproduced better at the expense mesopic range is generally considered to occur near of the blues (440-470 nm). 10+1 cd/m2 (See Section 2.1.1.1). Measurements in this field have a very large statistical range (nominally 3:1 or more between investigators).

A second condition (disease) occurring within this syndrome is mesotopia. Mesotopia is defined as a neurological condition wherein at least one of the adaptation mechanisms associated with the individual spectral photoreceptor channels has reached full amplifier gain and can no longer compensate for the quantum-mechanical nonlinearity associated with the phototransduction mechanism of the chromophore-neuron interface. Mesotopia is therefore more specifically defined than mesopia. It is closely related to the failure of the phenomenon of color constancy. It can arise in the presence of very high average illumination levels if the spectral content of the illumination is highly constrained with respect to one or more spectral channels. Twilight typically represents such a condition wherein the S–spectral channel is typically operating in the mesotopic condition while the L– and M–channels are not. As the M–channel enters the mesotopic condition, the Purkinje Peak appears in the perceived luminance of the scene (but not in the actual luminance of the stimulus). This peak is a result of the logarithmic signal processing within the neural system. 17.3.3.7.2 Equations of mesotopic vision

Equations 17.3.3-6 & 17.3.3-8, can be expanded to introduce the additional quiescent component, K, as was done in Section 17.3.3.2.3. The complete form of P and Q, under both mesotopic and scotopic conditions, can be written as 256 Processes in Biological Vision

P = Ln(K+S) - Ln(K+M) = Ln[(K+S)/(K+M)] or Ln[(1+S/K)/(1+M/K)] Eq. 17.3.3-16 Q=Ln(K+L 2) - Ln(K+M) = Ln[(K+L2)/(K+M)] or Ln[(1+L2/K)/(1+M/K)] Eq. 17.3.3-17 The formulations on the right show that the P and Q channels perform differently. There is now a square term in the Q channel signal. Both signals are dependent on the ratios of the S-, M- and L2 signals to K. For large values of these ratios, the P and Q signals become dominated by a second set of ratios, those of S to M and L2 to M. As these later ratios become small, the P and Q signals approach zero. This is similar to the photopic condition. However, there is another condition. As the signal levels decrease, the first set of ratios becomes small relative to 1, both the numerator and denominator of each logarithm approaches 1. P and Q approach zero regardless of the ratio of S to M and L2 to M. This situation describes the scotopic condition. The manner in which P and Q approach zero is slightly different at low signal levels. Looking initially at the condition where S, M and L2 are much larger than K, the equations become: P = Ln [S/M] --Mesotopic condition, K is small Eq. 17.3.3-18 Q = Ln[L2/M] --Mesotopic condition, K is small Eq. 17.3.3-19 For positive values of P and Q, if the signal level begins to decrease, the Q signal decreases faster than the P signal. This is the primary explanation for the loss in saturation of long wavelength scene elements relative to that of short wavelength scene elements.

For negative values of P and Q and low signal values, the situation is the same as for the photopic condition:

P = Q = -Ln[1 + M/K] --Mesotopic condition, M

Recognizing that the chromatic performance of the long wave trichromat degrades asymmetrically as the illumination level falls, as predicted by equations 17.3.3-16 & -17, it is useful to explore this effect on the New Chromaticity Diagram. The fundamental change is due to the nature of the equation for the Q channel signal. Since this region is characterized by the adaptation amplifiers beginning to operate at maximum gain and the variable internal negative feedback reaching a minimum, the square-law aspect of the L-channel signal is now clearly represented along the horizontal axis of the New Chromaticity Diagram. As the light level falls, the perception of color is lost at ever shorter wavelengths.

Equations 17.3.3-16 & -17 also illustrate a second feature of the visual system. As the light level falls, the values of both P & Q approach zero regardless of the spectral content of the light in object space. Thus, less and less chrominance information is transmitted to the brain. Any scene in object space appears less and less saturated. This is the situation in the mesotopic region of vision. When the values of P & Q both fall below the threshold for the channels, the visual system is left with only luminance information. This is the case in the scotopic region.

17.3.3.7.3 The New Chromaticity Diagram under reduced stimulus conditions

To simplify the discussion, it will be assumed that the stimulus is a 7053 K blackbody source and the physiological optical system is achromatic. This will insure that the photon flux as a function of wavelength is uniform at the retina. It is difficult to illustrate both the loss in chromatic range and the loss in saturation in a single plane of the New Chromaticity Diagram. The signal level available at the pedicle of the L–channel photoreceptors falls rapidly with light level in the mesotopic range. This fall causes the signal level in the Q–channel to become skewed toward the green. However, the M–channel signal is also falling. The result is that the Q–channel signal begins to decrease in absolute amplitude toward zero (the condition of achromatic operation within the Q–channel). The same circumstances occur in the P–channel. However, both the S– and M–channels are linear with respect to stimulation. Therefore, the decrease in P–channel signal amplitude remains symmetrical as the light level is decreased and the net signal converges on the achromatic point. Figure 17.3.3-12 describes the loss in performance of both the P– and Q–channels as the light level is reduced. In this figure, the P– and Q–channel scales are primary. Let the largest box be drawn for a stimulus level corresponding to the top of the mesotopic region (and the pupil size fixed). This box is approximately that available using a conventional (North American) tricolor monitor. At the top of the mesotopic region, the wavelength scales represent the actual wavelengths of the stimuli. A circle inscribed within the largest box would represent a Munsell Chroma of about 24. The individual boxes are caricatures meant to represent a Performance Descriptors 17- 257 change of 1.5"k:1 in logarithmic stimulus level compared to the adjacent boxes (where k can have any value). The individual boxes would represent different mesotopic brightness levels in a complete luminance-chrominance color space (See Section 17.4). At these lower stimulus values, the wavelengths corresponding to the sides of the boxes represent the perceived wavelengths of the light rather than the impressed wavelengths due to the tricolor monitor. The vertical and horizontal dimensions of each box define the maximum saturation level that can be achieved within the P– and Q– chrominance channels as a function of stimulus level. The lower the stimulus level, the smaller and narrower the box. The perceived chroma circles of Munsell become highly elliptical due to the precipitous loss in signal in the L–channel. This predicted condition is compatible with the results of Walkey, et. al. (even though they were measuring perceptions using the nonconformal CIE object spaces)316. Young has confirmed the change in perceived response with reduced stimulus level in the field of visual astronomy (Section 17.3.8.1.7). He notes, “A moderate yellow like Munsell 5Y 7/7 appears moderate olive if its reflectance is reduced 5 or 10 times, to 5Y 3/7.” He is speaking here using the conventional (relative) Munsell Color Scale. Using the new Absolute Munsell Color Scale defined in the above referenced section of this work, the second set of values given would be precisely 5Y 2/7 for a reduction of 10:1 in reflectance, or the product of reflectance and irradiance.

Reference may also be made to the performance of the chrominance channels individually as represented by the deutranope and tetartanope of Section 18.1.5. These may aid in understanding the independent operation of the P– and Q–channels with light level. 17.3.3.7.4 Curvature of some loci in the New Chromaticity Diagram

The above figure illustrates the loss in color constancy encountered under mesotopic conditions. The diagonals of the boxes change angle with stimulus level. Equally obviously, MacAdam circles (in this perceptual color space) become ellipses. It can be Figure 17.3.3-12 (Color) New Chromaticity Diagram at inferred from these conditions that color rendition is mesotopic levels. The series of decreasing box sizes are poor under mesotopic conditions. illustrative of the more rapid loss in red-green performance as the light level is reduced. Each box is If a loci is defined representing the corners of the meant to represent a change in stimulus level of 1.5@k:1 boxes, the resulting “radials” are curved. The from the adjacent box. Below a certain box size, the curvature of these radials represents a change in both visual system discards all chromatic information and saturation and color as a function of stimulus level. reverts to achromatic operation. These curvatures suggest a significant problem in the Munsell Color Space. It suggests that the Munsell radials are not perceived as of constant “value” as the light level is reduced. The square-law nature of the quantum-mechanical mechanism associated with phototransduction in the L–spectral channel has a significant impact on color rendition in the mesotopic region. 17.3.3.8 Features of the New Diagram [xxx overlaps with 17.3.4.2 ] The new Chromaticity Diagram for Research is fundamentally different from the engineering and commercially oriented C.I.E. Diagrams. This new diagram describes “perception space.” The C.I.E. Diagrams describe “object space” (although psychophysicists frequently use them to interpret their perceptual results). The relationship between these two presentations is dynamic due to the time constants of the adaptation amplifiers associated with each chromatic channel. The formulation of the new chromaticity diagram presents a number of attractive features:

