E. Gorbunova, A. Chertov
COLORIMETRY OF RADIATION SOURCES
St. Petersburg 2016
THE MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION
ITMO UNIVERSITY
E. Gorbunova, A. Chertov
COLORIMETRY OF RADIATION SOURCES
TEXTBOOK
St. Petersburg 2016
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E. Gorbunova, A. Chertov Colorimetry of radiation sources. Textbook. – SPb: ITMO University, 2016. – 124 pages
Theoretical framework and calculation methodology for tristimulus values and source radiation chromaticity coordinates are given. General outline of vision physiological basis is also presented. In addition, colorimetry basic terms and definitions as well as principles of color space construction are given. Besides, rules for color temperature (and correlated color temperature) calculation and calculation of color rendering index for the radiation source are given.
The textbook is intended for students majoring for a Master's degree 12.04.02 - "Optical Engineering". Recommended for publication by the Academic Board of the Laser and Light Engineering Department, Minutes No. 13 of December 13, 2016.
ITMO University is the leading Russian university in the field of information and photonic technologies, one of the few Russian universities with the status of the national research university granted in 2009. Since 2013 ITMO University has been a participant of the Russian universities' competitiveness raising program among the world's leading academic centers known as "5-100". Objective of ITMO University is the establishment of a world-class research university being entrepreneurial in nature, oriented at the internationalization of all fields of activity. ITMO University, 2016 E. Gorbunova, A. Chertov, 2016
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CONTENT
ABBREVIATIONS ...... 5 DESIGNATIONS ...... 6 1 COLOR PERCEPTION ...... 9 1.1 Constitution of the human visual apparatus ...... 9 1.2 The mechanism of light and color sensation ...... 15 1.3 Eye movements ...... 19 1.4 Adaptation of visual perception ...... 23 2 COLOR – CONCEPTS, DEFINITIONS AND PROPERTIES ...... 27 3 COLOR REPRESENTATION AND COLOR REPRODUCTION SYSTEMS (COLOR SPACES) ...... 35 3.1 Methods for color mixing ...... 35 3.2 Grassmann's Laws ...... 37 3.3 Properties of color spaces ...... 39 3.4 Color measurement systems ...... 40 4 PROPERTIES OF RADIATION SOURCES (ENERGETIC, SPECTRAL AND SPATIAL) ...... 46 4.1 Basic values and units of measurement ...... 46 4.2 Emitting diodes characteristics ...... 49 5 CALCULATION OF COLOR COORDINATES FROM THE SPECTRAL PROPERTIES OF RADIATION SOURCES ...... 56 6 COLOR TEMPERATURE CONCEPT ...... 64 7 RECALCULATION OF COLOR COORDINATES ...... 71 7.1 Calculation of color coordinates in CIE 2003 color space L*a*b* ...... 71 7.2 Color coordinates calculation in the CIE 1976 color space L*u*v* ..... 72 7.3 Color coordinates calculation in the CIE 1976 color space CIE LCH ...... 73 7.4 Conversion from XYZ color space into RGB color space ...... 75 8 DETERMINATION OF SMALL COLOR DIFFERENCES ...... 80 9 COLOR RENDERING INDICES OF RADIATION SOURCES ...... 86 9.1 Colour rendering index for radiation sources located on the Planck's curve ...... 89 9.2 Calculation of the colour rendering index for radiation sources located outside the Planck's curve ...... 91 10 MODELING OF RADIATION SOURCES WITH PREDEFINED CHROMATICITY ...... 95 LITERATURE REFERENCES ...... 101 APPENDICES ...... 103
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ABBREVIATIONS
CCT – correlated color temperature. CIE – International Commission on Illumination (Commission Internationale de l´Eclairage). CT – color temperature. ED – emitting diode. IR – infrared. L cones – visual receptor retina cells containing Rhodopsin 5 erithrolab pigment (photosensitive in the red spectral range). M cones – visual receptor retina cells containing Rhodopsin 7 chlorolab pigment (photosensitive in the green spectral range). S cones – visual receptor retina cells containing Rhodopsin 9 cyanolab pigment (photosensitive in the blue spectral range). UV – ultraviolet.
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DESIGNATIONS
A type source is a source with the relative spectral energy distribution in the visible portion of spectrum relevant to the radiation of a black body at the temperature equal to 2856°K (GOST 7721-89). A is the color. B type source is a source with the relative spectral energy distribution in the visible portion of spectrum relevant to the radiation of a black body at the temperature equal to 4874°K. It reproduces the conditions of direct solar lighting (GOST 7721-89). c is the speed of light in vacuum (3 108 m/s). C type source is a source with the relative spectral energy distribution in the visible portion of spectrum relevant to the radiation of a black body at the temperature equal to 6774°К. It reproduces the lighting conditions with diffused daylight (GOST 7721-89). CRI is complete color rendering index.
CRIi is particulate color rendering index. d is the distance from the point characterizing the radiation source under study to the nearest isothermal line on the CIE 1976 color diagram.
D65 type source is a source with the relative spectral energy distribution in the visible portion of spectrum relevant to the radiation of a black body at the temperature equal to 6504°K. It reproduces the lighting conditions with average daylight (GOST 7721-89). E is the illuminance. E is the color of a white surface illuminated with E type source. E type source is a source with the constant spectral radiant intensity in the visible portion of spectrum.
fQB is the distribution of carriers in the allowed bands of a nongenerated semiconductor. h is Planck's constant (h 6,6262 1034 J·s). h is photon energy. I is radiation intensity (luminous intensity). K is the weighting factor.
Km is maximum spectral luminous efficacy of radiation at 0,555µm
( Km 683lm/W). k is Boltzmann's constant (k 1,38067 1023 J/K).
kc is the multiplier.
kv is the quasi-wave vector. L is brightness. M is luminosity.
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M () is spectral luminosity distribution of the radiation source. me is effective electron mass. mh is effective hole mass. mr is reduced mass.
nair is air refractive index.
ns is semiconductor refractive index.
P () is distribution of source spectral radiant density according to the wave length.
P max is maximum distribution of source spectral radiant density. Q is energy.
QC is conduction band extremum energy.
QE is electron energy in the conduction band.
Qg is bandgap energy.
QH is hole energy in the valence band. Q is valence band extremum energy. V RGB is the three-color system utilizing three major colors R , G and B .
Ri () is radiation reflectivity spectral distribution of the i -th surface. r is the radius.
r0 () , g0 () , b0 () are color match physiological curves. (,)rf are chromaticity coordinates for color space Lu v characterizing adaptive colorimetric shift of coordinates (,)uv when using the illumination source under consideration. T is temperature in Kelvin degrees. t is the tangent of the isothermal line inclination.
Tc is the color temperature of the radiation source.
Tc is correlated the color temperature of the radiation source.
ts is the time. u , v are chromaticity coordinates on the CIE 1976 color diagram. V is the relative curve of eye visibility (relative spectral luminous efficiency of monochromatic radiation). x , y are chromaticity coordinates on the CIE 1931 color diagram. x , y , z are color coordinates of XYZ color space. x() , y() , z () are color match curves in XYZ color measurement system.
xWWW,, y z are color coordinates of a white light source in XYZ color space. is the three-color system utilizing three major colors X , Y and Z . 7
c is the limiting angle of total internal reflection. is the wavelength.
begin is the wavelength for the "beginning" of the spectral distribution.
dom is the dominant wavelength.
end is the wavelength for the "end" of the spectral distribution.
max is the wavelength for the maximum spectral distribution. Q is the energy-dependent combined density of energy states. is the flux. is the solid angle.
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1 COLOR PERCEPTION According to the definition [1], color is an affine tridimensional vector variable manifesting the quality common for all the radiation spectra which are visually indistinguishable under colorimetric observation conditions. The term "radiation" wherein should also be understood as the light which is reflected and permitted through by nonluminous bodies. Thus, the very concept of "color" is applicable exclusively to human visual apparatus. 1.1 Constitution of the human visual apparatus The eye is the main element of visual apparatus. In fact, it is a complex biological system of forming the image of the ambient environment [2, 3, 4]. Figure 1.1 shows the composition of the right eye-bulb.
Figure 1.1 – Internal composition of the human eye
Externally, the eye-bulb is covered with a nontransparent cover called sclera. It contains a small number of nerve endings and blood vessels. Six muscles allowing the eye movements are attached to the sclera. The whole sclera surface is nontransparent beside a small front area called cornea which is slightly convex. The cornea is highly transparent and transmits light to the aqueous chamber of the eye. The aqueous chamber is filled with a transparent liquid – aqueous humour. From the opposite side the aqueous chamber is limited with a nontransparent partition called iris which determines the color of the human eyes. There is a circular opening in the center of the iris which is called the pupil.
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The posterior chamber of eye is located behind the iris. The crystalline lens which is a "natural" lens of the eye is located in the front part of the posterior chamber. Normally, it is transparent and elastic and has the lamellar structure. The crystalline lens may be modified by ciliary muscles contraction (it may change its shape, almost instantaneously "bridging the image into focus") due to which a person has clear vision at both close and far distance. The main part of the eye posterior chamber if filled with a transparent tremellose (gelatinous) substance – the vitreous body. It maintains the shape of the eye-bulb and is involved in the intraocular metabolism. The choroid covers the back of the sclera; it is adjoined by the retina closely attached to it. The choroid is responsible for the blood supply of intraocular structures. It has no nerve endings, therefore no pains signalling any problems arise in case of its disease. The retina consists of photoreceptors which are sensitive to radiation in the visible spectrum range, and nerve cells. The receptor cells (or photosensitive cells) located in the retina are divided into two types: rods and cones. Light energy conversion into the electric energy of the nervous tissue takes place in these photosensitive cells. The rods are highly sensitive to light; they allow vision in poor lighting and are also responsible for peripheral vision. Vice versa, the cones require more light for their functioning, but they allow us to see small details (they are responsible for central vision) and make it possible to distinguish between colors. The largest cluster of cones is located in the macula (or the foveola), responsible for the highest visual acuity. The blind spot is an area of the retina where the nerve fibers coming from the receptors are collected and the optic nerve is formed. The position of the blind spot of the right eye does not coincide with the position of the blind spot of the left eye, so a person does not notice them. Retinal composition. Retina (Fig. 1.2) is a complex biological tissue consisting of several layers and having an extraordinary large number of nerve cells. Light penetrates the retina through the layers of neurons, nerve cells and nerve endings and strikes upon the real light sensors attached to the pigment epithelium – the rods and cones. It should be noted that the retina is not simply a layer of light-sensitive cells (rods and cones), it also accommodates a visual data pretreatment system (horizontal, bipolar, amacrine and ganglion cells), and the system for the recovery of light-sensitive cells after their light-striking (pigment epithelium). It should be noted that the number of synaptic connections of retinal cells can vary substantially from 20 to 40,000. Due to this variability of cell connections a kind of image compression takes place, allowing the transmittion to the brain only the required data concerning the image elements of the visible objects. Retinal visual receptor cells – rods and cones (Fig. 1.3). All these cells contain pigments that are sensitive to light. These pigments convert photons of light striking upon the cells in the electric signals. These signals are transmitted via the synaptic connections of the cells, first bipolar cells, then ganglion ones. 10
Then they are passed with the help of the axons to the optic nerve and the cerebral cortex.
Figure 1.2 – Retinal composition
Rods are visual receptor cells of the retina responsible for the twilight or night vision. Their number in the retina exceeds 120 million. The spectral sensitivity characteristics of the rods achieves maximum at the wavelength of about 495 nm. The rods have the ability to slow but effective adaptation to brightness changes. It should be noted that the sensitivity of the rods in the darkness is such that even a single quantum of light can cause the measurable signal. However, in order for the visual apparatus to be able to perceive light, at least 7 rods need to be activated. Cones are visual receptor cells of the retina responsible for color vision. Their number in the retina exceeds 6 million. They also play a big role in the spatial resolution of the eye. The cones have the ability to fast but weak adaptation to brightness changes. To obtain a measurable signal in the cone about one hundred photons are required. However, the reaction of the cone (approx. 70 ms) is 4 times faster than the reaction of the rod (approx. 300 ms). Cones themselves are divided into three groups that are sensitive to different spectral regions: red (L), green (M) and blue (S). Some women have demonstrated to possess the fourth kind of cones. Visual receptor cells are arranged in a mosaic-like structure similar to the mosaic of a bee hive (Fig. 1.13), and different people have a different structure of this mosaic. Most people have approximately 65% of the red cones, 35% of the green cones and only 4% to 2% of the blue cones. Besides, the blue cones are 11 completely absent in the center of the macula. On the other hand, the size of the cones in the macula is much larger than the size of the cone cells at the periphery, thus their light signal perceptive ability is higher.
Figure 1.3 – Visual receptor cells
If one cuts the retina of the right eye horizontally with the plane passing through the macula and the optic nerve, it is possible to trace the change in concentration of the visual receptor cells (Fig. 1.4).
Figure 1.4 – Location of receptors 12
Fig. 1.4 demonstrates that the cones are generally concentrated in the central area of the retina, and the rods are distributed simmetrically to the center. As mentioned above, in the center of the retina there is the macula having a diameter of about 3 mm and characterized by a small deepening in the center. It should be noted that the macula allows one to see the zone of no more than 14 degrees. Outside of this zone, the eye perceives practically no colors and the visual clarity is low. When a person continuously looks at the ambient world, it is the brain that continually reproduces the image of the world across the whole field of vision. In the central zone of the macula the largest number of cones is located. The number of cones increases from the center to the edge of the macula. In the very center of the macula the density of cones is about 160 thousand units per square millimeter, but there are absolutely no rods. The central part of the macula – foveola – is located here. It forms the zone of most acute vision. Angular field of the foveola does not exceed 2 degrees.
Figure 1.5 – Reaction of the neuron
The perception of visual information is based on a contradiction: on the one hand, there is a very large amount of information available; on the other hand, this information must be processed in the most efficient manner. Therefore, there are a lot more visual receptor cells in the retina than transmitting nerve fibers in the
13 optic nerve: more than 160 million rods and cones per approx. 1 million axons. Visual receptor cells, particularly rods, can "cluster" just as it is done when compressing images. It should be noted that neuromechanisms responding to special "image patterns" with various temporal and spatial characteristics have been found in the retina [4]. The eye distinguishes the movement, change of lighting and other properties of visual objects and sends them to the relevant brain areas using the minimum number of nerve fibers. Fig. 1.5 demonstrates the electric activity of a single nerve fiber which occurs in response to the change in the visual stimulus. Thus, multiple visual receptor cells can be attached to a single bipolar cell (Fig. 1.2). At the same time the number of "united" visual receptor cells can vary. For example, on the periphery of the retina it is possible to find up to 70 rods per one ganglion cell. Thus the sensitivity of the receptor increases at the expense of resolution. It should be noted that the peripheral vision is also sensitive to the perception of motion, although forms recognition remains unclear. Peripheral vision represents a zone of vigilance and anxiety.
