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C:\Vision\17Performance Pt 2.Wpd 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 2001 James T. Fulton Performance Descriptors, Pt II, 17- 1 17 Performance descriptors of Vision1 PART II: TEMPORAL & SPATIAL PERFORMANCE 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. [Author] Any comments are welcome. It will eventually include an evaluation of the bandwidth of the luminance and chrominance channels in support of the chapter on the tertiary circuits, Chapter 14, including the work of de Lange Dzn and Stockman, MacLeod & Lebrun in Section 17.6.6.5. 17.5 The Temporal Characteristic of the human eye The overall temporal characteristics of animal vision are difficult to quantify. It is frequently easier to perform experiments in either the transient or the steady state domain. To arrive at a unified mathematical model, it is necessary to analyze both classes of data and make the necessary mathematical manipulations to bring all of the data into a single domain. After a general discussion of background material, the main discussion will be separated into a transient section and a frequency response section in order to show how the model correlates with the data from various earlier investigators. A separate discussion of signal delay will be found in Section 17.6.5. The temporal asymmetries of the visual system result in a variety of Effects. These effects can frequently be associated with a specific temporal time constant of the visual system. Many of these effects are infrequently observed. As a result, their description in the technical literature has been spotty and frequently imprecise. An unusual facet of the literature concerning temporal characteristic of the human eye is that there is virtually no data on light adaptation of the eye, only on dark adaptation. A complete understanding of the temporal performance necessarily involves both sections of the overall temporal performance. Admittedly, the experiments of light adaptation are more difficult, especially for the subject. Poot, Snippe & van Hateren have recently provided new data recognizing the duality of this problem2. 17.5.1 Background No discussion was found in the recent literature of the immense range of time intervals that play a significant role in the visual process. The initial photoexcitation process has recently been shown to require less than 200 femto- seconds. On the other hand, subjects with diseases related to night blindness exhibit dark adaptation time constants of over 20 minutes. In between, there are significant processes related to the overall photoexcitation/de-excitation process with variable time constants of between 100 and 400 milliseconds, processes related to light adaptation with variable time constants of about XXX, and processes related to the iris and with dark adaptation with time constants of a few seconds. A full theoretical discussion of vision should address all of these parameters. 17.5.1.1 Other Investigations There has been considerable experimental activity with regard to the temporal performance of the human eye. However, it has been primarily exploratory and not always accompanied by careful analytical analysis consistent with an adequate model of the processes involved. This lack of a model has been due primarily to the state of the art in electronics and cytology at the time. Most of the activity falls into two independent categories. First, the exposition of the dark adaptation portion of the overall adaptation characteristic of the eye without accompanying 1Released April 30, 2017 2Poot, L. Snippe, H. & van Hateren, J. (1997) Dynamics of adaptation at high luminances J. Opt. Soc. Am. A vol. 14, no. 9, pp. 2499-2508 2 Processes in Biological Vision analysis. Second, a variety of experiments to determine the temporal bandwidth of the eye. This latter activity has in turn, suffered from two related problems. The various methods available to determine the temporal frequency characteristics have provided conflicting results, even when only one investigator was involved with several methods3. And, as expected, their conflicting results are due primarily to differences in assumptions concerning what they are measuring. None of these experimental methods have been implemented based on an adequate model of the system being evaluated. Most investigators have employed psychophysical experiments in which a linear model of the visual system is assumed in order to evaluate the results of their experiments. This linear model has been a single thread model. Many of the investigators have relied on “white light” illumination. The definition of the light used is normally shown by a single English word within quotation marks. This practice provides an indication of the precision employed in the work. In those experiments involving color, the investigators have generally not chosen illumination sources that only excited one of the chromatic channels of the vision process at a time. This use of illuminants that straddle the chromophoric absorption channels of vision has led to cross-talk in the signal processing that was not adequately anticipated nor recognized by the investigators. In fact, they have frequently relied upon the Principle of Superposition during the interpretation of their data without recognizing there is a chromatically selective subtraction process incorporated in the signal processing system of the retina. Most of these methods involve quite complex interactions with the visual system of the subject as seen from the overall block diagram. This is especially true where a transform is employed to convert a spatial stimulus into a temporal stimulus. These spatial techniques may employ edges, moving edges and patterns. All of the spatial techniques require a detailed knowledge of the optical system, mosaic characteristic of the retina and electrical circuits of the subjects visual system if accurate results are to be obtained. 17.5.1.1.1 Review of papers of Hecht and associates, pre-1940 The majority of the comprehensive experiments performed with respect to the transient performance of the eye are quite old. Most were performed and reported in the late 1930's by Hecht and his associates and graduate students at Columbia University. Their approach can be described as primarily exploratory as opposed to confirmatory since they relied upon no theoretical model other than the anecdotal functional relationship correlating with the putative physiological difference between rods and cones. Their instrumentation was typical of the time, pre-electronic revolution, and their interpretation was heavily dependent on the assumption of two separate photodetection mechanisms. Hecht was a leading proponent of the Duplex Theory based on functionally distinct rods and cones. Their experimental design was also typical of the time. No tight definition of the “white light” used or the spectral distribution of other lights employed. A few of their graphs, particularly figure 5 of 1937, have been redrawn in this work, based on their tabulations, to more clearly display the data points they relied upon in their discussion. While one might argue whether their instrumentation supports the three digit precision of their data, it appears there are systematic trends in the data not supported by either one or two monotonic functions. As stated in their original papers, the repeatability of their data was influenced by the 0.3 log unit day to day variation in the performance of a given subject, and they frequently made piecewise adjustments in their graphics to provide a more comprehensible presentation. Reference to this characteristic has never been found in a subsequent discussion of their work or republication of their graphs. A major problem with many of their findings was the dependence on data from only one subject. In the paper with Handelbaum4, sufficient subjects were tested to provide statistical relevance. However, statistical analysis frequently obscures systemic features. Artificial loci were drawn on the published data to encompass the data points (based on the rod/cone premise) instead of showing the actual error bars. They frequently selected the data of one subject for presentation and to press their point. The paper contains a good bibliography and analysis of the work of others during this time period. There is a significant mathematical problem in finding an equation to represent the conventional description of the dark adaptation characteristic as consisting of two first order mathematical, nominally exponential functions representing a rod and a cone component. Both the product of two exponentials and the sum of two exponentials still look like a single exponential. No “break” is seen in the resulting function. Alternately, a 3Wyszecki Stiles, Op. cit. Pg 567 4Hecht, S. & Mandelbaum, J. (1939) The relation between vitamin A and dark adaptation. Jour. A. M. A., vol. 112, no. 19, pp. 1910-1916 Performance Descriptors, Pt II, 17- 3 second order system is described by a “damped sinusoid” that, while continuous, does exhibit periodic slope reversals as can be seen in the typical dark adaptation characteristic. Hecht stressed precision and repeatability in his test instrumentation and listed six important parameters requiring control; (1) the illumination intensity and (2) the duration of the light present before dark adaptation begins, and (3) the area illuminated, (4) the retinal location, (5) the color and (6) the duration of the probe illumination. This work would suggest that their specification of (1) and (5) were inadequate in specifying spectral content adequately. Overlooking Hecht’s role as a primary proponent of the Duplex Theory during his day, the data in Hecht & Mandelbaum can be interpreted quite differently based on the more detailed foundation provided by this work.
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