316Walkey, H. Barbur, J. Harlow, J. & Makous, W. (2001) Op. Cit. 258 Processes in Biological Vision

Major Features; + The formulation of this chart does not require the use of Tristimulus values or other mathematical devices of any kind. The so-called real primary stimuli given by R,G,B and the imaginary primary stimuli given by X,Y,Z are not used. The coordinates of the presentation are directly in the wavelengths of the applied stimulus. + There are no “non-spectral” colors. + The presentation does not require any auxiliary lines, such as a Purple Line, or construction lines to specify a color as a “complementary wavelength.” All colors occupy individual and unique locations on the chart. The old Purple Line is replaced by two lines defining the actual limits of human color discrimination. The concept of an alychne, a line of zero luminance and defined as the line at y=0.0 in the conventional chromaticity diagram, is not used. Luminance is not present explicitly or implicitly in the New Diagram. It is orthogonal to the new color space. See Section 17.4. + The presentation clearly delineates the limits of color discrimination in human vision. + The coordinates of a given color may be described in terms of rectilinear values, associated directly with the dominant (or mean) wavelengths of the constituent lights, or in terms of circular coordinates based on the point defined as white. The white point is an intrinsic point that does not change with source illumination color temperature if sufficient adaptation time is provided. For circular coordinates, the saturation is indicated by the length of the radius line from W and the hue can be indicated by the angle from the horizontal line to the right of W or by using any other initial angle.

+ The presentation is completely independent of the Brightness perceived by the animal.

+ The saturation level is defined in mathematically verifiable terms. Contours of constant saturation can be drawn explicitly.

Other features include;

+ White is uniquely defined as the point W in normal “long wave” trichromats like humans. This point can be taken as 0,0 in circular coordinates to describe the hue and saturation of a unique individual color or the location of the centroid of a complex color.

-As the eye ages, the lens system loses transmission in the short wavelength spectrum. This effect is automatically compensated by the adaptation amplifiers. The subject always perceives white as white regardless of his age.

-When exposed to chromatic illumination for an extended period, the subject will still report “white” objects in object space as occurring at the W point in this diagram. The “white” object may appear as distinctly colored to a photoelectric spectrophotometer.

+ Certain colors can be given explicit names that are mathematically and uniquely defined in terms of the New Chromaticity Diagram for Research under Photopic conditions; Unique Aqua is defined as a monochromatic illuminant with a spectral wavelength of 494 nm. It can be approximated under broad band conditions by an illuminant with a mean spectral wavelength of 494 nm. and no spectral content at wavelengths longer than 570 nm. (P =0, Q is negative) Unique Yellow is defined as a monochromatic illuminant with a spectral wavelength of 570 nm. It can be approximated under broad band conditions by an illuminant with a mean spectral wavelength of 570 nm. and no spectral content at wavelengths shorter than 494 nm. (Q=0, P is negative) Unique Green is defined as a monochromatic illuminant with a spectral wavelength of 532 nm. It can be approximated under broad band conditions by an illuminant with a mean spectral wavelength of 532 nm. and no spectral content at wavelengths shorter than 494 nm. or longer than 570 nm. (P is negative, Q is negative, and P=Q) Unique Red is defined as a monochromatic illuminant with a spectral wavelength of 655 nm. It can be Performance Descriptors 17- 259

approximated at maximum saturation under broad band conditions by an illuminant with a mean spectral wavelength of 655 nm. and no spectral content at wavelengths shorter than 570 nm. (P=0, Q is positive) Unique Purple is defined as a monochromatic illuminant with a spectral wavelength of 400 nm. It can be approximated at maximum saturation under broad band conditions by an illuminant with a mean spectral wavelength of 400 nm. and no spectral content at wavelengths longer than 494 nm. (P is positive, Q=0) This definition only applies if the visual system is truly trichromatic and not that of a blocked tetrachromat. Similar definitions can be given for each of these unique colors under saturated conditions by defining the radial passing between them and “white.” This is easiest in circular coordinates with the red radial defines as zero angle. Under unsaturated conditions, the colors leading to these unique colors (but not the unique colors) can be described in terms of the length of the radial leading to the unique color. The length of the radial is an indication of the saturation level. + Under lower than photopic conditions, the same unique colors exist. However, they may not be perceivable because of the low average signal magnitudes in the P and Q chrominance channels. The perception of all colors approach zero saturation as the illumination conditions approach the scotopic value, i. e., the values of P & Q approach zero. + In absolute darkness, the brain receives a full set of null signals from the ganglion cells of the retina; - The null signals generated by the midget ganglion cells corresponds to a continuous pulse train of nominal pulse interval due to the bias condition of the cells. - The null signals generated by the parasol ganglion cells correspond to an absence of pulses at their output due to the bias condition of the cells.

+White is uniquely presented to the brain as a null signal in all (both) chromatic difference channels in the presence of any luminance signals.

+ In the presence of a scene with a spectral intensity other than that represented by an 8,000 K source, the adaptation amplifiers in the photoreceptor cells adjust their gain automatically in order to present a nominal signal level in the chromatic channels at the input to the midget ganglion cells centered around the coordinate point, W. This appears to be an open circuit adjustment, no feedback to the photoreceptor cells is required, because of the high degree of internal feedback found in the collector circuit of the adaptation amplifiers.

+ The automatic adjustment performed by the adaptation amplifiers makes calculation of an alternate “white point” for sources of other color temperature than nominal inappropriate, and meaningless.

- If desired, auxiliary constructs can be used associated with the two spectral axes to indicate the conversion of the radiation from a given spectral source into its perceived values on the new Diagram. It should be noted that the transfer functions are time dependent due to the time constant associated with the adaptation amplifiers in each chromophoric channel.

+ Following full adaptation (and while remaining within the photopic region), the perception of white is independent of the color temperature of the illumination source. As in the case of the Purple Line and alychne, there is no Planckian Locus in the New Chromaticity Diagram for Research.

17.3.3.8.1 An important feature of chromaticity diagrams

[ need ln terms in P equation ??] An important point shared with the C.I.E. Chromaticity Diagram relates to the underlying mathematics. The form of the expression defining each axis is important. For the short wavelength axis, P = S- minus M-. But the S- signal is the product of the gain of the S-channel amplifiers multiplied by the integral of the spectral luminance exciting the S- photoreceptor and the absorption coefficient of that photoreceptor. Thus P is the scalar difference between two integral terms. The chromatic character of the initial illuminance is lost in the integration process. The value of P is not uniquely defined in terms of the spectrum used to compute it. In essence, a chromaticity diagram is only precise when dealing with monochromatic specular lights. As the spectral width of each light broadens, the precision of the chromaticity diagram presentation becomes less precise. If the spectral distribution of a light becomes significantly different than a smooth curve typified by either the Fermi-Dirac or the Gaussian function, the presentation on the chromaticity diagram becomes even less precise. Finally, a spectral distribution that excites the S- and M- channel equally in the steady state will generate a null condition and the brain will interpret this light as a monochromatic light of 494 nm. wavelength. A similar analysis applies to the Q chromatic channel. 260 Processes in Biological Vision

The above situation prevents the use of simple auxiliary axes on the New Chromaticity Diagram to present the spectral distribution of the light presented to the eye. It is possible to use such axes if they are subdivided further to segregate the illumination received by each chromophoric detection channel. This segregation insures that the light is considered as part of the appropriate integral. Figure 17.3.3-13 provides a conceptual view of this extended diagram (for the vertical axis only). The line at 475 nm. Is the approximate point of equal absorption between the two spectrums. Such auxiliary axes cannot be applied to the C.I.E. Diagram at all since it is not an orthogonal presentation. However, the underlying mathematical concepts and resulting limitations on presentation precision do apply. The mathematics described above and associated with the signal processing in the chrominance channels of vision provide a general explanation for the special chromatic effects described by Land and incorporated in his Retinex Theory of color vison. See Section 17.8.4 for further discussion of these phenomena. It also explains a “counterintuitive” observation of Livingstone & Hubel317. In experiments using a small test source displayed against a dark or diffusely lit background, they observed “that monochromatic light seen as ‘blue’ added in the right amount to monochromatic light that we call ‘yellow’ produces the sensation of ‘white,’ a sensation also evoked by light containing all wavelengths; that cyan (blue-green) plus red similarly produces white; that red plus green gives yellow.” These statements may appear counterintuitive to someone trained using the C.I.E. (1931) Chromaticity Diagram but they are simply obvious based on the New Chromaticity Diagram for Figure 17.3.3-13 (Color) An extended New Chromaticity Research. Although using color names that are poorly Diagram and an arbitrary source spectrum. defined in the paper, they correspond conceptually to the four orthogonal colors of the Hering Theory when plotted on the New Diagram and shown in the Figures of the following sections.