Figure 1.6 – The principle of imaging by the human visual apparatus
Based on the above, the the structure of the human visual apparatus is such that prior to the visual signal getting to the brain there is its certain preprocessing (Fig. 1.6). This processing can be divided into several stages: colorimetric correction and compression. Colorimetric correction is necessary to reduce the effects of uneven distribution of the sensitive retinal elements (rods and cones),
14 and compression is caused by the fact that the number of fibers in the optic nerve is significantly lower than the number of visual receptor cells of the retina. The fibers of the optic nerve transmit the converted optical signal to the brain where it is interpreted and the person can see the color of the object, assume its shape, defects, spatial orientation, as well as character and direction of its movement, etc. 1.2 The mechanism of light and color sensation Biophysical nature of vision is based on the interaction of individual molecules (retinoids) with radiation. These molecules are derivatives of retinol (vitamin A1), which is responsible for the yellow-orange coloring of the retina. There is only one type of retinoids in the rods – rhodopsin, whereas cones contain many types. In general, there are more than twelve [5] different types, but there are four of them, especially prominent in the cones. These are rhodopsins 5, 7 and 9 (Table 1.1), as well as the substance sensitive to ultraviolet waves – rhodopsin 11 [6]. However, it should be noted that the cornea, aqueous humour, crystalline lens and vitreous body absorb most of the ultraviolet radiation (UV). The red, green and blue cones contain a mixture of all these retinoids but each type of cones has a larger concentration of one retinoid type, its proportion being 1000 times more significant than of all the others. In rods and cones cells there are thousands of membrane discs formed by the plasma membrane folds, long chains of retinoid molecules being attached to them (Fig. 1.3). Thus, a real fractal space to capture light is formed. Table 1.1 – Absorption parameters of some retinoids Spectral absorption Pigment begin , nm max , nm end , nm Rhodopsin 5 (erithrolab) 595 625 655 Rhodopsin 7 (chlorolab) 500 532 565 Rhodopsin 9 (cyanolab) 400 437 475 Rhodopsin 11 (sensitive to UV) 300 432 385 From the point of view of physics, all the considered molecules are similar to each other. They consist of seven long chains of opsin surrounding a small but particular molecule – 11-cis-retinal (Fig. 1.7). When a photon collides with such a molecule, there is a 50% probability that it [the molecule] will "unfold" and turn into isomer – trans-retinal. In the dark, 11-cis-retinal is tightly bound to the protein opsin. Capture of the photon causes isomerization of 11-cis-retinal into trans-retinal. During this process, opsin-trans-retinal is sufficiently quickly dissociated through several chemical reactions into opsin and trans-retinal [3]. Rhodopsin regeneration depends on the interaction of the pigment epithelium cells and the visual receptor cells. In case of eye-blinding, rhodopsin is recovered from the visual purple, that is, from retinoids of the pigment epithelium. 15
Figure 1.7 – Concerning the explanation of a photochemical reaction
This phenomenon forms the basis of the neuro-information. In the dark, there is a constant "dark current" in the outer segments of visual receptor cells (Fig. 1.3) [7]. As a result, constant membrane potential of visual receptor cells is approximately -40 mV. Inward current is transmitted in the dark mainly by sodium ions along the electrochemical gradient through cationic channels of the external segment of visual receptor cells. Cationic channels are closed under the influence of light. Thus, the value of the membrane potential is shifted to the value of the equilibrium potassium potential which is approximately -80 mV. Accordingly, there appear conditions for the emergence and transmission of optic signal along the axons of the neuro cells. Special spectral absorption of opsin molecules explains the spectral sensitivity of the cones, i.e. the basis of spectral sensitivity of the eye in case of night vision. Some studies of biophysical nature of vision (mainly, studies in the sphere of signals transmitted from bipolar cells through ganglion cells to the geniculate body of the brain) suggest that transmission of signals from sensory cells can occur in the following three ways (Fig. 1.8 a). – Achromatic channel, based on the opposition of the red-and-green signal and the total absence of signal; – Red-and-green channel, based on the opposition of signals received from the red and green cones; – Blue-and-yellow channel, based on the opposition of the red-and-green signal and the signal from the blue cones. This idea was first put forward by Ewald Hering (1834-1918). Hering challenged the theory by Hermann von Helmholtz about three types of visual receptor cells transmitting three specific types of signals. Hering's theory is supported by studies of retinal composition evolution in mammals and anthropoid apes (Fig. 1.8 b). Under the current theory of evolution, the divergence of blue and green cones occurred about 300-500 million years ago. Separation of red and green cones occurred much later, about 30-40 million years ago. Thus, the 16 structure of color perception signals can be logically deduced from the represented theoretical data.
Figure 1.8 – Evolution and structure of color perception
Maximum spectral sensitivity of cones for the so-called "standard observer" is 565 nm for the red cones, 540 nm for the green cones and 440 nm for the blue cones (Fig. 1.9), although various authors demonstrate different opinions and there are also differences in individuals under observation concerning this issue. It should be noted that the sensitivity of cones reaches its maximum at 495 nm which is right in the middle between blue and green cones.
Figure 1.9 – Sensitivity of visual receptor cells of the eye
Based on the absorption spectra analysis of visual receptor cells retinoids it is hard to escape the first conclusion: spectral sensitivity of red and green cones is quite close. In reality red cones have the maximum sensitivity to yellow color. 17
Therefore, they should rather be called yellow cones. However, mathematically and logically it is very difficult to develop a system of tricolor reproduction of the color image based on precise values of the cones sensitivity, as in this case the color space covered is too limited. Therefore, the International Commission on Illumination (CIE) adopted red, blue and green as the primary colors of the spectrum, the eye sensitivity peaks for these colors falling at 605 nm, 545 nm and 445 nm, respectively. In addition, the spectral sensitivity of the cones should be limited by the absorption of the yellow color with the macula. One should note the nonlinearity of brightness display of perceived radiation by the visual apparatus (Fig. 1.10) [2].
Figure 1.10 – Brightness perception
If one considers the graphs of spectral sensitivity of the red and green cones, it can be concluded that the feeling of saturated red color can be obtained only if the red cones transmit the color signal and the green cones – do not. The reverse assertion about the perception of the saturated green color is also obvious. Both systems work in opposition, otherwise it would be impossible to accurately distinguish colors in the range from green to red. By measuring the monochromatic radiation colors with subsequent energy normalization with the colorimeter color matching functions were obtained. These functions are set by the tables and represented graphically in the form of the so-called color match curves [8]. Fig. 1.11 represents the physiological color match curves r0 () , g0 () , b0 () for the system of the basic spectral colors 445, 545 and 605 nm. It should be noted that the normalization of the color match curves ordinates is made in view of the fact that the squares under the curves must be equal to each other.
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Figure 1.11 – Color match curves
Visual apparatus perception properties are such that the eye can be considered an ideal null meter, i.e. one can state, using it, with the maximum degree of confidence that the colors are different (or the same) under the given observation conditions, but it is impossible to accurately determine the divergence between the colors in case they are different (Fig. 1.12 а).
Figure 1.12 – Peculiarities of color perception
Besides, a person is unable to see more than seven color shades at the same time, that is why we see only seven colors in a rainbow (Fig. 1.12 b). If one takes a piece of a rainbow and looks at it, the eye will distinguish seven more various color shades – and this can continue for a very long time until the physiological threshold of color shade distinction is reached. 1.3 Eye movements The visual apparatus is capable of receiving the image not only due to the ability to perceive photons by visual receptor retina cells but also due to the constant eye movements – saccades (Fig. 1.13 a), microsaccades (Fig. 1.13 b), drift (Fig. 1.13 c) and tremor (Fig. 1.13 d). These movements are caused by the contraction of the six extraocular muscles attached to its outer surface. 19
When a person is reading, his/her eyes move rapidly from left to right in small jerks, so every next word consistently turns out to be in the focus of the image. After a bit of observing ourselves, we can perceive frequent contractions of extraocular muscles. Each fraction of a second they slightly shift the position of your eyeball automatically, without conscious effort on your part. Saccades (greater random eye movements) are very fast jerk-like movements which occur several times per second and are used by the eyes in such scanning motions as reading or examining an object (Fig. 1.13 a). Eyes synchronously leap from one small element of an object to another. At the moment when the saccades happen, vision is blurred, so that it stops between the leaps which gives the eye-brain system time to decipher the printed letters (to make meaningful phrases) or to recognize and remember the element of the object under examination.
Figure 1.13 – Eye movements
Saccades make only a small part of the physical workload on the extraocular muscles. Eyes never stop, even when the gaze is fixed. If it were possible to stop the eye movements at the moment of the gaze fixation, the static scene would simply cease to be perceived. Oddly enough, scientists have only recently begun to realize the great importance of the so-called fixative eye movements. The largest of these involuntary movements are microsaccades moving the image on the retina for 20 the width from tens to hundreds of visual receptor cells. However, without these tiny movements the eye does not perceive stationary objects [9]. The most important factor in determining the evolution of the nervous system of animals was the need to detect changes in the environment, as this ability ensures survival. Movement within the field of view may signal that a predator is approaching or the prey is escaping, causing visual neurons to respond with electrochemical impulses. Stationary objects usually do not carry any threat, so originally the brain of animals and their visual system were not intended to notice them. For example, a fly sitting motionless is invisible to the frog, like other static objects. However once the fly flies up, the frog will immediately notice and catch it. Frogs are incapable of seeing motionless objects as a constant stimulus leads to adaptation of neurons, which makes them gradually cease to react to the object. Adaptation of neurons saves energy but at the same time limits sensory perception. Human neurons also adapt with the invariability of the stimulus. However, our visual system copes much better with the perception of fixed objects, because the eyes create their own movements. Microsaccades move the entire visual scene on the retina, causing the visual neurons to work constantly, therefore counteracting adaptation (Fig. 1.14 a). Thus, they allow us to see motionless objects.
Figure 1.14 – Microsaccades and Troxler's test
One can test the microsaccades action with the help of Troxler's test 1 (Fig. 1.14 b). You must look at the red dot and watch the pale ring attentively.
1 In 1804, the Swiss philosopher Ignaz Troxler discovered that if one consciously fixates their gaze on something , the stationary surroundings of the fixation point will disappear.
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Soon, the ring will disappear, and you will only see the dot against the white background. Once you shift your gaze, the ring will appear again. Drift is a slow eye motion with a winding trajectory observed between rapid linear microsaccades. (Fig. 1.15 a).
Figure 1.15 – Drift and the black-and-white grid
There is a way of observing the effect of drift and saccades on the visual system. For this purpose it is necessary to look at the center of Figure 1.15 b attentively. Look at the black dot in the center of the image for a minute, then look at the white dot inside the black square. During this, you can see a light "blinking effect", which seems to be "bouncing", regardless of how strongly the observer tries to keep the eyes stationary. Note that the dark afterimage of the white cross lines is in continuous motion. This is due to the fixative eye movements. Tremors are the smallest eye movements overlapping the drift (Fig. 1.16 a). Tremors constantly and rapidly shake or rock the eyeball near its centre in a circular way, as well as make the cornea and retina of the eye rotate in a circular motion with an incredibly small diameter, approximately 0.001 millimeter. Tremor frequency is approximately 30 to 70 times per second. Although the tremors are not large enough to "see" them without magnification, without them, people would not be able to see. Consider, for example, what would happen if these and all other eye movements ceased while the observer was looking at someone's face. Along with this the retinal visual receptor cells are quickly "stabilized" and cease to transmit updated information to the observer's brain, resulting in the observed image disappearance within seconds, turning into monotonous gray background. If the person being watched by the observer smiled, his/her lips, and lips only, would instantly appear from visual emptiness (like the Cheshire Cat from "Alice in Wonderland").
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Thus, the constant change in the light that is reflected in every cell of the eye retina is extremely important to enable constant vision. Hence the need for tremors – without tremors a person would have to examine the object from different angles or constantly change its lighting to see the entire subject at once.
Figure 1.16 – Tremor and optical illusion
The tremor phenomenon can be observed due to various illusions of motion. If you let your eyes "wander" across the image (Fig. 1.16 b), you will soon see three "waves" rolling across it. However, if you fix the gaze at one of the spots in the center of the picture, the illusory motion will slow or even stop. 1.4 Adaptation of visual perception Human visual apparatus has an amazing feature – the invariance of color perception regarding the spectral composition of lighting in everyday conditions (i.e. color perception for most objects does not dependent on spectral composition of the lighting). This phenomenon is called color constancy. Besides, the human visual apparatus has the property of lightness constancy (lightness evaluation does not depend on absolute energy levels and is based on the comparison of reflection coefficients). Thanks to this property of vision, a person is able to assess a lump of coal as black and a piece of chalk as white under completely different lighting conditions. The lightness constancy is preserved when directly comparing coal and chalk, even if the absolute amount of light reflected from a piece of chalk at low levels of illumination is less than the amount of light reflected from coal at high levels of illumination. These properties of vision determine the capability of a person to see the world of stable color and brightness and not the unstable physical world with the constantly changing wavelength and the intensity of light reflected from the objects in the visual scene. The constancy is well preserved when observing an object with a textured surface in a complex visual scene containing other objects with relatively high
23 reflectivity. Then, assuming that the light source emits in a fairly wide range, many comparison reactions between the cells of the cerebral cortex associated with various retinal visual receptor cells become possible. Thus, the constancy is saved, even if the specter of lighting is intermittent or there is a mix of wavelength bands. However, under monochromatic lighting relationships of reactions tied to the color stimulus become distorted. Change in color perception is caused by the constancy distortion. This happens if there are noticeable changes in the spectral composition of radiation in the visual scene or if there are localized bright lights (for example, rays of sunlight penetrating the foliage in the square shaded by trees, or projectors for home or theatrical lighting). Then the correlation of the intensities of the reflected light with different wavelengths will not remain constant over the entire visual scene and there will be partial or total disruption of constancy. The fewer comparisons of the reflection coefficients for the wavelengths take place in the field of vision, the lower is the possibility for the visual apparatus to retain constancy. Similarly, the constancy is usually distorted when there are isolated objects observed against a black background. Constancy is violated in case of observing small objects, with minimal changes to the spectral reflection coefficient and surface texture. Moreover, there is a gradual distortion of constancy with a decrease of the visual field to a very small angular size, which represents the so-called "tunnel vision". Visual apparatus has a variety of mechanisms for the implementation of the "optimal" vision mode regardless of changes in lighting conditions or properties of the observed object – adaptation mechanisms. Adaptation can be local or global, in time and/or in space, to the brightness and/or color. Global adaptation is the total readjustment of the whole visual apparatus, for instance, on entering a dark room from a light space or, conversely, when leaving a dark entrance hall and going into a brightly sunlit street, etc. Local adaptation of the visual apparatus is presented by the changes in perception of the observed object or its certain area (Fig. 1.17). It must be borne in mind that adaptation mechanisms of the visual apparatus are always activated with the appearance of the contrast in brightness or color. At this, contrast can be simultaneous or sequential. The phenomenon of simultaneous contrast ir related to the opposition of brightness and color of closely located areas. Sequential contrast is due to the opposition of color and brightness parameters of the object in case of its observation for a certain period of time and at the moment of its disappearance.
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Figure 1.17 – Local adaptation to brightness, color, brightness and color
Spatial adaptation is based on the simultaneous contrast of colors. One and the same colour shade will seem different when observing it against different backgrounds. It should be noted that the spatial adaptation can be: – to brightness (Fig. 1.17 a) – the observed shade seems darker against a light background and lighter against a dark background (with unchanged color of the shade), – to color (Fig. 1.17 b) – the observed shade seems to have additional colority which is opposite to the background color (with unchanged color of the shade), or – simultaneously to brightness and color (Fig. 1.17 c) – the observed shade seems to have changed both the color and the brightness. Adaptation in time is caused by the speed of retinal visual receptor cells reaction to a light stimulus. Perception physiology peculiarities are such that the cones feature fast but limited adaptation, whereas the rods are characterized by the slower but higher adaptation [2]. The adaptation period for the cones is approximately 10 minutes (Fig. 1.18). Adaptation of the rods can last up to an hour and a half.
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Figure 1.18 – Adaptation curves of the visual receptor cells of the eye
Adaptation in time leads to the fact that on appearance of a strong light and/or color stimulus the visual apparatus perceives a sequential color contrast and, accordingly, the person sees an additional brightness and/or color dominant after the disappearance of the previous dominant.
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2 COLOR – CONCEPTS, DEFINITIONS AND PROPERTIES There are various interpretations of the word "color": – color as the property of the visual sensation is the two-dimensional qualitative characteristic of quantitative photometric values (CIE). – color is an affine tridimensional vector value manifesting the quality common for all the radiation spectra which are visually indistinguishable under colorimetric observation conditions (GOST) [1]. The term "radiation" should also be understood as the light which is reflected and permitted through by nonluminous bodies. From this point onwards the colors are indicated using symbols of vector values, e.g. color A. All colors as a combination of affine tridimensional vectors can be geometrically represented in the space which is called affine color space. It includes both real and unreal affine color vectors. Real colors are colors of any radiations which are physically achievable. Unreal colors are color vectors specified as linear combinations of the real color vectors, being such, however, that do not not have any correspondent real radiations. In order for the color to be "measured", the coordinate system is set in the color space using primary colors. Thus, primary colors are three conditionally selected linearly independent colors serving as single vectors of the coordinate system. This being said, the three-color system of color measurement is defined in the color space. This system is a set of three linearly independent primary colors through which any color A can be expressed using some vector equation. The specified equation is called the color equation. It must be borne in mind that the coefficients of the color equation can be either positive or negative, depending on the choice of primary colors. Wherein, color equity means that the colors are completely visually indistinguishable from each other under colorimetric observation conditions. Let us select any three linearly independent colors as primary colors of the measurement system, such as X , Y and Z , and depict them in space as three noncomplanar vectors (i.e. none of the vectors , and is coplanar with the other two). Thus, a three-color measurement system XYZ is defined. Wherein, the direction of the vectors in space can be chosen voluntarily, as well as their length. Then, any color A which can be measured in this system is represented as a diagonal of the parallelepiped formed by the three of its components (Fig. 2.1). Wherein, the lengths of the basic vectors , and play the role of measurement units, therefore, color itself can be represented as a color equation A xX yY zZ , (2.1) where x , y and z , being color equation coefficients, are called color coordinates of the predetermined color space XYZ. 27
Figure 2.1 – Vector representation of color
It should be emphasized that only one vector in the color space corresponds to each color, and colors arranged along one and the same ray going out of the reference point and differing in intensity only, are regarded as different colors from colorimetry positions. These colors according to Schrödinger [10] are called colors of the same type of stimulation . If the primary colors X , Y and Z are chosen in such a way that for the color of a white surface W illuminated with a light source of a predefined spectral composition color coordinates are equal to one ( x y z 1), then all the w w w colors of the reflecting grey objects will lie on the ray w (Fig. 2.2) connecting the point representing the white color with the reference point (black color). The color equation for determining the color of the grey reflecting objects is as follows: nW1 nxX 1w nyY 1 w nzZ 1 w , n1 1, (2.2) where n1 is a certain fraction with its value less than 1. If some color is expressed using the color equation nW2 nxX 2w nyY 2 w nzZ 2 w , n2 1, (2.3) where the fraction n2 is greater than 1, then this color is the neutral color of a self-luminous object, or in other words of the source of radiation. For convenience of representation of the example achromatic colors are given in shades of red on Fig. 2.2. In addition, grey colors are not the only colors of one type of stimulation, there are many such colors.
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Figure 2.2 – Colors of one type of stimulation
It should be noted that there is the notion of the ideally white surface in colorimetry, i.e. of a surface scattering the radiation of all wavelengths of the visible spectrum equally in all directions and without absorption. Besides, there is the notion of achromatic (grey) colors, i.e. a number if colors arranged in the color space on a straight line passing through the reference point and the color of a white surface under current lighting conditions [1]. If two colors result in an achromatic color after mixing they are called complementary colours. Colors of monochromatic radiations having various intensity in any system of real primary colors, e.g. R , G and B , have one or two negative coordinates and are located outside the pyramid built on the main measurement axes (Fig. 2.3). This happens even in color measurement systems based on saturated spectral colours as primary colors. Wherein, the colors of monochromatic radiations having various intensities form a conical surface of infinite length which is called the color cone. By definition, a color cone is a part of the color space representing the whole area of real colors, limited by a conical surface of infinite length (with the vertex at the reference point), representing the geometric locus of colors of monochromatic radiation. The conical shape of a real color space is defined by a purely experimental approach as a result of measurement of all really existing monochromatic colors of the visible spectrum. All other colors lying outside this cone are not perceptible to the eye – those are unreal colors. However, as will be demonstrated below,
29 unreal colors are used for the construction of color measurement systems, e.g. for the physiological system of eye receptors and for the international XYZ system. The color cone is limited by a plane including pure purple colors obtained as a result of mixing monochromatic red and blue colors lying at the ends of the spectrum.
Figure 2.3 – Spatial arrangement of colors
If two or several colors are mixed, the resulting color is represented as a vector with coordinates along the measurement axes present sums of the relevant coordinates of the colors being mixed. Then, the following is valid for the RGB color space A r R g G b B 1 1 1 1 NNNN A2 r 2 R g 2 G b 2 B A Ai R r i G g i B b i (2.4) i1 i 1 i 1 i 1 ANNNN r R g G b B where r , g and b are color coordinates in the RGB color space. The color cone of infinite length includes the colors of self-luminous objects (radiation sources: luminophors, lamps etc.), and the colors of reflecting 30 and transparent objects under predetermined lighting conditions occupy only a certain area within the color cone which is called the color solid. The geometrical shape of the color solid was given a strict mathematical definition by R. Luther and N. Nyuberg based on the analysis of colors with optimum reflection spectra (optimal colors). Optimal colors are colors of the color solids having the light transmission factor (or the light reflection factor) equal to 1 in the entire visible area of the transmission spectrum (reflection spectrum), and equal to 0 in the entire visible area of absorption spectrum, there being not more than two points of discontinuity (transmission leaps from 0 to 1). Optimum colors lie on the surface of the color solid, they determine the boundary beyond which no color with the actual transmission and reflection spectra can lie. It must be borne in mind that the shape of the color solid varies with the change of the spectral composition of the light source. The ratio of each of the color coordinates to their sum is called the chromaticity coordinates. For the RGB color space chromaticity coordinates r , g and b are calculated according to the formulas r g b r , g , b . (2.5) r g b r g b r g b However, the third chromaticity coordinate (in this case b ) is usually omitted as the dependent one, since the sum of the three chromaticity coordinates is always equal to one: r g b 1. A plane can be drawn through the ends of the unit vectors in the chosen color measurement system (Fig. 2.3). A part of this plane lying inside the triangle formed by the ends of the unit vectors presents the geometric locus of points characterizing the colors with positive chromaticity coordinates, and is called the color triangle. Wherein, the right-angled triangle with the legs being the chromaticity coordinates variation axes is called the chromaticity diagram. The intersection of the color cone surface with the plane of a color triangle forms the geometrical locus of points relevant to the chromaticity of pure spectral radiations. This geometrical locus is called the spectral radiations locus or the spectral locus. Let us take color space XYZ (Fig. 2.4) as an example. This figure demonstrates the tristimulus color space determined by the primary colors X , Y and Z . Additionally, it demonstrates the examples of colors A of monochromatic stimuli with different wavelengths. Wherein, the varying wavelength takes values from 400 nm to 700 nm which corresponds to the limits of the visible spectrum. The points of intersection of vectors A with the single plane taken together form a line consisting of the straight and the curved areas. This line is often called the line of pure spectral colors on the chromaticity diagram or the locus. The line of spectral colors starts at the wavelength value of
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400 nm and ends at 700 nm. Chromaticity points of stimuli A which we can obtain by mixing in various proportions the stimuli with the wavelengths 400 and 700 nm are located along the straight line connecting these points. This line is also called the purple boundary, as the purple stimuli are obtained by mixing blue and red stimuli.
Figure 2.4 – Construction of XYZ color space
If one considers the monochromatic stimuli of constant radiance at all wavelengths, then colors A of these stimuli will be depicted as a continuous combination of vectors with their ends forming a curve starting close to the reference point (0) for color 400 and ending in approximately the same position for color 700 in the tristimulus color space. Components of any of these vectors, naturally, represent the specific tristimulus values determined based on the condition of the equienergy character of the spectrum. The combination of pure spectral colors A and various additive mixtures of stimuli forms a cone containing colors A of any additive mixtures of monochromatic colors in the tristimulus color space. The surface of the cone is the boundary for all real colors. The colors lying outside the system gamut are often referred to as unreal colors. The system primary colors are unreal colors. In order to determine whether any given color is related to the real or unreal colors it will suffice to consider the position of its point on the color diagram. If a lies within the area limited by the lines of the spectral and purple 32
colors or coincides with any point of these lines then A is a real color. If not, represents an unreal color.
Figure 2.5 – Color solids of spaces L*u*v* (a) and L*a*b* (b)
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The coordinates of any real color will never take negative values, since all the cone of real colors is entirely located in the positive quadrant of the color space defined by the primary colors. Specific tristimulus values are a special type of color coordinates only inasmuch as they belong to monochromatic stimuli in the all visible spectrum. Relevant A colors are depicted as vectors directed along the generatric line of the cone and represent real colors. The color of the equienergy stimulus (achromatic colors) is depicted as a vector crossing the single plane in the center of the color triangle; its chromaticity coordinates are the same and equal to 1/3. This is a natural consequence of an arbitrary but a viable choice of unit values determining the scale on the axes of the primary colors. A similar normalization is usually made in any other tristimulus color space. One consequence of such normalization is that the squares under the curves of all the three color matching functions are identical. Fig. 2.5 represents color solids of the objects and radiations calculated for color spaces L u v and L a b .
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3 COLOR REPRESENTATION AND COLOR REPRODUCTION SYSTEMS (COLOR SPACES) All the color representation and color reproduction systems are based on the phenomenon of metamerism, when the radiations of different spectral composition seem visually indistinguishable. Therefore, there exists the possibility to determine the combination of the color equity of a certain color A and a combination of primary colors. Wherein, the color equity can be written in different ways – methods for color mixing. 3.1 Methods for color mixing Additive color mixing (from the Latin tem additio – addition) is based on the mixing (summation) of different radiations (Fig. 3.1).
Figure 3.1 – Additive color mixing Wherein, the color A in the additive color space, e.g., RGB, is expressed by the following color equation
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A rR gG bB, where r , g and b are color coordinates in the color space defining the proportions of the added emissions of colors R , G and B . Additive color mixing takes place in the following cases: – upon overlapping of light fluxes having various colors through their projection on a white screen (optical mixing); – in the case of the rapid rotation of color sectors on a peg top or a whizzer, as Maxwell did in his experiments (colors are mixed because the eye does not have time to distinguish between color flashing); – in the case of spatial color mixing, i.e. observing small colored dots from a distance (pointillism in painting, dot pattern on the screen of a color TV-set, tonal printing in the printing industry). Subtractive color mixing (from the Latin subtragere – subtract) is based on the "subtraction" from the incident white light of monochromatic radiations absorbed by the colored layers (Fig. 3.2).
Figure 3.2 – Subtractive color mixing
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Wherein, the color A in the subtractive color space, e.g., CMY, is expressed by the following color equation A W cC mM yY , where c , m and y are color coordinates in the color space defining the proportions of the subtracted emissions of colors C , M and Y of their white color W . Subtractive color mixing occurs in case of the sequential transmission of light through colored media (glasses, films, solutions). In this case, the media absorb (subtract) those colors from the luminous flux transmitted through them that correspond to the absorption zones. Only in the case of zonal transmission spectra of color media the subtractive mixing can be reduced to the additive mixing of colors of the luminous flux divided by them into zones. It should be noted that in case of paints mixed on the palette or in solutions, there usually occurs a complicated case of combining additive and subtractive color mixing. 3.2 Grassmann's Laws Color measurements became possible after the experimental discovery by J. Maxwell and precise mathematical formulation by H. Grassmann of color mixing laws. These laws apply only to the case of additive color mixing in which the color of the sum does not depend on the spectral composition of mixed colors, i.e. the 1-st Grassmann's law proves true. In subtractive mixing of colors this law is not observed, since the same colors with a different spectral composition can form mixes of quite various colors in case of subtractive mixing with other colors. J. Maxwell experimentally established the laws of additive color mixing using a whizzer - the first simple colorimetric device. Subsequently he developed a better visual colorimeter (the so-called Maxwell's box) with optical color mixing. First Grassmann's law – the qualities of colors in mixtures do not depend on their spectral composition. Therefore, it is possible to operate not with radiations but with colors. As the experiments demonstrate that three primary colors are enough to reproduce the test color, i.e. the following expression is correct: Atest a test A a test A a test A , (3.1) 1 1 2 2 3 3 test where A is the test color, A1 , A2 and A3 are the primary colors of the test test test measurement system, a1 , a2 and a3 are the color coordintates determining the proportions of the added radiations of the measurement system primary colors. Thus, if two colors in these conditions have the same color coordinates, they are equal (regardless of spectral composition).