17.3.3.8.2 Display device overlays

[XXX The art in the following figure is inadequate for the purpose intended and will be reconfigured.]

Figure 17.3.3-14 provides an estimated capability of two classes of display devices in terms of the New Chromaticity Diagram, those using active (emitting) sources and those using passive (absorptive) techniques. As in the case of the C.I.E. Chromaticity Diagram, it is seen that neither of these classes of devices can provide a completely adequate reproduction of the chromatic capability of the human eye using only three spectral channels.

The active source display can provide the broadest representation of the visual color space. However, the use of only three phosphors in a kinescope selected to provide maximum brightness as well as good spectral separation frequently limits the performance in the extreme short and long wavelength regions. An active display superior to any current kinescope display can be, and has been, provided using three individual laser light sources at 400 nm, 532 nm and 650 nm. Such a machine has been in commercial use for many years as both a television projector and a kinescope recorder. In the New Chromaticity Diagram for Research, the available color gamut for active sources is defined by the area enclosed by asymptotes drawn perpendicular to the axes at the centroidal wavelength of the individual light sources. The area is normally rectangular. The passive display device based on subtractive (process) color, typically ink on paper, has been severely limited in its ability to reproduce the visual color space. This capability is so limited that a fourth color, black, is usually used to improve the color rendition leading to the nomenclature CMYK or four color printing. The printer frequently

317Livingstone, M. & Hubel, D. (1984) Anatomy and physiology of a color system in the primate visual cortex. J. Neurosci. vol. 4, no. 1, pp 309-356, pg. 348. Performance Descriptors 17- 261

adjusts the specific cutoff wavelengths of his inks to improve performance in a specific area when a customer insists. However, to achieve better performance, the printer will introduce spot color when necessary. Spot color involves adding an additional step in the printing process using a narrow spectral band, and frequently highly reflective, ink.. In recent commercial printing, a new six color subtractive process has been introduced to attempt to compete in quality with the additive color representations available in the marketplace. Any printed representation of the New Chromaticity Diagram for Research, which is meant to describe the performance of the human eye will be found wanting unless spot color or a six color process is employed. 262 Processes in Biological Vision

Figure 17.3.3-14 (Color) XXX A comparison of additive and subtractive (process) color “sets” with the capabilities of the long wavelength trichromats normal color space. The additive color set can reproduce any color within the triangle formed by connecting the centroids of the R,G & B emission sources. The subtractive color set exists in two forms. C, Y & M filters can be used to create a projected color image. The achievable range is shown by the pass band of the three filters. The deepest blue achievable is that shown for the filter itself. Similarly, the deepest red is that of the magenta filter. C,Y & M inks can also be used in printing. To avoid a series of problems, the inks are usually restricted to narrower spectral ranges as indicated by the dashed box. They reproduce a narrower process color pallet by varying the percentage of pigment covering the surface. The result is dependent on the color temperature of the illuminant and the reflectivity of the paper used. Performance Descriptors 17- 263

17.3.3.8.3 Auxiliary axes

There are two special sets of auxiliary axes that can be applied to the New Chromaticity Diagram using W as the auxiliary reference point. They are illustrated in Figure 17.3.3-15. (See Section 17.4.1.1 for similar extensions in three dimensional space.) A set of “Hering” axes can be defined using axes parallel to the axes of the spectrum locus. In this case, the “blue- yellow” axis is a vertical line at 570 nm. The “red-green” axis is a horizontal line at 494 nm. A set of “NTSC” axes can be defined using axes at an angle to the axes of the spectrum locus. These axes are used because of the difference in bandwidth required to transmit an adequate representation of a scene using television techniques. The “I” and “Q” axes of this system are rotated 33 degrees counter clockwise from the “Hering” axes. The Q axis is transmitted using only about one quarter of the bandwidth of the I axis.

Whereas the nominal zero angle of the NTSC axes were chosen to represent a Caucasian skin tone, a more theoretically defendable zero angle for the new Chromaticity diagram corresponds to an angle with its apex at “white” and measured from the displaced horizontal axis at a wavelength of 494 nm.

Figure 17.3.3-15 (Color) Alternate axes applied to the New Chromaticity Diagram. Solid axes are the “Hering” set. I and Q axes are the “NTSC” set. 264 Processes in Biological Vision

17.3.3.9 A Chromaticity Diagram for Short Wave Trichromats

Section 17.3.3.1 developed a theoretical structure appropriate for describing the color space of all animals. The remainder of Section 17.3.3 has concentrated on long wavelength trichromats, in particular humans. Figure 17.3.3- 16 presents a 2-dimensional color space for short wavelength trichromats for completeness. Although the human has no way of knowing what a short wavelength trichromat animal (many if not all arthropods) perceives as the color of an object, that performance can be portrayed in chromaticity space. In this figure, that portion of the color space shared with long wavelength trichromats is shown as humans perceive it. However, no data could be found describing the null wavelengths of the O- and P- channels of arthropod vision. The values of 388 and 486 qualify as “WAG’s (wild ass guesses) in some communities. The intersection of the axes drawn through these two null wavelengths would describe the “white” point of such a visual system. It is assumed that the sharing of the S-channel signals between the O = LnS - LnUV and the P = LnS - LnM chrominance channels, would result in the same shape to the Primary Axes as for long wavelength trichromats. The color perceived at the intersection of the 486 axis with the spectral locus is shown as “greenish-blue,” and is a low saturation color similar in concept to the aqua of human vision. The color perceived at the intersection of the 388 axis with the spectral locus is shown as “bluish-triangle,” a low saturation color similar in concept to the aqua or yellow of a long wavelength trichromat. As the wavelength of excitation is reduced below 388 nm, the animal would perceive a more saturated “triangle.”

Proceeding up along the 486 axis, the animal would initially experience a sensation similar to aqua, pass through ‘white’ and then approach the complement of aqua shown here as a large “square.”