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test 1 A a A a A a A 1 1 2 2 3 3 AAtest12 test . (3.2) test 2 A a1 A 1 a 2 A 2 a 3 A 3 Second Grassmann's law – colors can be mixed. Besides, if two test colors Atest 1 and Atest 2 are mixed, the resulting color will be characterized by the sums of the coordinate pairs relating to the color of the mixed colors. test1 test 1 test 1 test 1 A a A a A a A 1 1 2 2 3 3 test2 test 2 test 2 test 2 A a1 A 1 a 2 A 2 a 3 A 3 . (3.3) test1 test 2 test 1 test 2 test 1 test 2 test 1 test 2 AA aaAaaAaaA1 1 1 2 2 2 3 3 3 That is, if the color of one radiation is equal to the color of another test 3 radiation and, similarly, if the color of the third radiation A is equal to the color of the fourth radiation Atest 4 , one can argue that the color of the sum of the first and the third radiations will be equal to the color of the sum of the second and the fourth radiations. test12 test AA AAAAtest1 test 3 test 2 test 4 . (3.4) test34 test AA Third Grassmann's law – color is an affine three-dimensional vector and all the colors are transformed according to the laws of vector algebra. This law is the most important because it determines the possibility of measuring colours. Maxwell experimentally proved that it is necessary and sufficient to have three linearly independent colors, each of which being impossible to obtain by mixing the other two, in order to reproduce all the color diversity by adding these three colors in various quantitative proportions. The word "linear" means that the color equities are in essence first degree equities, i.e. if test A a1 A 1 a 2 A 2 a 3 A 3 , then test A a1 A 1 a 2 A 2 a 3 A 3 . (3.5) The choice of the groups of three colors being linearly independent can be arbitrary. In strict mathematical formulation this law reads as follows: between any four colors there is always a linear dependence, although there are an unlimited number of linearly independent sets of three colors. To measure a color means to express it through three colors of the selected measurement system. There are various optical devices – colorimeters, developed for this purpose. As the colors are mixed in a linear way it is possible to build a simple algorithm for determining the proportions of radiations being mixed concerning the primary colors of the measurement system, or otherwise color coordinates. Let us assume that spectral radiation of the source can be considered a weighted sum of radiations of separate sources with narrow radiation spectrum (i.e. sources 38 emitting at one wavelength). Since the operation for the color expression is linear, the combination of the primary colors describing the radiation of the composite source can be obtained by adding color coordinates of sources with narrow radiation spectrum (see formula (3.3)). If all the color coordinates relating to the colors determining for each radiation source with narrow radiation spectrum in the visible spectrum are known, it is possible to find the color coordinates for the radiation of an arbitrary spectral composition. The color matching functions for the colors f , f 1 2 and f are obtained experimentally for any given set of primary colors A , 3 1 A2 and A3 of the given color measurement system. These functions are called color matching functions and represent a set of color coordinates for monochromatic radiations of a fixed relative energy distribution in the form of a functional dependence on the wavelength.
Therefore, the color of monochromatic radiation source P 1 emitting at wavelength can be described as follows: 1 P 1 f 1 1 A 1 f 2 1 A 2 f 3 1 A 3 . (3.6)
In case source P is described by a sum of a huge number of monochromatic sources emitting with a certain intensity, formula (3.6) is translated as follows: P a1 A 1 a 2 A 2 a 3 A 3 . (3.7) PfdAPfdAPfdA 1 1 2 2 3 3
3.3 Properties of color spaces One should note the following properties of the color spaces. Affine properties 1. The order of the lines and surfaces remains unchanged. That is, a direct line will always remain direct, a plane will always be a plane, curves and second degree surfaces will be curves and second degree surfaces, etc. 2. The notion of a part of the whole. For instance, – a point lying on a certain line, as well as a line lying on a certain surface are transformed in the points and lines lying on the transformed lines and surfaces; – an angle being part of another angle will always remain less that that other angle after transformation, therefore, a direct line lying between the other two direct lines located on the same plane will always lie between the adjacent direct lines after transformation.
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3. Infinitely remote points cannot become finite points. In particular, parallelism is preserved, as well as the ellipsoid and the ellipse cannot become a hyperboloid or a hyperbola or a parabola. 4. Dividing a segment in this regard. Due to the above, as well as due to maintaining parallelism, the relations of parallel segments, i.e. the relations of distances along one and the same or along parallel lines are kept unchanged. Nonaffine properties 1. In case of affine transformation any of the three vectors not lying on the same plane can be transformed into any three others (in size and direction), not lying on the same plane. For instance, any angle (with the exception of angles divisible by ) can be changed into any other. In addition, a right triangle can turn into any other. 2. Distance relationship between any two pairs of points (unless these pairs lie on the same line or parallel lines) can vary in case of transformation. For example, any ellipse can be transformed into any other, in particular, into a circle. 3. The relationship between the values of any two angles can vary in case of transformation. Thus, the notions of dividing an angle into equal parts, and particularly the notion of a perpendicular are nonaffine. 3.4 Color measurement systems In accordance with [1] one can draw the following classification of the most widely used color measurement systems.
Linear color measurement systems 1) RGB color measurement system 2) XYZ color measurement system 3) RGB physiological color measurement system 0 0 0 4) FFFз с к zone color measurement system Nonlinear color measurement systems 1) abq barycentric color measurement system 2) pB polar color measurement system color measurement system In this color measurement system the primary colors are set as the colors of monochromatic radiations with the wavelength equal to 700nm for R , 546.1nm – for and 435.8nm – for taken at such powers as to satisfy the color equation: G B ERGB , (3.8) where E is the color of a white surface lit with an E -type source (a source with the constant spectral radiant intensity in the visible portion of spectrum). color measurement system is characterized by the color match curves stated in GOST 13088-67 [1] and represented in Fig. 3.3.
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Figure 3.3 – Color match curves of RGB color measurement system XYZ color measurement system The primary colors of this color measurement system cannot be physically realized, i.e. they are unreal colors. system is set through system by the following transformation formulas. Vector color equations relating colors X , Y and Z to colors R , G and B are as follows XRGB2,36460 0,51515 0,00520 YRGB 0,89654 1,42640 0,01441 . (3.9) ZRGB 0,46807 0,08875 1,00921 There also exist scalar numerical equations relating color coordinates x , A yA and zA of a random color A in system with its [color ] coordinates rA , g A and bA in system: x0,49000 r 0,31000 g 0,20000 b A AAA
yAAAA0,17697 r 0,81240 g 0,01063 b . (3.10)
zAAAA0,00000 r 0,01000 g 0,99000 b The formulas stated in (3.10) are used to calculate color match curves x , y and z for system , represented in Fig. 3.4. It should be noted that in order for mixture curve to coincide with the relative eye sensitivity curve V , calculation results by formulas (3.10) are multiplied by the factor equal to 5.6504.
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Figure 3.4 – Color match curves of XYZ color measurement system RGB color measurement system 0 0 0 RGB0 0 0 is a physiological system, color matching functions r0 , g0 and b are spectral sensitivity curves of the retinal cone apparatus (Fig. 1.11). 0 FFFз с к color measurement system Zone color measurement system was proposed by N. Nyuberg [8]. This system was also used successfully by Ovechkis in colorimetric studies of photographic processes and for color reproduction. Unlike system, zone system is demonstrative, i.e. one can assess the character of the reflection spectrum (or the transmission spectrum) of the specimen by the color coordinates of this system. This system is characterized by the fact that the radiation spectrum of light source P is divided into the three zones with different wavelegth intervals. zone zystem is determined by the primary colors of the green, blue and red radiation with their coordinates xз,, y з z з , xс,, y с z с and xк,, y к z к in system determined by the formulas 480 480 480 xс Pxdy с Pydz с Pzd 380 380 380 560 560 560 xз Pxdy з Pydz з Pzd , (3.11) 480 480 480 720 720 720 xк Pxdy к Pydz к Pzd 560 560 560 42
where x , y and z are color match curves of XYZ system, P is the spectral radiation distribution for one of the standard light sources. Zone color measurement system is suitable for those applications of colorimetry which deal with the mixing of colors with small diffusion, for example, in color cinematography. abq color measurement system The color triangle is used quite often as a color representation method in practice (Fig. 3.5). In the color triangle the vector of color A is characterized by the position of point A in the triangle based on the primary colors, as well by the weight (or mass) defining the vector length. This name of the third coordinate which has long been recognized is due to the fact that the color conversion in this system is subject to the rule of mass addition in mechanics. During the mixture of colors the "masses" are added and the location of the color in the mixture is based on the direct line connecting the colors being mixed in inverse proportion to their "masses". The coordinates of this system, which is also called barycentric, are not subject to homogeneous linear transformations – they follow the projective transformations.
Figure 3.5 – Construction of the barycentric color measurement system
Barycentric coordinates a , b and q are calculated by the known color coordinates in the linear color measurement system ABC which is being used ( a , b and c ) with the help of the formulas a b a , b , q a b c . (3.12) a b c a b c
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Wherein, the obtained coordinates a and b are called the chromaticity coordinates. Similarly, chromaticity coordinates x and y are calculated for barycentric system xy based on XYZ system. It should be noted that q coordinate is called differently in the literature sources, e.g. "color quantity" by Helmholtz and Maxwell, "color moment" in certain German literature sources or "color module" by some American authors. It should also be borne in mind that color calculations in the color triangle (for example, determining the sum of two or more colors on the basis of the center of gravity) are always made in the barycentric system. pB color measurement system Visual additive colorimeters were used in early XIX century, e.g., Netting colorimeter, where the measured color was obtained as a result of mixing a monochromatic color with the white color. A color in this measurement system is characterized by three parameters, such as – dominant wavelength of monochromatic radiation (obtained by the dom intersection of the beam emitted from point W designating the white color and the measured color A passing through that point, with the spectral locus – see Fig. 3.6), – color purity p characterizing the brightness proportion of a monochromatic color in the general resulting color brightness of the mixture and calculated using the formula e p 1 , (3.13) ee12 where e1 is the distance on the chromaticity diagram from the point of white color
to the point of the measured color ; e2 is the distance on the chromaticity diagram from the point of the measured color to the point defining on the spectral locus. Besides, color purity can be calculated using the known values of the photometric brightness B of monochromatic component and the general brightness B of the measured radiation: B p . (3.14) B – brightness of the resulting color B expressed in relative or absolute photometric units. This color measurement system is considered as a certain physical basis of the generally accepted Munsell system having the similar psychophysiological coordinates: color hue, saturation and lightness. Therefore, the polar color measurement system is considered demonstrative. However, this demonstrativeness does not compensate its colorimetric inapplicability in vector
44 transformations and it may serve, essentially, just as the means for color designation.
Figure 3.6 – Example construction of the polar color measurement system pB
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4 PROPERTIES OF RADIATION SOURCES (ENERGETIC, SPECTRAL AND SPATIAL)
4.1 Basic values and units of measurement The main values characterizing the properties of the radiation source, are: flux , luminosity M , illuminance (irradiance) E , radiation intensity (luminous intensity) I and brightness L (Fig. 4.1).
Figure 4.1 – Basic values
Wherein, these values can be measured using different units of measurement: energetic, photonic and light (see Table 4.1). These values can also describe spectral and spatial qualities of the radiation attributed to the source (Fig. 4.1). Suppose there is a certain value P characterizing the source. Then designation Pe indicates that this value is measured in energetic units, e.g. watts. If the specified value describes the spectral qualities of the radiation attributed to 46 the source, the spectral density of the value is designated as Pe, and determined according to the formula dP P e , (4.1) e, d wherein the measurement units of are W/µm. The distribution of the spectral density of the value across the wavelengths is designated as Pe, and has the same measurement units as . Wherein,
Pee P, d . (4.2) If the value under consideration describes the spatial qualities of radiation (qualities of of radiation attributed to the source in the direction described by angles and – Fig. 4.1), then the spatial density of the radiation attributed to the source is designated as Pe,, and is determined according to the formula dP P e , (4.3) e,, dd wherein, the measurement units are W/(rad∙rad). The distribution of the spatial density of the value across angles and is designated as Pe,,, and has the same measurement units as . Wherein,
Pee P,,, d d . (4.4) If the properties of the radiation in space are described using one angle or , then the missing angle is excluded from the inferior index in the designation. In the case where the context of the text or the calculation makes it possible to understand which are the exact units used for measuring the stated value P , then the index of the measurment units can also be omitted. Table 4.1 – Measurment units of the values Energetic units Photonic units Light units Flux W photon/sec lm Radiation intensity (luminous intensity) W/sr photon/(sr∙sec) cd = lm/sr I Luminosity M W/m2 photon/(sec∙m2) lm/m2 Illuminance W/m2 photon/(sec∙m2) lx = lm/m2 (irradiance) E Brightness L W/(sr∙m2) photon/(sec∙sr∙m2) cd/m2 = lm/(sr∙m2)
Flux is the ratio of energy Q transferred by the radiation to time ts of the transfer, considerably exceeding the period of self-oscillation: dQ . (4.5) dts 47
Figure 4.2 – Radiation intensity (luminous intensity) of the source
Radiation intensity I is the ratio of radiation flux which is evenly distributed from the radiation source within solid angle containing the selected direction (Fig. 4.2): d I . (4.6) d If is measured in energetic or photonic units, it is called radiation intensity. If is measured in light units, it is called luminous intensity.
Figure 4.3 – Luminosity of the source (a) and illuminance (irradiance) from the source (b)
Luminosity M is the ratio of radiation flux emitted from the surface containing the point under consideration to the square of that surface S within which the radiation can be considered homogeneous across the surface (Fig. 4.3 a): d M . (4.7) dS
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Irradiance E is the ratio of radiation flux incident on the surface containing the point under consideration to square S of that surface (Fig. 4.3 b): d E . (4.8) dS If is measured in energetic or photonic units, it is called irradiance. If s measured in light units, it is called illuminance. It must be noted that luminosity M is a direct characteristic of the source, and illuminance an indirect characteristic, as it describes the illuminated surface.
Figure 4.4 – Brightness of the source
Brightness L is the ratio of radiation flux transferred by a narrow beam from small square S containing the point under consideration within small solid angle containing direction I and making angle with the normal line to S (Fig. 4.4): d 2 L . (4.9) d dS cos Recalculation of each value from the energetic units of measurement into light ones is as follows
Pv K m V P e, d , (4.10) where Km 683 is maximum spectral luminous efficacy of radiation at 0,555 µm; V is the relative spectral luminous efficiency of monochromatic radiation. 4.2 Emitting diodes characteristics Emitting diodes (ED) parameters are directly connected with the processes of spontaneous radiative recombination of electron-hole pairs (Fig. 4.5). It is assumed that the electron energy dependencies in the conduction band QE and hole energies in valence band QH from wave vector kv are described with parabolic relations:
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2 2 hk/2 v QQEC for the electrons in the conduction band, (4.11) 2me 2 2 hk/2 v QQHV for the electrons in the valence band, (4.12) 2mh where me and mh are effective electron mass and effective hole mass, h is the
Planck's constant, kv is the quasi-wave vector, QC and QV are extremum energies of the conduction band and the valence band.
Figure 4.5 – Dispersion law for the electrons and the holes
According to the energy conservation law the photon energy is equal to the difference of electron energy QE and hole energy QH
hv QE Q H Q g . (4.13) If the thermal energy is small compared with the bandgap energy
( kT Qg ) the photon energy is approximately equal to Qg . Therefore, when selecting a semiconductor with a corresponding bandgap it is possible to create an ED emitting at the desired wavelength. In the optical range the photon impulse is considerably less than the impulse of the charge carriers, i.e., after the recombination act with photon extraction the electron transfers from the conduction band to the valence band practically without changing the quasi momentum. Such transfers are depicted in Fig. 4.5 as vertical arrows showing that the electrons are recombined only with the holes having the same quasi momentum or the quasi-wave vector value kv . Based on the equality of the electrons and holes quasi momenta, one can deduct the ratio for the calculation of photon energy: 2 2 hk/2 v hv Qg , (4.14) 2mr
50
1 1 1 where mr is reduced mass . mr m e m h Using (4.14), one can express the combined density of energetic conditions depending on energy Q [11]: 3/2 12m QQQ r . (4.15) 22 g 2 h /2 Distribution of carriers in the permitted bands of a nongenerated semiconductor fQB is defined by Boltzmann distribution Q fQB exp. (4.16) kT The dependence of the radiation intensity on energy is a function proportional to the product of equations (4.15) and (4.16) (Fig. 4.6).
Figure 4.6 – Theoretical radiation spectrum of and ED
Wherein, the maximum radiation spectrum corresponds to energy kT QQ. (4.17) g 2 Spectral line width is determined at the level equal to half of maximum radiation intensity 1,8kT 2 Q1,8 kT or . hc If the radiation at the interface between the semiconductor and the air undergoes total internal reflection, it does not leave the semiconductor (Fig. 4.7). Radiation can leave the semiconductor if the angle of incidence of the rays on the interface region is close to the normal line to the surface. Total internal reflection
51 greatly reduces the external quantum yield of radiation, especially for the ED from the materials with high refractive indices.
Figure 4.7 – Total internal reflection
Let angle be the angle of incidence of the rays at the semiconductor-air interface from the semiconductor side. Then angle of reflectance of this ray from the interface surface can be deducted from the Snell law of refraction
nnssin air sin , (4.18) where ns and nair are refractive indices of the semiconductor and the air. Based on the condition 90 , one can calculated the critical angle of the total internal reflection c
nair c arcsin. (4.19) ns Semiconductors generally have relatively high refractive indices. Therefore, the value is very small and it is possible to use the approximation sincc . Then, the critical angle of the total internal reflection c is deduced from the equation
nair c . (4.20) ns The angle of the total internal reflection determines the angle of radiation output. The rays falling within the cone bounded by c can leave the boundaries of the semiconductor, the rest cannot. To determine the proportion of radiation falling within the angle of the radiation output it is necessary to calculate the surface area of the spherical cone with radius r (Fig. 4.8 a and 4.8 b). The area of the sphere surface segment defined by radius and angle is calculated as follows:
52
S dS 2 r22 sin d 2 r 1 cos . (4.21) 0
Figure 4.8 – The angle of radiation output
Consequently, the intensity of the radiation leaving the semiconductor is defined by the ratio of the segment surface area to the surface area of the whole sphere multiplied by the initial radiant intensity of the source in the depth of the semiconductor. Then the ratio of the intensity of the radiation leaving the semiconductor to the original radiant intensity is defined by the fraction 2r2 1 cos 1 c 1 cos . 4r2 2 c As the materials with high refractive indices are characterized by relatively small values of the critical angles of total internal reflection, cosc can be represented as a power series.
Figure 4.9 – Model of obtaining a Lambert source
53
Figure 4.10 – Indicatrices of ED radiation: theoretical planar (a) and tridimensional (b), as well as actual tridimensional (c)
54
Then, the ratio of intensities will be equivalent to 2 11c 2 11 c . 2 2 4 Using the formula (4.20), the ratio of intensities will be 2 1 nair 2 . 4 ns Accordingly, it can be seen that only a few percent of the radiation generated within the material leave the boundaries of the planar EDs. The differences between the refractive indices of the emitting material and the environment lead to the anisotropy of the spatial radiation distribution. The flat (planar) EDs based on the materials with high refractive indices are characterized with Lambertian radiation distribution (Fig. 4.9). This figure shows a point source of radiation located slightly below the semiconductor-air interface. The ray emitted by the source at angle with the normal line to the interface is also refracted at angle to the normal line. Wherein, the resulting expression for finding the radiant intensity of this ED in the air from angle will be in direct proportion to cos [11]. Consequently, this source is the Lambert source. Fig. 4.10 schematically depicts Lambertian spatial radiation distribution (directive diagram or the distribution of the spatial density of radiant intensity with reference to angle – I ) of the planar ED. Also, Fig. 4.10 depicts examples of distributions for EDs with surfaces of another geometrical form. A hemispherical ID with the radiating area in the center of the sphere is characterized by an isotropic distribution of the radiant intensity spatial density: I const . When the surface is of parabolic shape the distribution with a distinct focus is obtained. However, an ED with a parabolic or hemispherical surface is much more difficult to manufacture. Fig. 4.10 b depicts tridimensionally the theoretical distributions of the radiant intensity spatial density according to angles and – I , for the Lambert source and a source with a radiation dip in the center. Fig. 4.10 c depicts real distributions from a red ED of L-934SRC-J brand and a green ED of BL-L324PGC brand.
55
5 CALCULATION OF COLOR COORDINATES FROM THE SPECTRAL PROPERTIES OF RADIATION SOURCES Color parameters of the radiation attributed to the sources are characterized by color coordinates in the CIE 1931 color space. ( x , y , z ), chromaticity coordinates on the CIE 1931 color diagram. ( x , y ) and chromaticity coordinates on the CIE 1976 color diagram. (u ,v ).
For a given distribution of spectral density P () related to the value of measuring the radiation attributed to the source, color coordinates in the CIE 1931 color space can be calculated using the equations [12]: x kc P ()() x d 0 y kc P ()() y d , (5.1) 0 z kc P ()() z d 0 where x() , y() and z () are color match curves in XYZ color measurement system, kc is a multiplier. Since color match curves , and are usually determined by the relative values of the ordinates, the color coordinates calculated according to them will have a relative nature [13, 14]. In many cases, when the purpose of the calculation is to determine the chromaticity coordinates that is enough. Therefore, the common multiplier kc can be omitted. When the absolute quantitative measure of color is required, usually its brightness is measured. To calculate the absolute brightness values a ratio is used, stating that 1 W of monochromatic radiation flux with a wavelength of 555 nm is equal to 683 lm of the light flux. Relative brightness can be estimated [15, 16] by calculating 100 kc . (5.2) P ()() y d 0 Consequently, for the radiation source color coordinate 100 y P ()() y d is always numerically equal to 100. 0 P ()() y d 0 In case of numerical determination of the color coordinates expression (5.1) is not used directly, since neither color match curves nor spectral characteristics are usually simple functions suitable for integration. Besides, color match curves are usually set in tabular form for discrete wavelength values (see 56
Appendix 1). Therefore, in practical calculations integration (5.1) is substituted by summing the corresponding products for a range of wavelengths, i.e.: n x kc P ()() i x i i1 n y kc P ()() i y i , (5.3) i1 n z kc P ()() i z i i1 in this case, the expression (5.2) will look as follows: 100 kc n . (5.4) Py ()()ii i1 There are two ways to determine the color coordinates according to (5.3): method of weighted ordinates and method of selected ordinates.
When using the method of weighted ordinates products of Px ()()ii,
Py ()()ii and Pz ()()ii are summed for a number of values relating to the wavelengths in the visible spectrum with the same interval . In most cases sufficient calculation accuracy is achieved at intervals of 10 nm. For the spectral characteristics of radiation with steep slopes summing with the interval of 5 nm is resorted to, and in case of smooth characteristics sometimes it is sufficient to use the calculation accuracy with the interval of 20 nm [12]. In general, when choosing the spectral interval for calculating the color coordinates one can follow the rule that the interval should be such as not to cause considerable influene on the calculation result in case of using a smaller interval. For sources with a narrow radiation spectrum, in particular the LEDs, it makes sense to sum at intervals of 1 nm. Color coordinates calculations according to (5.3) are obviously an approximate determination of the areas under curves , and . These areas are divided into sections with the width equal to , and the latter are approximated by rectangles, as shown in Fig. 5.1, at 20 nm. The heights of the rectangles are equal to the values of functions , and for the wavelengths located at the midpoints of the intervals . In calculations according to (5.3) and (5.4) the ordinates of the function of radiation spectral distribution are weighted by the three distribution coefficients, therefore this calculation method is called the method of weighted ordinates.
57
Figure 5.1 – Illustration of calculating color coordinates by the method of weighted ordinates [12]
When considering a source with a mixed radiation spectrum consisting of continuous background and individual spectral lines, e.g. a fluorescent lamp with the spectrum depicted in Fig. 5.2, corrections should sometimes (in case of which is not small enough) be introduced in the calculation results by the method of weighted ordinates.
Figure 5.2 – Spectrum of a fluorescent lamp
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The spectral radiation characteristic for the source of this type is depicted sl by demonstrating values of P on the wavelengths of spectral lines i as areas of sl bands with the midpoints in and heights P i (see Fig. 5.2). Wherein, the bandwidth is usually taken as equal to the wavelength interval
used. If, when measuring P , values can be obtained, then these sl sl sl values are multiplied by the relevant values of x i , y i and z i . This produces several additional components for formulae (5.3) and (5.4). If values exist only for the wavelengths with interval, and wavelengths fall within these intervals, then formulae (5.3) and (5.4) represent the values of color coordinates of continuous background. Then the existence of radiation in lines with the intensity which can be represented by the bands with heights is taken into account by introducing corrections in the values of PX P x , i ii PY P y , PZ P z products and the products of i ii i ii PX P x , PY P y , i ii i ii PZ P z for the boundary wavelengths of and i ii i
i intervals including the narrow spectral lines of the radiation attributed to source . Correction of these values is performed by adding to them parts of sl sl sl sl sl sl Px ii , Py ii , Pz ii products which are in reverse proportion to distances from to and on the wavelength scale. The revised values can be calculated by the following formulae sl PX sl ii PX PX i ii sl PY sl ii PY PY i (5.5) ii sl PZ sl ii PZ PZ i ii and
59
sl PX sl ii PX PX i ii sl PY sl ii PY PY i . (5.6) ii sl PZ sl ii PZ PZ i ii The method of selected ordinates is based on the principle according to which interval is made constant and its spectrum values can be selected in such a way as to obtain Px ()()i i i , Py ()()i i i and
Pz ()()i i i product values equal for all i (Fig. 5.3). Then the product value can be placed outside the summation sign and the formula for distributing the spectrum at n intervals looks as follows: n x kc P ()() i x i i i i1 n y kc P ()() i y i i i . (5.7) i1 n z kc P ()() i z i i i i1 The product values before the summation sign are different for each color match curve x() , y() and z () and for each radiation source.
Figure 5.3 – Illustration of calculating color coordinates by the method of selected ordinates
60
Thus, we can assume that in determining the color coordinates according to the method selected ordinates we also calculate areas under the three curves obtained when weighing the curve of the resulting spectral distribution of radiation attributed to the source against three distribution coefficient, but unlike the method of weighted ordinates, areas under curves are approximated by rectangles of unequal width. On condition of changing the wavelength chart scale so that these rectangles have the same width, it would be enough to determine the area by the spectral radiation characteristic plotted on this chart in order to find the coordinate of the color. One should keep in mind that the modification of the wavelength scale is different for each combination of the summation curve and the radiation source, in the same way as is different the location of selected ordinates on the wavelength scale for each similar combination.
Calculation of chromaticity coordinates on the CIE 1931 color diagram In order to simplify the representation of defined colors the CIE 1931 color diagram is used [8] (Fig. 5.4). E point represents the color of a white surface illuminated with an E -type source (point of white color).
Figure 5.4 – CIE 1931 color diagram
In order to plot it chromaticity coordinates x , y and z are used, being relative color coordinates
61
x x x y z , (5.8) y y x y z where x , y and z are color coordinates in the CIE 1931 color space which can be calculated by the spectral characteristics of the radiation attributed to the source under analysis using the color match curves. Wherein, the ratio of chromaticity coordinates is taken into account x y z 1, Therefore, only chromaticity coordinates are used on the CIE 1931 color diagram (,)xy. Whereas the color is defined by three parameters, color coordinate y is often added to chromaticity coordinates as a brightness characteristic.