If the animal were exposed to 580 nm light plus a light of decreasing wavelength, the animal would perceive a yellow light passing through a low saturation color Figure 17.3.3-16 (Color) A 2-D Chromaticity Diagram shown as “small circle” and proceed to a more for Short Wave Trichromats. See text for details. saturated sensation labeled here as a large “circle.” 17.3.3.9 A chromaticity diagram for optically blocked tetrachromats

The previous material in this section has assumed that the human visual system can be described as that of a long wavelength trichromat. This has been in spite of the known sensitivity of the human retina to ultraviolet light. The human retina, even in maturity, exhibits an ultraviolet sensitivity equivalent to its sensitivity in the blue and green regions of the spectrum. If the signals from such ultraviolet photoreceptors participate in the formation of a third chrominance signal (even if significantly blocked), this must be considered. The response of such an O-channel must be considered when determining what colors a person perceives. It would still be useful to have a two-dimensional color space for human vision on the assumption that the UV photoreceptors and the O-chrominance channels were fully functional. Such a color space would correctly account for the entire spectrum of the human eye. The color space would begin near 395 nm (the limit set by the absorption of the lens). It would end near 655 nm (but be expandable to at least 1000 nm when required). This can be done as long as the exciting irradiance is of narrow spectral bandwidth (typically 10 nm, FWHM). It is accomplished by not folding the spectral locus at 437 nm. The resulting graph is shown in Figure 17.3.3-17. The region at wavelengths greater than 437 nm is completely conformal when the exciting radiation has negligible energy at less than 437 nm. Thus it is useful for nearly all laboratory experiments and practical applications where the color temperature of the source is less than 3000 Kelvin. The area above the 437 nm line is a one dimensional color space that cannot be properly shown in this coordinate system. The graphs of [Figures 17.3.3-1 or 17. 3.3-2] must be used to properly display the chromatic performance of a blocked tetrachromat on flat paper. Performance Descriptors 17- 265

CHAPTER 17 CONTINUES WITH SECTION 17.3.4 IN PART 1b OF THE CHAPTER AT www.neuronresearch.net/vision/pdf/17Performance1b. pdf

Figure 17.3.3-17 (Color) A more simplified foundation for a human oriented color space. The human is assumed to be a blocked tetrachromat with a functioning O- chrominance channel. Under this condition, the figure is only conformal at wavelengths longer than 437 nm. 266 Processes in Biological Vision

TABLE OF CONTENTS 4/30/17

17 Performance descriptors of Vision ...... 1 17.1 Introduction ...... 1 17.1.1 Baseline human visual system required to understand this chapter ...... 2 17.1.1.1 Historical Background ...... 2 17.1.1.2 Baseline...... 3 17.1.1.2.1 Regions of the radiometric and illumination environment ...... 4 17.1.1.2.2 The baseline schematic of the visual system ...... 5 17.1.1.2.3 The baseline for operations leading to perception and cognition . . . 5 17.1.1.2.4 Past difficulties in performing experiments ...... 5 17.1.1.2.4 Separation of the CIE functions from the threshold functions of this work ...... 7 17.1.1.3 Goal...... 8 17.1.1.4 Perspective...... 8 17.1.1.4.1 Closed loop feedback in the motor-neural circuits of vision ...... 9 17.1.1.4.2 Other feedback within the signal processing circuits of vision . . . 10 17.1.1.4.3 Application of various mechanisms...... 10 17.1.2 Terminology...... 13 17.1.2.1 Photometric units are archaic in research ...... 13 17.1.2.1.1 Limitation on the Troland, an archaic unit of photometry ...... 14 17.1.2.1.2 Available commercial photometers lack precision ...... 14 17.1.2.1.3 Precision requires photon-flux based radiometric units ...... 15 17.1.2.2 The precise definition of “color”...... 15 17.1.2.2.1 Expanding the definition of colorimetry...... 16 17.1.2.3 Metameres, initial conceptual definitions ...... 16 17.1.2.4 The “expanded exponential sinusoid” SCREWED UP ART ...... 19 17.1.2.5 Nomenclature associated with the composite ERG and LERG...... 20 17.1.2.6 Concepts relating to optics ...... 22 17.1.2.6.1 Spatial characteristics of the physiological optics and retina ..... 22 17.1.2.6.2 Computing the limiting optical performance of the visual system . 23 17.1.2.7 Concepts involving resolution and bandwidth ...... 23 17.1.2.7.1 Temporal bandwidth of the signal generated by the P/D process . . 24 17.1.2.7.2 Temporal bandwidth of the generator waveform ...... 24 17.1.2.7.3 Temporal bandwidth of signal resulting from signal summation . . 24 17.1.2.7.4 Temporal bandwidth of signal due to signal differencing ...... 24 17.1.2.7.5 Temporal bandwidth of the spatial signal from the foveola...... 25 17.1.2.7.6 Temporal bandwidth of the channel supporting signaling ...... 26 17.1.2.8 Cartography requires conformality ...... 26 17.1.2.9 Conceptual loading of the signaling channels...... 27 17.1.3 Glossary ...... 28 17.1.4 The simplified block diagrams used to define the descriptors of vision...... 30 17.1.4.1 The key role of adaptation in the visual process ...... 30 17.1.4.2 The signaling matrix applicable to luminance and chrominance descriptors . . 31 17.1.4.3 The block diagram applicable to temporal descriptors ...... 32 17.1.4.4 The block diagram applicable to oculomotor performance descriptors...... 35 17.1.5 Problems with “black,” univariance, “silent substitution” and arbitrary normalization . . 36 17.1.5.1 The phenomenology of “black” ...... 36 17.1.5.2 The Univariance Principle...... 37 17.1.5.3 The silent substitution method ...... 38 17.1.5.4 Problems leading to expansion of the CIE functions, V(l) and V’(l) ...... 39 17.1.5.5 Problems associated with arbitrary renormalization ...... 42 17.1.6 Problems with center-surround experiments ...... 43 17.1.7 Historical composite descriptors of vision ...... 44 17.1.7.1 The CIE Standard Observer and other (largely archaic) descriptors...... 46 17.1.7.2 The use of empirically based standards and templates ...... 46 17.1.8 “Rod intrusion” as a concept...... 47 17.1.9 Particularizing the photometry and colorimetry of vision ...... 50 Performance Descriptors 17- 267

17.1.9.1 Stimulus matching methods ...... 51 17.1.9.2 Problems with luminance descriptors ...... 53 17.1.9.3 Problems with chrominance descriptors ...... 53 17.1.9.4 Threshold performance descriptors...... 54 17.1.9.5 Internal calibration of the human visual system ...... 55 17.1.10 Other individual descriptors...... 55 17.1.10.1 Frequency Domain Descriptors...... 56 17.1.10.1.1 Specific definitions related to contrast functions versus frequency ...... 56 17.1.10.1.2 Attempts to differentiate between temporal and spatial contrast . 57 17.1.10.1.3 Lack of attempts to differentiate between chromatic and temporal or spatial contrast ...... 58 17.1.10.1.4 Temporal Frequency Domain Descriptors...... 59 17.1.10.1.5 Spatial Frequency Domain Descriptors ...... 60 17.1.10.1.6 Chromatic Frequency Domain Descriptors ...... 61 17.1.10.2 Parametric properties clarified...... 61 17.1.10.3 Anomalies and Effects...... 62 17.2 The Luminance Characteristic of the human eye...... 62 17.2.1 Determination of the luminosity related functions of the visual system...... 65 17.2.1.1 Historical determination of the luminosity function ...... 65 17.2.1.2 Theoretical Background ...... 67 17.2.1.2.1 Energy related matters...... 67 17.2.1.2.2 Noise related matters ...... 68 17.2.1.3 Operational considerations ...... 68 17.2.1.3.1 The relationship between dark, light and chromatic adaptation . . . 69 17.2.1.3.2 A chromatic spectrum for reference...... 69 17.2.1.3.3 Chromatic filters for laboratory use ...... 70 17.2.1.3.4 A light source for laboratory use ...... 71 17.2.1.3.5 The systemic variation in retinal sensitivity with spatial position . 71 17.2.1.3.6 The systemic variable related to ageing...... 73 17.2.2 The relationship between brightness and luminance in vision ...... 73 17.2.2.1 The perceived intensity of sound versus its actual intensity ...... 74 17.2.2.2 The perceived intensity of light versus its actual intensity ...... 75 17.2.2.3 Analysis of the brightness/luminance relationship ...... 81 17.2.2.4 Compression factors found in other sensory modalities ...... 82 17.2.3 The luminance threshold (AKA luminous efficiency function) of the human eye ...... 83 17.2.3.1 The tetrachromatic spectral sensitivity of the human retina ...... 84 17.2.3.1.1 Effect of aging on ultraviolet vision...... 88 17.2.3.2 The spectral characteristics of the physiological optics of the human eye . . . 89 17.2.3.2.1 The primary in-band spectral absorption of the physiological optics ...... 90 17.2.3.2.2 The spectral absorption of the macular area...... 92 17.2.3.3 The tetrachromatic spectral sensitivity of the complete human eye ...... 92 17.2.3.3.1 The spectral sensitivity of the complete human eye (except in macular) ...... 92 17.2.3.3.2 The spectral absorption of the complete human eye in the macular ...... 94 17.2.3.3.3 The measurement of the reflectance of the retina through the physiological optics ...... 94 17.2.3.4 Comparison with the ultraviolet research literature ...... 94 17.2.3.5 Comparison with the photopic research literature ...... 95 17.2.3.5.1 The photopic research literature–normal broadband ...... 95 17.2.3.5.2 The photopic research literature–infrared ...... 109 17.2.3.5.3 The photopic research literature–chromatic adaptation (A MAJOR PROBLEM) ...... 111 17.2.3.5.4 The photopic research literature–Difference spectra ...... 114 17.2.3.5.5 The photopic research literature–Foveal ...... 117 17.2.3.6 Interpretation of the photopic standards literature ...... 117 17.2.3.6.1 State of the Photopic Standard ...... 117 17.2.3.6.2 Individual factors not addressed in the CIE Standard ...... 118 17.2.3.6.3 Light versus dark adaptation ...... 123 17.2.3.6.4 Calculation of the neural component of the CIE luminous efficiency function...... 124 268 Processes in Biological Vision