Calculation of chromaticity coordinates in the CIE 1976 color space Lu’v’. Attempts to bring the CIE 1931 color diagram to such condition as to make MacAdam ellipse take the form of circles led to the creation of CIE 1976 color diagram (Fig. 5.5). This is considered to be a uniform chromaticity scale diagram, as the distance between any two points located on it is proportional to the number of chromatic thresholds. This color space is described with one color coordinate L and two chromaticity coordinates u and v . Usually a standard E -type source is used as the point of white color. Wherein, L color coordinate characterizes the source brightness and is equated with y color coordinate Ly , chromaticity coordinates (,)uv are calculated by the following ratios [17] 4x u x15 y 3 z , (5.9) 9y v x15 y 3 z where x , y and z are color coordinates in the CIE 1931 color space which can be calculated by the spectral characteristics of the radiation attributed to the source under analysis using the color match curves. The thrid chromaticity coordinate w1 u v . Chromaticity coordinates (,)uv can also be calculated by the known values of chromaticity coordinates on 1931 diagram as follows [8]:
62
4x u 2xy 12 3 . (5.10) 9y v 2xy 12 3
Figure 5.5 – CIE 1976 color diagram
63
6 COLOR TEMPERATURE CONCEPT The white color has special color characteristics. There exist a lot of optical radiation spectra which enable the creation of a white color radiation. Among these spectra one can distinguish radiation spectrum of a black body, often called Planck's radiation. This spectrum is the basis of a precise and very useful standard which allows one to describe the radiation spectrum using a single parameter – color temperature. Moreover, natural daylight spectrum of radiation is close to the radiatin spectrum of a Planck's radiation source.
Spectrum of solar radiation White color is usually characterized by a wide spectrum of radiation which usually extends over the entire visible wavelength range.
Figure 6.1 – Dependence of spectral density relating to solar radiation intensity on photons energy and wavelength, measured in different conditions
Sunlight is a typical model of white light. Fig. 6.1 shows optical spectra of the Sun in the upper atmosphere and at sea level at the moments of the Sun being overhead, at sunset and at dawn. The spectrum of sunlight occupies the whole visible spectrum. However, the intensity of solar radiation depends on the time of day, time of year, altitude, weather and other factors [11, 18–20]. Since the proportion of infrared (IR) and ultraviolet (UV) components is quite high in the sunlight, it is hardly possible to get the effective white color source in case of exact reproduction. Therefore, the Sun is not a good example of an efficient white light source. Even if it were possible to exclude from the solar
64 spectrum IR and UV components, still it could not be called optimal due to the high radiation intensity at the interface visible light – IR-radiation and visible light – UV-radiation.
Radiation spectrum of a black body Radiation spectrum of a black body defined by only one parameter, the temperature of the emitting body, is often used as an independent standard characterizing the white light. Max Planck was the first to deduce in 1900 the formula describing the distribution of the spectral density of black body luminosity at the specified temperature. 2hc 2 M () , (6.1) 5 hc exp 1 kT where is the wavelength, c is the speed of light ( 3 108 m/s), h is Planck's constant ( h 6,6262 1034 J·s), k is Boltzmann's constant (k 1,38067 1023 J/K), T is the emitter temperature in degrees Kelvin. Fig. 6.2 represents radiation spectra of a black body at different temperatures.
Figure 6.2 – Spectral distributions of radiation intensity relating to a black body according to the wavelengths measured at different temperatures.
65
The wavelength corresponding to the maximum intensity of the radiation emitted by a black body at a predetermined temperature can be calculated on the basis of Wien's law: 2898 .At "low" temperatures of a black body (e.g. 3000 K) radiation max T occurs primarily in the IR wavelength range. With increasing temperature, the maximum radiation shifts towards shorter wavelengths, i.e. in the direction of the visible spectrum range. Fig. 6.3 demonstrates the position on the CIE 1931 color diagram of radiation spectrum chromaticities relating to a black body which is often referred to as the black body locus or Planck's curve. Along with the growth of the black body temperature the position of its radiation on the diagran is shifted from the area of the red colors closer to the center of the diagram.
Figure 6.3 – Colour diagram 1931 which shows Planck's curve and the position of standard white light sources of radiation: sources of types A, B , C , D65 and E
66
The temperature of the black body radiating the white light typically falls within the range 2500 10000 К. Fig. 6.3 also demonstrates the position on the color diagram of several standard radiation sources identified by CIE: sources of types A, B , C , D65 and E .
Figure 6.4 – Planck's curve on a uniform chromaticity scale color diagram CIE 1976 and the position of standard white light radiation sources: sources of types , , , and E
Fig. 6.4 represents Planck's diagram and various values of a black body temperature on a uniform chromaticity scale CIE 1976 color diagram, as well as the position on the color diagram of seceral standard white light radiation sources identified by the CIE: sources of types , , , and .
Correlated Colour Temperature At first glance, the color temperature may seem quite a strange value, as the color and temperature parameters are not directly related to each other [21, 22]. However, having analyzed the behavior of a black body, one cannot fail to see the relationship between these parameters. Along with increasing temperature the color of a black body emission changes from red to blueish and white (red → orange → yellowish and white → white → blueish and white). Color temperature 67
(CT) Tc of a white color source which is measured in Kelvin is determined by the temperature of a black body located on the color diagram in the same position as the radiation source under consideration. If the white light source under consideration is not located on the Planck's curve, correlated color temperature (CCT) Tc is used for its description. This value is also measured in Kelvin, and is determined by the temperature of a black body with the color as close to the color of the analyzed white light source as possible. To determine the CCT of a radiation source on the CIE 1976 color diagram plotted in coourdinates (,)uv, it is necessary to determine the point which is closest to the source on Planck's curve (i.e. the shortest geometric distance). The temperature of a black body located at this point will correspond to the CCT of the source under consideration. Due to the uneven character of the CIE 1931 color diagram it is impossible to use it in order to determine the correlated color temperature employing the algorithm described above. In order to determine correlated color temperature on the CIE 1931 color diagram one should plot lines on it, corresponding to the constant values of the correlated color temperature. The chromaticity coordinates of incandescent lamps on the color diagram are close to the coordinates of a black body, although there is no complete coincidence. Therefore, color temperature is determined quite accurately for this kind of sources. Table 6.1 – Correlated color temperature of the most common sources of artificial and natural light Light source Correlated color
temperature Tc, К Flame of a wax candle 1500 – 2000 Flame of a standard candle 2000 Incandescent lamp 60 W 2800 Incandescent lamp 100 W 2850 Halogen lamp 2800 – 3200 Fluorescent "warm white" light lamp 3000 Fluorescent "cold white daylight" lamp 4300 Fluorescent "actual daylight" lamp (with color adjustment) 6500 White flame of a carbon arc 5000 Xenon arc (not filtered) 6000 Summer sunshine (before 9:00 or after 15:00) 4900 – 5600 Summer sunshine (from 9:00 till 15:00) 5400 – 5700 Direct sunlight 5700 – 6500 Sunlight dimmed by the clouds 6500 – 7200 Clear blue sky 8000 – 27000 68
Color temperatures of standard incandescent lamps are in the range of 2000 to 2900 degrees K, and of quartz halogen lamps – in the range of 2800 to 3200 degrees K. Other radiation sources such as metal halide lamps, are significantly distant from Planck's curve on the color diagram. Therefore it is necessary to determine the correlated color temperature for them. For example, the correlated color temperature for the lamp of a bluish-white color is about 8000 degrees K. Table 6.1 represents the correlated color temperature values of the most common sources of artificial and natural light.
Calculation of the correlated color temperature value The correlated color temperature value T of a radiation source with color c I (Fig. 6.5) can be determined from the formula [23]:
TTcc21 Tcc T11 d , (6.2) dd12 where Tc1 and Tc2 are Planck's emitter color temperature values of the nearest isothermal lines to the point characterizing the radiation source under analysis
(see Appendix 2), whereas d1 and d2 are distances to the stated isothermal lines, respectively.
Figure 6.5 – Isothermal lines (constant value lines of CCT ) and the process of value calculation of CCT
Distances d should be calculated to each of the known isothermal lines in order to have the possibility to determine the two lines closest to the source under analysis.
d1 and can be calculated by the following formulae:
69
v v t u u 00jj j d , (6.3) j 2 1 t j where (,)uv are the color coordinates of the source under analysis in the specialized color space Lu v which are calculated by the formulae [23–25]: 4x u x15 y 3 z ; (6.4) 6y v x15 y 3 z
For u0 , v0 and t values see Appendix 2. color space was created specifically for the purpose of calculating the correlated color temperature. It is different in that the isothermal lines located in it which characterize Planck's emitters radiation are arranged evenly. Chromaticity coordinates (,)uv of a black body, the Planck's emitter, for different values of color temperature in mired are stated in the appendices (Appendix 2). The color temperature value calculated using the formula (6.2) will have the dimension in Mired – units of measurement reciprocal to degrees Kelvin. To obtain the value of correlated color temperature in degrees Kelvin, one should recalculate the obtained value by the following formula 106 Tc[°K] . Tc[μ]
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7 RECALCULATION OF COLOR COORDINATES
7.1 Calculation of color coordinates in CIE 2003 color space L*a*b* This color space is characterized by the presence of a fixed white point ( D50-type source). This point is the basis for building the L axis (Fig. 7.1), it is located in the center of the color graph for any value of . Consequently, other sources of white light have a certain chromaticity. Thus, the color parameters of the source under analysis are calculated using the color parameters of a D50-type source. Calculation of color coordinates in the given color space begins with calculating the values of parameters fx(), fy() and fz() according to the following laws [24] (these parameters make it possible to take into account the peculiarities of color perception by human visual apparatus at different illuminance levels): 1/3 xx if 0,00885645 xxDD50 50 fx() , x 903,3 16 116 otherwise xD50 1/3 yy if 0,00885645 yyDD50 50 fy() , (7.1) y 903,3 16 116 otherwise yD50 1/3 zz if 0,00885645 zzDD50 50 fz() , z 903,3 16 116 otherwise zD50 where x , y and z are color coordinates of the source under analysis in the CIE 1931 color space which can be calculated by the spectral radiation characteristics of the source under analysis with the help of color match curves; xD50 , yD50 and zD50 are color coordinate of a D50-type source in the CIE 1931 color space. Formulae (7.1) were suggested for consideration by the CIE in 2002 and introduced as a calculation standard in 2003.
71
Figure 7.1 – L a b color space
Then the values of color coordinates L , a and b are calculated by the following ratios [26]: L 116 f ( y ) 16 a 500 f ( x ) f ( y ) . (7.2) b 200 f ( y ) f ( z )
7.2 Color coordinates calculation in the CIE 1976 color space L*u*v* This color space is characterized by the presence of a specific white point. For this purpose any (standard or specifically chosen for the experiment) radiation source can be chosen. Thus, the color coordinates of the source under analysis are calculated using the color parameters of a standard radiation source selected as the point of reference and are in essence relative color coordinates.
First, similarly to (7.1), the value of f y yW parameter is calculated [24] (characterizing the brightness of the radiation source under analysis in relation to the selected reference):
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1/3 yy if 0,00885645 yyWW f y yW , (7.3) y 903,3 16 116 otherwise yW where y is the color coordinate of the source under analysis in the CIE 1931 color space which can be calculated by the spectral radiation characteristics of the source under analysis with the help of color match curves; yW is the color coordinate of the selected white point in the CIE 1931 color space. The next step is the calculation of values of color coordinates L , u and v using the formulae [24]: L116 f y yW 16 u13 L u uW , (7.4) v13 L v vW where u and v are values of color coordinates of the source under analysis in the CIE 1976 color space CIE Lu v ; uW and vW are values of color coordinates of the selected white point in the CIE 1976 color space CIE .
7.3 Color coordinates calculation in the CIE 1976 color space CIE LCH Color solid of the CIE 1976 color space CIE LCH , similarly to the color solid of the space CIE L a b (Fig. 7.1), is a cylinder. It should be borne in mind that color coordinate H in this color space is expressed as an angular measure, unlike color coordinates L and C . That is, color space is a space with a cylindrical coordinate system unlike the previously mentioned color space or, for instance, XYZ . Besides, it should be borne in mind that unlike space , coordinates in space cannot be negative! Color coordinates can be calculated using two different color spaces: CIE and CIE L u v .
Calculation by using color coordinates CIE L*a*b* Color coordinates values in space are calculated according to the previously calculated values of color coordinates L , a and b by way of the following calculations [27]:
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LL
22 Cab a b
b arctan withab 0 и0 a b Hab arctan 360 with a 0 and b 0 a b , (7.5) arctan 180 in other cases a where L , a and b can be calculated using the formulae (7.2).
It should be noted that the calculated value of color coordinate Hab must fall within the range [0°; 360°]. The resulting color coordinates should be denoted with an inferior index
( ab ).
Calculation by using color coordinates CIE L*u*v* Color coordinates values in space LCH are calculated according to the known values of color coordinates L u v by way of the following calculations [27]: LL
22 Cuv u v
v arctan withuv 0 и0 u v Huv arctan 360 with u 0 and v 0 u v , (7.6) arctan 180 in other cases u where , u and v can be calculated using the formulae (7.4).
It should be noted that the calculated value of color coordinate Huv must fall within the range [0°; 360°]. The resulting color coordinates should be denoted with an inferior index
( uv ).
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7.4 Conversion from XYZ color space into RGB color space Conversion from CIE 1931 color space CIE XYZ into any of the possible RGB color spaces will be considered in this section2. The specified conversion is carried out in two main stages 1. Conversion from XYZ color space into linear R′G′B′ color space; 2. Conversion from linear R′G′B′ color space into nonlinear RGB color space; Let's take a closer look at these stages.
Stage 1: Conversion from XYZ color space into linear R′G′B′ color space Color coordinates in the linear RGB color space ( r,, g b ) can be calculated according to the following ratio [27]: rx g M1 y , (7.7) bz where x , y and z are color coordinates in the CIE 1931 color space CIE XYZ , and M 1 is the reverse (inverse) recalculation matrix M .
Calculation of direct recalculation matrix Direct recalculation matrix is determined by the formula:
Sr x r S g x g S b x b M Sr y r S g y g S b y b , (7.8) Sr z r S g z g S b z b where xr,, y r z r , xg,, y g z g and xb,, y b z b are color coordinates (in the CIE 1931 color space CIE XYZ) of the primary colors in the used type of RGB color space which can be calculated by the known chromaticity coordinates xyrr, ,
xygg, and xybb, (see Appendix 4); Sr , Sg and Sb are conversion coefficients for the red, green and blue channels [27]. Color coordinates values for the primary colors are calculated as follows:
2 Different RGB spaces were calculated and designed for different applications, for example, to render color images in television technology when using a variety of sources that implement basic colors, etc.