17.2.3.6.5 Extended remarks on the familiar C.I.E. Luminosity Standards . . 130 17.2.3.6.6 Obtaining the familiar C.I.E. Luminosity Function by smoothing T(8,F)...... 133 17.2.3.7 Comparison with the photopic standards literature ...... 134 17.2.3.7.1 State of the theoretical description...... 135 17.2.3.7.2 Comparison of the theory and empirical data...... 135 17.2.4 Resolving the difference between spectra of the chromophores and other spectra ..... 138 17.2.4.1 Comparing the long pulse versus flicker photometry ...... 138 17.2.4.2 Reviewing other the measurements based on long pulse photometry ...... 140 17.2.5 Predicted versus measured spectra and color-matching functions ...... 140 17.2.5.1 Interpretation of the Thornton work ...... 146 17.2.5.2 Reviewing the measurements supporting “cone-fundamentals” ...... 148 17.2.5.3 Rationalizing “cone-fundamentals” and p-parameters with other spectral parameters ...... 152 17.2.5.3.1 The design and interpretation of spectral sensitivity experiments ...... 152 17.2.5.3.2 Background from the literature ...... 153 17.2.4.5.3 Conclusions ...... 156 17.2.4.5.4 Graphic comparison of spectral characteristics ...... 157 17.2.6 The performance of the eye under unusual illumination conditions ...... 162 17.2.6.1 The full eye at very reduced irradiance (Scotopic region)...... 162 17.2.6.1.1 Comparison with the scotopic research literature ...... 162 17.2.6.1.2 Comparison with the scotopic standards literature ...... 163 17.2.6.2 The full eye under transition conditions (Mesopic and Mesotopic regions) . 164 17.2.6.2.1 The physiological mechanisms associated with the mesopic region...... 165 17.2.6.2.2 Brief summary of the neurological phenomonology and mechanisms ...... 165 17.2.6.2.3 Caricature of the mesotopic luminance threshold function, T(l,F) ...... 167 17.2.6.2.4 Comparison with the Mesopic literature ...... 167 17.2.6.3 The full eye at excessive irradiance (Hypertopic region) ...... 174 17.2.6.4 The full eye with enhanced long wavelength irradiance (Purkinje Effect) . . 175 17.2.6.5 The full eye with suppressed mid wavelength amplifier performance (Bezold Effect)...... 176 17.2.6.5.1 Background ...... 176 17.2.6.5.2 Analysis...... 177 17.2.6.5.3 A projected Bezold-Brucke Effect near 395 nm ...... 178 17.2.6.6 The so-called Purkinje Shifts of the literature ...... 179 17.2.6.7 The use of the above Effects in precision research ...... 179 17.2.7 Luminance threshold & other descriptors related to performance ...... 179 17.2.7.1 The Noise and threshold characteristics of the human eye ...... 180 17.2.7.1.1 Critical circuit features in low light vision...... 183 17.2.7.1.2 A combined achromatic/chromatic threshold performance graph ...... 184 17.2.7.1.3 Discrimination of luminance differences...... 186 17.2.7.2 Thresholds as a function of field position ...... 187 17.2.7.3 Defining the quantum efficiency of vision ...... 189 17.2.7.3.1 Background ...... 190 17.2.7.3.2 Structural configuration of the outer segments...... 193 17.2.7.3.3 Define bleaching in the context of photon absorption at the outer segment...... 193 17.2.7.4 Defining “bleaching” in the context of the P/D equation ...... 193 17.2.7.5 Reaction time as a function of illuminance ...... 193 17.3 The Chrominance Characteristic of the human eye...... 194 17.3.1 Historical background & the definition of color ...... 196 17.3.1.1 Early philosophical models; Young, Maxwell, Hering & Kries ...... 197 17.3.1.2 Early empirical model of Munsell and the C.I.E...... 199 17.3.1.2.1 The Munsell perspective ...... 200 17.3.1.2.2 Hue and Saturation are not intrinsic...... 201 17.3.1.3 The C.I.E. (1931 & 1964) concept of color space is invalid for research . . . 202 Performance Descriptors 17- 269

17.3.1.3.1 Analyses by other investigators...... 203 17.3.1.3.2 Analyses based on this work ...... 204 17.3.1.3.3 The C.I.E. color space is nonconformal ...... 205 17.3.1.3.4 The interpretation of the C.I.E (x,y) Chromaticity Diagram .... 205 17.3.1.3.5 An interpretation of the Planckian Locus on the CIE Diagram . . 206 17.3.1.3.6 The interpretation of the C.I.E (a*,b*) or CIELAB Chromaticity Diagram ...... 207 17.3.1.4 The early electrophysiological measurements; Svaetichin and Tomita ..... 207 17.3.1.5 More recent psychophysical models ...... 207 17.3.1.5.1 Recent psychophysical model of McLeod & Boynton ...... 207 17.3.1.5.2 The DKL model of Derrington, et. al. based on electrophysiology ...... 208 17.3.1.5.3 The Chatterjee & Callaway data based on electrophysiology . . . 209 17.3.1.6 Recent measurements in the mesotopic region ...... 209 17.3.1.7 Continuing difficulties in empirical experiment design ...... 209 17.3.1.7.1 The persistent introduction of pigment triangles and tetrahedrons ...... 209 17.3.1.7.2 A critical problem with CIE conforming color measurements ...... 210 17.3.1.8 A new conformal color space based on electrophysiology is required ..... 210 17.3.2 The chromatic discrimination function, C(8,F) ...... 210 17.3.2.1 Background ...... 210 17.3.2.2 Theoretical capability ...... 211 17.3.2.2.1 Simplified calculation of the amplitude portion of the C(8,F)... 212 17.3.2.2.2 Calculation of the complete chromatic threshold function...... 213 17.3.2.2.3 Apparent equal participation of the spectral channels in forming C(8,F)...... 214 17.3.2.2.4 C(l,F) under mesotopic conditions ...... 214 17.3.2.3 Comparison with the literature ...... 214 17.3.2.3.1 Discrimination versus fixation...... 219 17.3.2.3.2 Discrimination versus Illumination ...... 220 17.3.2.3.3 Discrimination versus spatial integration...... 221 17.3.2.3.4 Color discrimination in cases of anomalous color vision...... 221 17.3.2.3.5 Discrimination versus other independent variables ...... 221 17.3.2.4 Comparison of the C(l,F), T( l,F) and V(l) functions...... 221 17.3.2.5 Features of the new function...... 222 17.3.3 Definition of a “New” Chromaticity Diagram ...... 223 17.3.3.1 Conceptual framework for the new chromaticity diagrams...... 225 17.3.3.1.1 Background ...... 226 17.3.3.1.2 The morphological location supporting the New Diagram ...... 226 17.3.3.1.3 Development of fundamental chrominance signals ...... 227 17.3.3.2 Defining the tetrachromatic chromaticity diagram ...... 227 17.3.3.2.1 What colors does a tetrachromat perceive? ...... 228 17.3.3.2.2 What colors does a human perceive?...... 230 17.3.3.2.3 A simplified three-dimensional framework for true trichromats . 233 17.3.3.3 A New Chromaticity Diagram for human vision...... 234 17.3.3.3.1 A chromaticity diagram under optimal illumination ...... 234 17.3.3.3.2 A chromaticity diagram under incandescent illumination ...... 236 17.3.3.3.3 Fundamental, primary and cardinal axes ...... 236 17.3.3.3.4 Hue and saturation are not fundamental parameters ...... 236 17.3.3.3.5 The New (hypertopic & photopic) Chromaticity Diagram for Research...... 237 17.3.3.4 Limitations on the presentation of the New Chromaticity Diagram ...... 241 17.3.3.4.1 Broad versus narrow irradiances in the laboratory...... 241 17.3.3.4.2 Capability of displays ...... 241 17.3.3.4.3 Remaining functional complications ...... 242 17.3.3.5 Auxiliary Constructs applied to the New Chromaticity Diagram ...... 243 17.3.3.5.1 Theoretically achievable chromatic discrimination capability . . . 243 17.3.3.5.2 Achievable discrimination capability versus test field RESERVED ...... 244 17.3.3.5.3 Achievable discrimination capability in color deficient subjects . 244 17.3.3.5.4 Action potentials of the optic nerve vs illumination spectrum . . . 244 17.3.3.5.5 Definition of Hue and Saturation...... 245 17.3.3.6 Perception and display of color spaces ...... 246 270 Processes in Biological Vision