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xxrbxg xr x g x b yr y g y b
yr1 y g 1 y b 1 . (7.9)
(1xr y r )(1xygg ) (1 x b y b ) zr z g z b yr y g y b
Conversion coefficients values for the red, green and blue channels Sr , Sg and Sb can be determined by the following equation 1 Sr x r x g x b x W S y y y y , (7.10) g r g b W Sb z r z g z b z W where xr,, y r z r , xg,, y g z g and xb,, y b z b are color coordinates of the primary colors in the used type of the color space previously calculated by the formulae (7.9), and (,,)xWWW y z are color coordinates of the white point in the used type of the color space (see Appendix 3 and Appendix 4)
Colorimetric correction Colorimetric correction is used for the conversion of the source color coordinates of xp,, y p z p space with the white point color coordinates
xWp,, y Wp z Wp into the required coordinates xd,, y d z d with the white point color coordinates xWd,, y Wd z Wd [27]. That is, this correction should be done if and only if the white point in the space from which the conversion is done, and the white point in the space into which the conversion is done, do not match. The main conversion formula is:
xxdp y M y , (7.11) d c p zzdp where Mc is the correction matrix calculated by the ratio
dp 00 1 MMMc A 00 d p A , (7.12) 00dp 1 where M A is the inversed correction matrix M A (Appendix 5 contains colorimetric correction matrices for various methods – XYZ Scaling, Bradford and Von Kries the calculation is performed according to one of the stated methods 76
– it is considered that Bradford and Von Kries methods are more precise), and
p,, p p and d,, d d are correction vectors of the source color space and the required color space, respectively. Correction vectors of the source space and the required space are calculated by the following equations
p x Wp p My A Wp , (7.13) p z Wp
d x Wd My . (7.14) d A Wd d z Wd
Stage 2: Conversion from the linear R′G′B′ color space into nonlinear RGB color space This conversion depends on the type of RGB color space into which it is necessary to recalculate the color coordinates XYZ. Conversions can be performed with the help of [27] – gamma conversion, – sRGB conversion and – brightness conversion. Let us consider the conversion data in more detail.
Gamma conversion Gamma conversion is performed for those RGB color spaces for which there is a set value of parameter (see Appendix 4). Wherein, RGB color coordinates are calculated by the ratios rr 1/ gg 1/ , (7.15) 1/ bb where is the multiplier determined for the majority of RGB color spaces types. It must be remembered that the obtained color coordinates (,,)r g b will be normalized to 1. In order to obtain the customary values of color coordinates [0,255], the obtained values of (,,)r g b must be multiplied by 255.
sRGB conversion This conversion is performed only for sRGB color space. Wherein, color coordinates in this color space are calculated by the following ratios 77
12,92rr with 0,0031308 r 1/2,4 1,055rr 0,055 with 0,0031308 12,92gg with 0,0031308 g 1/2,4 . (7.16) 1,055 gg 0,055 with 0,0031308 12,92bb with 0,0031308 b 1/2,4 1,055bb 0,055 with 0,0031308 It must be remembered that the obtained color coordinates (,,)r g b will be normalized to 1. In order to obtain the customary values of color coordinates [0,255], the obtained values of must be multiplied by 255.
Brightness conversion This conversion is performed only for ECI RGB v2 color space. Wherein, color coordinates in this color space are calculated by the following ratios r with r r 100 1/3 1,16rr 0,16 with g with g g 100 , (7.17) 1/3 1,16 gg 0,16 with b with b b 100 1/3 1,16bb 0,16 with where and are parameters with the following values 216 (0,008856), 24389 24389 903,3. 27 It must be remembered that the obtained color coordinates will be normalized to 1. In order to obtain the customary values of color coordinates , the obtained values of must be multiplied by 255.
Algorithm of recalculation XYZ-RGB The sequence of recalculation from XYZ color space into RGB color space is presented in Fig. 7.2.
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Correction vectors Correction matrix calculation calculation x,, y z
p p p p,, p p
Mc d,, d d ion
Calculation
Coefficients Coordinates correct Colorimetric calculation xr,, y r z r recalculation SSS,, xg,, y g z g r g b xd,, y d z d xb,, y b z b
Matrix Linear Non-linear calculation coordinates coordinates calculation calculation M r,, g b r,, g b
Figure 7.2 – Algorithm of recalculation XYZ – RGB
Thus, first and foremost colorimetric correction is performed (if necessary). Wherein, the conversion vectors are calculated first by the formulae (7.13) and (7.14). Then the correction method XYZ scaling, Bradford or Von
Kries is selected and the calculation of conversion matrix Mc is performed according to the ratio (7.12), as well as corrected values of color coordinates
( xd , yd , zd ) are calculated by the equation (7.11). Then follows gradual calculation of color coordinates for the primary colors in the type of RGB color space under analysis using the ratios (7.9), calculation of recalculation coefficients Sr , Sg and Sb using the equation (7.10), calculation of recalculation matrix M using the formula (7.8) and the calculation of coordinates in the linear RGB system by the ratio (7.7). The final step is the nonlinear transformation using one of the previously presented expressions (7.15), (7.16) or (7.17) depending on the type of RGB color space for which it is necessary to perform the recalculation.
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8 DETERMINATION OF SMALL COLOR DIFFERENCES There are more than 100 different variants to determine small color differences (created for various productions, dyes, refernce radiation sources, conditions and analyzed chromaticity areas). Let us consider five possible options that CIE recommended in different years for pilot-testing and practical application. Small color differences can be calculated according to the following methods: – Method of calculating small color differences based on the CIE recommendations for 1950. – Method of calculating small color differences based on the CIE recommendations for 1976. – Method of calculating small color differences based on the CIE recommendations for 1994. – Method of calculating small color differences based on the CIE recommendations for 2000. – Method of calculating small color differences based on the recommendations of the color measurement committee.
Method of calculating small color differences based on the CIE recommendations for 1950. Based on the curvilinear conversion of CIE 1931 color space CIE XYZ color space L a b was developed, for which in 1950 it was recommended to determine small color differences between two compared colors using the formula [8, 28, 29]:
2 2 2 E L2 L 1 a 2 a 1 b 2 b 1 , (8.1) where (,,)L1 a 1 b 1 and (,,)L2 a 2 b 2 are color coordinates of the first and the second compared colors, respectively, in CIE L a b color space which can be calculated using the formulae (7.1) and (7.2).
Method of calculating small color differences based on the CIE recommendations for 1976. Based on the collineatory conversion of CIE 1931 color space CIE XYZ color space L u v was developed, for which in 1976 it was recommended to determine small color differences between two compared colors using the formula [2, 24, 27]:
2 2 2 E L2 L 1 u 2 u 1 v 2 v 1 , (8.2)
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where (,,)L1 u 1 v 1 and (,,)L2 u 2 v 2 are color coordinates of the first and the second compared colors, respectively, in CIE L u v color space which can be calculated using the equations (7.3) and (7.4).
Method of calculating small color differences based on the CIE recommendations for 1994. This method is used to calculate small color differences between two compared colors based on the analysis of color coordinates in the CIE L a b color space. Wherein, the color difference is determined using the equation [27]: 222 LCH E , (8.3) KSKSKSLLCCHH where LLL 12
CCC 12 ,wherein H a2 b 2 C 2
22 C1 a 1 b 1 ,
22 C2 a 2 b 2 , a a12 a , b b12 b , furthermore,
SL 1 SKCC 1 11 , SKCH 1 21 where 2 when analysing textiles KL 1 in other cases
КС 1 ,
КH 1 and 0.048 when analysing textiles K1 , 0.045 in other cases
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0.014when analysing textiles K2 . 0.015 in other cases
Method of calculating small color differences based on the CIE recommendations for 2000. Like the previous method, this method is used to calculate small color differences between two compared colors based on the analysis of color coordinates in the CIE L a b color space. Wherein, the color difference is determined using the equation [27]: 222 LCHCH ER T , (8.4) KSKSKSKSKSLLCCHHCCHH where
KL 1, 2 0.015L 50 S 1 , L 2 20L 50 wherein LL L 12 2 and LLL 21 . Furthermore,
KC 1,
SCC 1 0.045 , where CC C 12, 2 wherein
2 2 2 2 C1 a 1 b 1 , C2 a 2 b 2 , where a11 a (1 G ), a22 a (1 G ) . Wherein, C 7 1 C 77 25 G , 2 where
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CC C 12, 2 at
22 22 C1 a 1 b 1 , C2 a 2 b 2 , and
CCC 21 . Also,
KH 1, SCTH 1 0.015 , where THHH1 0.17 cos 30 0.24 cos 2 0.32 cos 3 6 , 0.20 cos 4H 63 at hh 360 12 ,hh 180 2 12 H . hh 1 ,hh 180 2 12 in this case h1 and h2 are measured in angular units and calculated according to the formulae: b1 arctan withab11 0 and 0 a1 b1 h1arctan 360 with a 1 0 and b 1 0, a1 b arctan1 180 in other cases a1 b2 arctan withab22 0 and 0 a2 b2 h2arctan 360 with a 2 0 and b 2 0. a2 b arctan2 180 in other cases a2 Furthermore, h HCC212 sin, 2 where 83
h2 h 1 h 2 h 1 180 h h2 h 1 360 h 2 h 1 180 ; h 2 h 1 . h2 h 1 360 h 2 h 1 180 ; h 2 h 1 Wherein,
RRTC sin 2 , where 2 H 275 30 exp 25 and C7 R 2 . C C77 25
Method of calculating small color differences based on the recommendations of the color measurement committee. Like the two previous methods, this method is used to calculate small color differences between two compared colors based on the analysis of color coordinates in the CIE L a b color space. Wherein, the color difference is determined using the equation [27]: 222 LCH E , (8.5) lSLCH cS S where (,)lc are chromaticity coordinates in Lch color space calculated by the coordinates values in CIE 1976 color space LCab H ab or LCuv H uv by the ratios (7.5) or (7.6), wherein lL /100, and cC . However, in this case these values are not calculated, instead one of the two variants of (;)lc combinations is used: when analyzing the reproduction of color shades (2;1) and when analyzing the reproduction of color shades (1;1) . Only such parameters are calculated as LLL 12 , 0.511L1 16 S , L 0.040975 L1 L1 16 1 0.01765 L1 and
CCC 12 ,
84 where
22 C1 a 1 b 1 ,
22 C2 a 2 b 2 , also,
0.0638C1 SC 0.638. 1 0.0131 C1
Furthermore, H a2 b 2 C 2 , where a a12 a , b b12 b and
SSFTFHC 1 , where
0.56 0.2 cosHH11 168 , if 164 345 T , 0.36 0.4 cosH 35 1 4 C1 F 4 C1 1900 and b1 arctan withab11 0 and 0 a1 b1 H1arctan 360 with a 1 0 and b 1 0. a1 b1 arctan 180 in other cases a1
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9 COLOR RENDERING INDICES OF RADIATION SOURCES Assessment of the ability of the tested radiation source to render colors is performed by its comparison to a reference light source. In experimental color rendering index determination of the tested source besides the analyzed and the reference emitters reference reflective surfaces are also used. However, in order to achieve international standardization in determining color rendering factors of real emitters a special set of 14 color surfaces is used. This set was selected from the set of colors originally proposed by Munsell. Restrictions applied to the calculation. According to the CIE recommendation in order to perform the calculation the reference source is selected based on the following considerations: – if the chromaticity coordinates of the analyzed source lie on Planck's curve, then a black body having the same color temperature as the tested emitter should be chosen as a reference source.
– one of the standard CIE sources (e.g. D65 ) can be used as the reference source. An ideal case would be if the tested and the reference light sources had the same chromaticity coordinates and equal luminous fluxes. It has been proven by way of experiment that the quality of the white light sources decreases sharply along with their chromaticity coordinates on the color diagram x and y becoming more than 0.01 distant from the Planck's curve. This value corresponds to the size of about four MacAdam ellipses – a standard adopted for lighting fixtures. However, it should be noted that the "0.01 deviation criterion" is required but insufficient for obtaining high-quality lighting sources. It was agreed to consider that a reference light source has the ideal color rendering parameters, i.e. its colour rendering index CRI = 100. Wherein, it was assumed that natural daylight is similar in parameters to a black body radiation, and therefore can be rightly considered to be a standard reference light source. Reference reflective surfaces mentioned above are determined through their spectral reflectivity (ratio of the surface reflection spectral distribution to the spectral distribution of the reference white source reflection). Fig. 9.1 demonstrates the reflection spectra of eight international color standards listed in Appendix 6. Total color rendering index is calculated based on the measurements while using all the eight reference surfaces (i 18). Sometimes in order to analyze the ability of emitters to reproduce colors in more detail six additional reference reflective surfaces are used (Appendix 7). These additional surfaces are characterized by colors: 9 – intense red, 10 – intense yellow, 11 – intense green, 12 – purple blue, 13 – body color, 14 – tree leaves color [11, 30].
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0,9 0,9 0,8 R1 0,8 R2 0,7 0,7 Dark desaturated 0,6 Light desaturated red 0,6 yellow 0,5 0,5 0,4 0,4 0,3 0,3 0,2 0,2 0,1 , nm 0,1 , nm 0 0 400 500 600 700 800 400 500 600 700 800 0,9 0,9 0,8 R3 0,8 R4 0,7 0,7 0,6 Saturated green 0,6 yellow Yellowish-green 0,5 0,5 0,4 0,4 0,3 0,3 0,2 0,2 0,1 , nm 0,1 , nm 0 0 400 500 600 700 800 400 500 600 700 800 0,9 0,9 0,8 R5 0,8 R6 0,7 0,7 0,6 Light bluish-green 0,6 Light blue 0,5 0,5 0,4 0,4 0,3 0,3 0,2 0,2 0,1 , nm 0,1 , nm 0 0 400 500 600 700 800 400 500 600 700 800 0,9 0,9 0,8 R7 0,8 R8 0,7 0,7 Light-purple 0,6 0,6 0,5 0,5 0,4 0,4 0,3 0,3 Light reddish-purple 0,2 0,2 0,1 , nm 0,1 , nm 0 0 400 500 600 700 800 400 500 600 700 800 Figure 9.1 – Reflectivity of eight CIE reference color surfaces
Reflection spectra of the six additional surfaces with the numbers 9-14 have more intense colors and relatively narrow peaks. Coefficients CRI9 CRI 14 are called particulate color rendering indices.