17.3.3.6.1 Comparing the new diagram with MacAdam, Farnsworth, etc. . . 246 17.3.3.6.2 Difficulty in documentation and display ...... 248 17.3.3.6.3 Typical achievable color spaces ...... 250 17.3.3.7 The New Chromaticity Diagram for Research at Mesotopic levels...... 251 17.3.3.7.1 Mesopic versus mesotopic vision...... 251 17.3.3.7.2 Equations of mesotopic vision...... 251 17.3.3.7.3 The New Chromaticity Diagram under reduced stimulus conditions ...... 252 17.3.3.7.4 Curvature of some loci in the New Chromaticity Diagram ..... 253 17.3.3.8 Features of the New Diagram ...... 253 17.3.3.8.1 An important feature of chromaticity diagrams...... 255 17.3.3.8.2 Display device overlays...... 256 17.3.3.8.3 Auxiliary axes ...... 257 17.3.3.9 A Chromaticity Diagram for Short Wave Trichromats...... 259 CHAPTER 17 CONTINUES WITH SECTION 17.3.4 IN PART 1b OF THE CHAPTER ...... 260 Performance Descriptors 17- 271 Chapter 17 Equations Some complex equations are inserts and are not shown explicitly here “The Expanded Exponential Sinusoid” Eq. 17.1.1-a ...... 19 “Alternate Expanded Expon.Sinusoid” Eq. 17.1.1-b ...... 19 “Extended Exponential” Eq. 17.1.1-c ...... 20 “Vector form of R(t) and constructs” Eq. 17.1.2-1...... 27 C = xR + yG + zB Eq. 17.2.1-1...... 67 R = lnC = ln xL2 + ln yM + ln zS Eq. 17.2.3-2...... 125 R = lnC = ln xL + ln yM + ln zS Eq. 17.2.3.-3...... 125 R =LnC = [Ln(KL x L) + Ln(KM x M) + Ln(KS x S)]/Const. Eq. 17.2.3-4...... 126 O = LnUV - LnS Eq. 17.3.3-5...... 227 P = LnS - LnM Eq. 17.3.3-6...... 227 Q = LnL - LnM Eq. 17.3.3-7...... 227 Q =LnL2 - LnM Eq. 17.3.3-8...... 227 P = Ln(K+S) - Ln(K+M) = Ln[(K+S)/(K+M)] or Ln[(1+S/K)/(1+M/K)] Eq. 17.3.3-16...... 251 Q=Ln(K+L 2) - Ln(K+M) = Ln[(K+L2)/(K+M)] or Ln[(1+L2/K)/(1+M/K)] Eq. 17.3.3-17...... 251 P = Ln [S/M] --Mesotopic condition, K is small Eq. 17.3.3-18...... 252 Q = Ln[L2/M] --Mesotopic condition, K is small Eq. 17.3.3-19...... 252 272 Processes in Biological Vision

Chapter 17 Figures 4/30/17

Figure 17.1.1-2 Top level schematic of the visual system of Chordata...... 9 Figure 17.1.1-3 An overall descriptor of the illumination range of the eye ...... 10 Figure 17.1.2-1 Test configuration for metameric matching...... 18 Figure 17.1.2-2 Concept of optimizing the performance of an imaging system ...... 23 Figure 17.1.2-3 Concept of the temporal spectrum utilization ...... 27 Figure 17.1.4-1 The luminance, chrominance and appearance channels of the eye ...... 32 Figure 17.1.4-2 The large signal circuit diagram of the fundamental signal paths ...... 34 Figure 17.1.4-3 Overall Servomechanism of the human visual system...... 35 Figure 17.1.5-1 A photopic operating visibility function, Vo(l), for the rhesus monkey ...... 40 Figure 17.1.5-2 Operational visibility functions shown on the same graph for HS ...... 42 Figure 17.1.9-1 Three major matching geometries of photometry & colorimetry ...... 51 Figure 17.2.1-1 (Color ln) The tetrachromatic luminous efficiency function of human vision ...... 64 Figure 17.2.1-2 Variation of increment threshold in traverses through the dark-adapted foveal and parafoveal area ...... 72 Figure 17.2.2-1 The perceived audio loudness as a function of sound intensity in humans ADD ...... 74 Figure 17.2.2-2 Proposed template for the perceived visual brightness as a function of luminance intensity in humans ADD...... 76 Figure 17.2.2-3 Relationship between lightness-scale value V and luminance factor Y...... 77 Figure 17.2.2-4 The human visual response based on the Munsell Color Book ...... 79 Figure 17.2.2-5 Brightness functions for various levels of adaptation ...... 80 Figure 17.2.2-6 The theoretical performance of the visual modality with adaptation as a parameter ...... 83 Figure 17.2.3-1 (Color ln) Comparison of aphakic vision and the theoretical model...... 85 Figure 17.2.3-2 Heterchromatic brightness sensitivity change per decade ...... 88 Figure 17.2.3-3 CR Light transmission through the physiological optics ...... 89 Figure 17.2.3-4 “Equation for optical density of physiological optics” Eq. 17.2.3.1 ...... 90 Figure 17.2.3-5 The equivalent optical density of the physiological optics of the eye ...... 90 Figure 17.2.3-6 (Color ln)The theoretical absorption of the macular. Compare with the empirical data ...... 92 Figure 17.2.3-7 (Color ln) Calculated tetrachromatic spectral sensitivity of the normal human eye compared with the best data ...... 93 Figure 17.2.3-8 A comparison of aphakic and phakic eyes based on Griswold & Stark...... 94 Figure 17.2.3-9 Early spectral sensitivity curves...... 96 Figure 17.2.3-10 Comparison of theoretical and empirical spectral sensitivity functions (luminous efficiency functions)...... 97 Figure 17.2.3-11 Incremental threshold spectral sensitivity of two normal human subjects ...... 98 Figure 17.2.3-12 Visual sensitivity of the rhesus monkey ...... 99 Figure 17.2.3-13 A human spectral response confirming all of the curves and shoulders predicted by the theoretical model...... 101 Figure 17.2.3-14 High precision spectral data for SG...... 102 Figure 17.2.3-15 Increment-threshold spectral sensitivity for rhesus monkeys ...... 104 Figure 17.2.3-16 Increment-threshold data for Rhesus monkeys corrected for color temperature ...... 106 Figure 17.2.3-17 Comparison of luminous efficiency functions for absolute threshold and for heterochromatic brightness matching...... 107 Figure 17.2.3-18 ...... 109 Figure 17.2.3-19 The predicted dark adapted photopic luminosity function in the infra-red ...... 110 Figure 17.2.3-20 Wald figure 4 with overlay ...... 112 Figure 17.2.3-21 The spectrum of the “blue monochromat” ...... 113 Figure 17.2.3-22 Comparison of difference spectra with the CIE Photopic Luminosity Standard ...... 114 Figure 17.2.3-23 Annotated Stockman et al. data compared to the proposed theoretical peaks ...... 116 Figure 17.2.3-24 The signal flow schematic used for calculating the luminance function ...... 120 Figure 17.2.3-25 Equations for the spectral absorption of the physiological optics of the eye...... 122 Figure 17.2.3-26 The summing circuit at the output terminals of four photoreceptor cells...... 124 Figure 17.2.3-27 The theoretical photopic luminosity function ...... 128 Figure 17.2.3-28 Comparing a theoretical human spectral sensitivity function and its smoothed counterpart . . . 133 Figure 17.2.3-29 Comparison of the theoretical and empirical Photopic Luminosity Functions...... 138 Figure 17.2.4-1 Comparing spectral sensitivity based on 1o 10 ms test flashes and flicker photometry ...... 139 Figure 17.2.5-1 Three-color matching functions for a fixed power “standard light.”...... 143 Figure 17.2.5-2 Tabular comparison of peak absorption wavelengths ...... 145 Figure 17.2.5-3 Absorption spectra based on power measurements...... 145 Performance Descriptors 17- 273

Figure 17.2.5-4 Comparison of measured and theoretical spectra...... 146 Figure 17.2.5-6 The effects of flicker frequency on the observed spectral sensitivity curves in humans ...... 154 Figure 17.2.5-7 The luminosity function and partially isolated spectral responses of the human eye ...... 155 Figure 17.2.5-8 A comparison of various spectra claimed to represent human vision ...... 158 Figure 17.2.5-9 Predicted long wavelength peak versus flicker frequency ...... 160 Figure 17.2.5-10 The flicker frequency versus peak spectral wavelength relationship...... 161 Figure 17.2.6-1 The difference spectrum recorded psychophysically in the human retina ...... 163 Figure 17.2.6-2 Comparison of the theoretical and other scotopic data...... 164 Figure 17.2.6-3 ERG data showing the change in spectral sensitivity with stimulus level ...... 165 Figure 17.2.6-4 Caricature of human luminance threshold response under mesotopic conditions ...... 167 Figure 17.2.6-5 Theoretical and putative empirical shift in spectra going from photopic to scotopic vision. . . . 168 Figure 17.2.6-6 Luminous efficiency functions at nine retinal-illuminance levels; two subjects ...... 169 Figure 17.2.6-7 Luminance sensitivity variation from photopic to scotopic regimes ...... 171 Figure 17.2.6-8 Overlay of measured data with theoretical function from this theory ...... 172 Figure 17.2.6-9 A comparison of theoretical and empirical curve fitting to mesopic measurements ...... 172 Figure 17.2.6-10 Recent MOVE data on luminous efficiency ...... 173 Figure 17.2.6-11 Plot of logEref versus log Etest ...... 174 Figure 17.2.6-12 Theoretical foundation for the Purkinje (brightness) Effect...... 175 Figure 17.2.6-13 Theoretical foundation for the Bezold-Brucke Effect...... 176 Figure 17.2.7-1 The noise model of the visual system...... 181 Figure 17.2.7-2 Combined chromatic and achromatic thresholds for the steady state ...... 185 Figure 17.2.7-3 The island of vision (left) based on threshold (static) perimetry...... 187 Figure 17.2.7-4 Profile perimetry along the zero degree meridian for 8 different states of adaptation ...... 188 Figure 17.2.8-1 The laws of probability theory applicable to visual sensing ADD ...... 191 Figure 17.3.1-1 A foundation for both Newton’s and Young’s conception of color space ...... 199 Figure 17.3.1-2 The appearance of 10 degree fields arranged for metameric matches with different combinations of spectral lights...... 210 Figure 17.3.2-1 The signal flow schematic used for calculating the chromatic discrimination function of human vision (and other chordate vision) ...... 212 Figure 17.3.2-2 (a)The transfer function between the logarithm of the input illumination and the output of the lateral cells of the chrominance channels...... 213 Figure 17.3.2-3 The proposed wavelength discrimination function for human vision ...... 216 Figure 17.3.2-4 Observations of hue reversal in the deep red...... 217 Figure 17.3.2-5 Plot of equivalent wavelengths-wavelengths giving the same colour sensation...... 217 Figure 17.3.2-6 Wavelength discrimination as a function of wavelength...... 219 Figure 17.3.2-7 Measured and predicted values of the wavelength discrimination function ...... 220 Figure 17.3.2-8 Wavelength discrimination functions for various tests field sizes...... 221 Figure 17.3.2-9 Comparison of the chromatic and luminous discrimination functions ...... 222 Figure 17.3.3-1 (Color ) The foundation for the chromaticity diagram of tetrachromatic vision ...... 228 Figure 17.3.3-2 Theoretical composite human color discrimination function under high contrast photopic conditions ...... 232 Figure 17.3.3-3 Effect of source color temperature on the color discrimination capability of the human eye . . . 233 Figure 17.3.3-4 (Color) A simplified foundation for a three- dimensional color space ...... 233 Figure 17.3.3-5 A complete color space for blocked tetrachromats (including humans) ...... 235 Figure 17.3.3-6 [Color] A physiology-based Chromaticity Diagram for Humans applicable to the Hypertopic and Photopic regions...... 238 Figure 17.3.3-7 [Color] Illustration of extended new Chromaticity Diagram to show ideal and theoretically achievable chromatic discrimination capability ...... 244 Figure 17.3.3-8 [Color] New Chromaticity Diagram extended to show the interpulse interval of the action potentials of the chrominance channels ...... 245 Figure 17.3.3-9 [Color] Hue and Saturation coordinates applied to the New Chromaticity Diagram ...... 246 Figure 17.3.3-10 A re-plot of MacAdam ellipses compared to the new Chromaticity Diagram...... 248 Figure 17.3.3-11 Realizable human color space using kinescope and printing techniques ...... 250 Figure 17.3.3-12 (Color) New Chromaticity Diagram at mesotopic levels ...... 252 Figure 17.3.3-13 (Color) An extended New Chromaticity Diagram and an arbitrary source spectrum...... 255 Figure 17.3.3-14 (Color) XXX A comparison of additive and subtractive (process) color “sets” ...... 257 Figure 17.3.3-15 (Color) Alternate axes applied to the New Chromaticity Diagram...... 257 Figure 17.3.3-16 (Color) A 2-D Chromaticity Diagram for Short Wave Trichromats...... 259 Figure 17.3.3-17 (Color) A more simplified foundation for a human oriented color space ...... 259 274 Processes in Biological Vision

(Active) SUBJECT INDEX (using advanced indexing option) 2-exciton...... 111, 192 2-photon ...... 145, 192 3D...... 77 3-D...... 241 95% ...... 126 action potential...... 153, 183, 184, 189, 207 Activa...... 10, 111, 123, 124, 153, 181, 182 adaptation . . 2, 5, 8, 10, 11, 13, 15, 19, 20, 24-26, 28-32, 37, 38, 40, 41, 43, 45, 47-50, 59-61, 64, 65, 69, 73-76, 78, 80-83, 86, 96, 98, 107-109, 111-118, 120, 123-127, 129, 130, 134, 135, 137, 138, 149-153, 155- 158, 162, 166, 167, 169, 170, 172, 175-185, 187-189, 195, 200, 206, 207, 212, 217, 220, 225-228, 232, 237-240, 243, 251-255 adaptation amplifier..... 5, 10, 11, 24, 26, 28, 38, 69, 74, 75, 82, 111, 112, 125, 175, 176, 181-185, 187, 207, 220, 225 alarm mode...... 4 amplification ...... 11, 28, 30, 31, 45, 61, 69, 120, 121, 180-183 analytical mode ...... 57 arborization ...... 242, 243 attention...... 13, 58, 79, 80, 157, 180, 189, 215 axoplasm ...... 125 a-wave ...... 21 band gap...... 67, 68, 180, 183 Black Body...... 8, 13, 71, 121, 128, 136, 242 bleaching ...... 12, 30, 31, 41, 112, 163, 193 BOLD...... 240 broadband...... 6, 19, 24, 47, 58, 66, 78, 95, 141, 142, 152, 190, 201 b-wave ...... 21, 22 C.I.E. . . 1, 13, 14, 26, 37, 39, 46, 53, 54, 62, 65, 66, 71, 83, 84, 97, 107, 115, 118, 128-138, 162-164, 197, 199-209, 216, 217, 224, 226, 234, 237, 239, 244, 245, 247, 248, 250, 253, 255, 256 calibration...... 13, 55, 78, 80, 105, 106, 165, 170 Central Limit Theorem...... 96, 113 cerebellum ...... 4, 35 CIE . . . 1, 7, 8, 13, 15, 17, 39, 41, 42, 46, 47, 53, 77, 78, 105, 106, 108, 114, 117-119, 121, 124, 129, 130, 132, 133, 141, 143, 146, 148, 149, 163, 165, 167, 168, 171-173, 177, 194, 197, 199, 201-207, 209, 210, 221, 222, 237, 252 CIE 1960 ...... 206 CIE UCS ...... 201 CIELAB...... 46, 207 CIELUV...... 46, 207 cis- ...... 84, 229 colliculus ...... 9 color-rendering ...... 148 compensation...... 38, 73, 106, 134, 220, 232 computation ...... 9, 127, 167, 204, 250 computational...... 43, 62, 100, 133, 180, 218, 222, 241 cone fundamentals ...... 108, 109, 114, 116, 149, 162 confirmation...... 60, 106 continuum ...... 58, 240 critical color flicker ...... 159 critical flicker frequency ...... 116, 158, 159, 161 cross section...... 193 cross-section...... 62, 193 cut-in ...... 75, 192 dark adaptation...... 19, 20, 31, 47, 49, 69, 76, 123, 129, 153, 162, 169, 175, 184, 189 data base...... 25, 128, 135 database ...... 83, 95, 133, 194 decoder...... 125, 159, 184 DG ...... 165 Performance Descriptors 17- 275

diencephalon ...... 153 diode...... 61, 124, 126, 127, 225 disparity...... 48, 118, 219 Duplex Theory...... 20, 23 dynamic range ...... 4, 10, 11, 36, 54, 55, 74, 120, 128, 129, 135, 162, 165, 185, 186, 225 EOG...... 21 equilibrium ...... 80, 81 ERG...... 20, 21, 112, 165 evolution...... 2, 209, 249 expanded ...... 19, 40, 53, 143, 164, 191, 212, 223, 244, 251 external feedback...... 10, 242, 243 feedback...... 4, 9, 10, 41, 57, 75, 81, 121, 123, 124, 225, 238, 242, 243, 252, 255 feedforward ...... 200 flicker frequency ...... 28, 29, 51, 52, 108, 116, 154, 156-161 Fourier transform...... 22 free running ...... 27 Gaussian...... 22, 67, 68, 70, 113, 133, 136, 138, 164, 171, 255 genetics...... 47 Grassman’s Laws...... 16, 37, 38 half-amplitude ...... 70, 97, 105, 106, 111, 116, 147, 179, 185, 237 hole...... 111 homogeneous...... 89, 224 hydronium ...... 183 illusion ...... 15 internal feedback ...... 121, 123, 225, 238, 255 inverting...... 10 lateral geniculate ...... 104, 208 light adaptation...... 31, 48, 49, 69, 108, 109, 200 lips ...... 210 long term memory ...... 196 lookup table ...... 227 LOT ...... 23, 140 Maxwell’s Spot ...... 19, 52, 59, 171, 210 mesotopic . . 5, 11, 14, 28, 30, 36, 38, 41, 43, 44, 53-55, 58, 65, 69, 100, 120, 123, 125, 127, 164-167, 172-174, 176, 177, 181, 184, 185, 187, 207, 209, 214, 220, 224, 225, 227, 240, 245, 251-253 metamers ...... 16 midbrain...... 4 modulation ...... 6, 23, 57, 153, 157, 159, 184, 188, 209 narrow band...... 29, 66, 67, 112, 116, 141, 142, 150, 157, 198, 242 noise . 2, 6, 7, 11, 21, 23, 28, 31, 36, 37, 41, 54, 55, 67, 68, 73, 95, 119-121, 129, 135, 152, 162, 165-167, 172, 180- 185, 187, 189, 190, 192, 213, 214 P/D equation...... 175, 185, 189, 193 pain...... 11, 28, 187 parametric...... 61, 241 parietal lobe ...... 4 Pauli exclusion principle ...... 102 percept ...... 87 perceptual space...... 135, 162, 166, 196, 198, 202, 234, 236-239 perigeniculate...... 4 perigeniculate nucleus ...... 4 perimetry ...... 187, 188 poditic ...... 10 POS ...... 4, 35 Pretectum...... 9, 26, 35, 120, 212 probabilistic ...... 28, 29 protocol . . . 19, 52, 58, 71, 87, 101, 104, 106, 111, 112, 116, 119, 127, 140, 149, 150, 153, 154, 156-158, 165, 172, 219 pulvinar ...... 4 quantum-mechanical ...... 142, 192, 251, 253 reading...... 4, 49, 64, 131, 142, 148, 195, 198 resonance...... 123 rod intrusion...... 47-49, 147, 148, 174 saliency map...... 4, 196, 227 276 Processes in Biological Vision

segregation...... 255 servo loop...... 35 servomechanism...... 30, 35 signal-to-noise ...... 152 signal-to-noise ratio...... 152 spectral colors...... 141, 205, 225, 237 square law ...... 11, 37, 38, 43, 68, 69, 86 square-law ...... 15, 44, 142, 145, 150-152, 162, 166, 176, 184, 207, 211, 213, 214, 216, 219, 220, 225, 252, 253 sRGB ...... 242 stage 0 ...... 30, 152 stage 1 ...... 30, 40, 121, 157, 190 stage 2 ...... 31, 32, 37, 40, 157, 159, 226 stage 3 ...... 37, 40, 50, 52, 58, 62, 106, 139, 157, 159, 161, 226, 227 stage 4 ...... 37, 153, 157, 159 stage 5 ...... 40 stage B...... 84 Standard Observer ...... 1, 17, 39, 40, 46, 53, 118, 129, 130, 133, 141, 146, 167, 168, 202, 205, 222 stellate ...... 32, 106, 166, 167, 214, 226, 227 Stiles-Crawford ...... 89, 165, 172 stress...... 46, 141, 168, 208, 225 superior colliculus ...... 9 synapse...... 124 syndrome ...... 5, 28, 247, 251 tetrahedron...... 226 thalamic reticular nucleus...... 4 thalamus...... 4 threshold . . . 5, 7, 8, 23, 28, 29, 31, 40-43, 46, 49, 54-56, 58, 59, 63, 67, 68, 71, 72, 80, 83, 86, 95, 98, 104, 106-108, 111, 116-119, 121, 124, 133, 135, 139, 140, 153, 155-157, 162, 166-168, 173, 179-190, 192, 208, 212-215, 219, 221, 222, 227, 245, 252 topography ...... 21 topology ...... 21, 124, 247 transcendental functions...... 201 transduction ...... 32, 47, 54, 106, 176 translation...... 65, 86 trans-...... 29 tremor...... 7, 24, 25, 27, 56, 57, 60, 219-221 verification...... 81, 83, 208 visual cortex...... 70, 127, 209, 240, 256 vitamin A1...... 46, 144 vitamin A2...... 144 xxx....73, 77, 78, 81, 82, 95, 104, 106, 110, 143, 147, 148, 154, 155, 158, 159, 163, 189, 192, 193, 203, 207, 208, 210, 239, 257 [xxx . . 1, 1, 41, 48, 50, 65, 68, 78, 79, 81, 87, 116, 122, 130, 140, 142, 146, 153, 158, 165, 183, 190, 193, 203, 230, 253, 256

(Inactive) DEFINITIONS INDEX (Use individual marks) Principle of Univariance Retinal illuminance Transport delay net photoreceptor