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A black body located closest to the point with chromaticity coordinates of the source under test is used as a reference source. Therefore, the color temperature of the reference light source is equal to the correlated color temperature of the tested emitter. Four points are used in calculations of the color rendering index. It should be noted, however, that the term "color" used by the CIE does not exactly correspond to the term "chromaticity". A more complete CIE definition of color includes characteristics such as tonality, saturation and brightness. Tonality and saturation are determined by the location of the points on the color diagram, and in order to represent graphically the brightness of the object or of the emitter it is necessary to introduce the third axis, which is depicted in Fig. 9.2 as illustration. Color difference of the physical object in case of its alternate lighting with the reference and the tested light sources is determined by the differences of chromaticity and brightness corresponding to the geometric distances between two points in Fig. 9.2. This representation of chromaticity is not a CIE standard and is given here only for the sake of education.
Figure 9.2 – Color difference in the three-dimensional color space Lu v .
Introduction of a universal color space concept by the CIE was dictated by the need to provide quantitative assessment of color taking into account the color and brightness characteristics. Universal color space should provide direct proportionality between the color difference of the two points and the geometric distance between them. This means that the color difference in such a universal color space is uniquely determined by the distance between two points in it. Universal color space is particularly suitable for the quantitative assessment of the color difference.
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9.1 Colour rendering index for radiation sources located on the Planck's curve This calculation is valid for the emitters located either directly on the Plank's curve or at a very short distance from it (color difference E 0,01).
Calculation of colour coordinates L*u*v* Values of coordinates in L u v color space determining the color difference of the reference surface and the reference emitter are calculated using the following equations [11]: 1/3 y ref Lref 116i 16 i ref y ref ref ref ref ui13 L i ( u i u ) , (9.1) ref ref ref ref vi13 L i ( v i v ) ref ref ref where values of coordinates yi , ui and vi describe the color of the i -th reference surface in case of lighting with the reference source, and values of coordinates y ref , uref and vref describe the radiation color of the reference white light source itself. Values of coordinates in color space determining the color difference of the reference surface and the tested source are calculated by the formulae: 1/3 y test Ltest 116i 16 i test y test test test test ui13 L i ( u i u ) , (9.2) test test test test vi13 L i ( v i v ) test test test where yi , ui and vi describe the color of the -th reference surface in case of lighting with the tested source, and y test , utest and vtest describe the radiation color of the tested white light source. It should be noted that in calculating the color rendering index the reference source (Planck emitter) is selected so that yytest ref , uutest ref and vvtest ref . Wherein, x 9y u ,v ,where u and v are calculated by the x15 y 3 z x15 y 3 z parameters of the reference source spectrum (superscript ref ), by the parameters of the tested source spectrum (superscript test ), by the radiation spectrum of the reference source reflected from the reference surface (superscript ref and subscript i ) and by the radiation spectrum of the tested source reflected from the reference surface (superscript test and subscript i ). 89
Calculation of color differences Value Ei being the color difference of the reference surface lit by the reference and the tested sources is determined by the formula 2 2 2 Ei ()()() L i u i v i , (9.3) where Li , ui and vi are differences between the coordinate values in color space L u v defining the color difference of the reference surface and the reference emitter and coordinate values in color space defining the color difference of the reference surface and the tested source, calculated by the following formulae: ref test LLLi i i , ref test ui u i u i , ref test vi v i v i . It must be noted that this calculation does not present unambiguous results, since the numerical coefficients in the formulae were determined on the experimental basis and they can not be considered optimal.
Calculation of the color rendering index Particulate color rendering indices (CRIs for one of the reference surfaces) are determined by the formula [11]: CRIii100 4,6 E , (9.4) respectively, a complete color rendering index is calculated using the equation 1 N CRIgi CRI . (9.5) N i1
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9.2 Calculation of the colour rendering index for radiation sources located outside the Planck's curve If chromaticity coordinates of the tested source do not belong to the Planck's curve (color difference E 0,01), then the reference source must by a black body having the same correlated color temperature as the tested emitter. The following calculations are valid for the tested radiation sources located outside the Planck's curve These calculations take into account the adaptive color shift that occurs due to the human ability to color adaptation.
Determination of color coordinates Calculation starts with determining chromaticity coordinates of the reference and the tested radiation sources on the uniform chromaticity scale color diagram Lu v , as well as determining chromaticity coordinates of the reference reflecting surfaces lit by the reference and the tested sources, i.e. (,)uvref ref , test test ref ref test test (,)uv, (,)uvii and (,)uvii. Wherein, x 9y u , v , u and v are calculated by the x15 y 3 z x15 y 3 z spectral parameters of the reference source (superscript ref ), by the radiation spectrum of the reference source reflected by the reference surface (superscript ref and subscript i ), by the radiation spectrum of the tested source (superscript test ) and by the radiation spectrum of the tested source reflected by the reference surface (superscript test and subscript i ). It should be noted that the reference radiation source in the form of a Planck's emitter is selected so that the correlated color temperature of the tested ref test source is equal to the color temperature of the reference source (TTcc ).
Calculation of the adaptive color shift In order to determine the adaptive color shift of coordinates (,)uv in value ref ref test test test test pairs (,)uv, (,)uv and (,)uvii are transformed into coordinates (,)rf using the following equations [11]: 4uv 10 r v . (9.6) (1,708vu 0,404 1,481 ) f v It must be noted that these two equations conceal six formulae transforming ref ref test test test test ref ref test test (,)uv, (,)uv and (,)uvii into (,)rf , (,)rf and test test (,)rfii, respectively, which are used to determine the chromaticity
91 coordinates of the reference surfaces after the adaptive color shift test test (uvii, ): ref ref rf test test 10,872 0,404 rfii 4 rftest test utest i ref ref rf test test 16,518 1,481test rfii test rf . (9.7) 5,520 vtest i ref ref rf test test 16,518 1,481test rfii test rf Accordingly, chromaticity coordinates of the tested emitter after the adaptive color shift (uvtest, test ) are determined by the formulae 10,872 0,404 rfref 4 ref uutest ref 16,518 1,481 rfref ref . (9.8) 5,520 vvtest ref 16,518 1,481 rfref ref Values utest and vtest are chromaticity coordinates of the light source taking into account the adaptive color shift (we will note once again that uutest ref , vvtest ref ).
Calculation of the color rendering index Now with the help of coordinates in the universal color space one can find the desired value of the color difference: 2 2 2 Ei ()()() L i u i v i , (9.9) where Li , ui and vi are differences between the coordinate values defining the color difference of the reference surface and the reference emitter and coordinate values defining the color difference of the reference surface and the tested emitter, calculated by the following formulae: ** ref test LLLi i i , ref test ui u i u i , ref test vi v i v i . ref ref ref Wherein, coordinates (,,)Li u i v i determining the color difference of the object and the reference emitter are found using the equations:
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ref 1/3 ref yi L i 116 16 y ref ref ref ref ref ui13 L i ( u i u ) , (9.10) ref ref ref ref vi13 L i ( v i v ) ref ref ref where yi , ui and vi describe the color of the i -th reference surface in case of lighting with the reference source, and y ref , uref and vref describe the radiation color of the reference white light source.
Figure 9.3 – Graphic representation of reflectivity for the six additional reference reflecting surfaces
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test test test Coordinates (,,)Li u i v i defining the color difference of the reference surface and the tested source taking into account the adaptive color shift are determined by the formulae: test 1/3 test yi L i 116 16 y test test test test test ui13 L i ( u i u ) , (9.11) test test test test vi13 L i ( v i v ) test where yi describes the color of the i -th reference surface lit by the tested source, y test describes the radiation color of the tested white light source, and test test test test u i , u , v i and v were calculated during the determination of the adaptive color shift. Using the obtained values of color difference Ei for the i -th reference surface, particulate and complete color rendering indices are determined by the formulae (9.12) and (9.13). In order to obtain complete understanding of color rendering relating to the radiation sources particulate color rendering indices
CRIi are determined for the six additional reference reflective surfaces (i = 9-14) (Fig. 9.3). Particulate color rendering indices are defined by the formula: CRIii100 4,6 E , (9.12) respectively, a complete color rendering index of the tested source is calculated using the equation: 1 N CRIgi CRI . (9.13) N i1
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10 MODELING OF RADIATION SOURCES WITH PREDEFINED CHROMATICITY Combination or additive mixing of radiations from two or more sources is often used in practice. For example, three types of LEDs are used in LED screens: producing red, green, and blue light, mixing their radiation, so that a person looking at the screen, actually perceives a wide range of colors as a combination of these three kinds of radiation. Other examples of mixing colors are white light sources based on two-color or three-color radiation sources. Fig. 10.1 represents the principle of additive color mixing and gives an example of additive radiation mixing of LEDs.
Figure 10.1 – Additive mixing principle for the three primary colors (a). Additive mixing of LED radiation (b)
Knowing the principles of color mixing helps to understand the location of the different LEDs on the color diagram. It should be borne in mind that the interface of the color diagram in the red color range is almost a straight line, so the red LEDs, despite the thermal spectrum spreading, are located on this interface. Due to the fact that in the green color range the diagram has a pronounced curvature, green LEDs are shifted from the interface to the center of the diagram due to the spectral spreading. The area of reproducible colors (color scale) is a complete set of colors which can be obtained from a set of source (primary) colors, it is displayed in the color diagram as a polygon with the tops being the location of the primary colors. The number of primary colors used defines the shape of the polygon. For instance, in case of two primary colors the color scale is a line (Fig. 10.2), and three source primary colors form the color scale as a triangle, as shown in Fig. 10.3. All colors obtained by additive mixing of the color scale primary colors corresponding to the vertices of the polygon are always located inside it. Colors located outside of the color scale cannot be reproduced using the given primary colors.
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The principle of mixing two colors is demonstrated on Fig. 10.2. Two colors A and A with the relevant chromaticity coordinates (,)xy, (,)xy are 1 2 11 22 mixed. On the color diagram the resulting color A is located on the direct line joining the points denoting the two primary colors - the colors of radiation sources A1 and A2 which are being used. Consequently, any color (including white) located between two points on the color diagram may be obtained by mixing these two colors.
Figure 10.2 – Principle of color mixing. Two primary colors A and A , as well 1 2 as the resulting color A are considered.
Fig. 10.3 represents mixing of the tree primary colors located in the red ( A1 ), green ( A2 ) and blue ( A3 ) ranges of the color diagram. The three selected points on the diagram can, for instance, correspond to the radiation of the red, green, and blue LEDs. The area inside the triangle of the dashed lines connecting these three colors together is the area of the resulting chromaticities, as all the colors within this range can be obtained by mixing the three primary colors: red 96
A1 , green A2 and blue A3 . The ability to reproduce as many colors as possible is one of the most important features of the monitors, for instance. The larger the scope of the color scale, the higher the quality of the screen.
Figure 10.3 – Principle of color mixing. Three primary colors A , A and A , as 1 2 3 well as the resulting color A are considered.
Let us consider the problem of determining the chromaticity coordinates of the radiation formed by three sources emitting light in three discrete wavelength ranges. Let us proceed from the assumption that the width of radiation spectrum relating to each of the color sources used as primary colors , and of the color scale is considerably narrower than any of the color match curves: x , y and z . Suppose the three stated sources have the distribution of spectral density 1 2 3 related to the value of measuring the radiation P () , P () and P () with the
97 maximum intensity values on the wavelengths max1 , max 2 and max3 respectively. Let us assume that these three radiation sources have the chromaticity coordinates (,)xy, (,)xy and (,)xy respectively. 11 22 33 Then the resulting color A can be represented in the color space XYZ using the following three color coordinates: 1 2 3 xA P x d P x d P x d 0 0 0
x()()()max1 P 1 x max 2 P 2 x max3 P 3 1 2 3 yA P y d P y d P y d 0 0 0 , (10.1)
y()()()max1 P 1 y max 2 P 2 y max3 P 3 1 2 3 zA P z d P z d P z d 0 0 0
z ()()()max1P 1 z max 2 P 2 z max3 P 3 where P1, P2 and P3 present the optical flux of three radiation sources used as the primary colors. Consequently, the coordinates of the radiation color obtained by additive mixing of the N amount of primary colors formed by the narrow-spectrum radiation sources, are calculated using the following ratios
x x(max1 ) P 1 x ( max 2 ) P 2 ... x ( maxi ) P i ... x ( max N ) P N N xP()maxii i1
y y(max1 ) P 1 y ( max 2 ) P 2 ... y ( maxi ) P i ... y ( max N ) P N N . (10.2) yP()maxii i1
z z(max1 ) P 1 z ( max 2 ) P 2 ... z ( maxi ) P i ... z ( max N ) PN N zP()maxii i1 Let us continue calculating the chromaticity coordinates for the radiation formed by the three sources. Let each of the three sources of radiation used contributes to the creation of the resulting radiation in proportion to the following weighting factors
K1 x()()() max1 P 1 y max1 P 1 z max1 P 1
K2 x()()() max 2 P 2 y max 2 P 2 z max 2 P 2 . (10.3)
K3 x()()() max3 P 3 y max3 P 3 z max3 P 3
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One can deternine the chromaticity coordinates of the resulting color from the equations (10.2) – (10.3) : x K x K x K x 1 1 2 2 3 3 KKK 1 2 3 . (10.4) y K y K y K y 1 1 2 2 3 3 KKK1 2 3 Thus, the problem is solved. Accordingly, the coordinates of the radiation chromaticity obtained by additive mixing of the N amount of primary colors formed by the narrow-spectrum radiation sources, are calculated using the following ratios N xKii i1 x N Ki i1 . (10.5) N yKii i1 y N Ki i1 These equations demonstrate that the chromaticity coordinates of a multi-component color are linear combinations of chromaticity coordinates of each source with weighting factors Ki . Let us assume that we have to solve the opposite problem – to determine the optical flux of radiation sources used to obtain radiation with the predetermined chromaticity coordinates (,)xy. We shall consider the solution of this problem for the color scale formed by three colors A1 , A2 and A3 of the radiation sources. Let us assume that the chromaticity coordinates of the stated three radiation sources (,)xy11, (,)xy22 and (,)xy33, аs well as the distribution of 1 2 spectral density related to the value of measuring the radiation P () , P () and 3 P () with the maximum intensity values on the wavelengths max1 , max 2 and
max3 respectively are known values. Therefore, the problem is reduced to the necessity to calculate the weighting factors Ki from the system of equations (10.4). However, there are only two equations whereas there are three weighting factors. Then let the weighting factor for the second source K2 1, for example. Therefore, it is easy to ascertain that the remaining coefficients can be calculated from the following ratios
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K2 1
()()()()y2 y x x 1 y 1 y x 2 x KK32 . (10.6) ()()()()y y3 x x 1 y y 1 x 3 x
K2()() x 2 x K 3 x 3 x K1 ()xx 1 Then, proceeding from (10.3), one can calculate the optical flux of three radiation sources used as the primary colors, P1, P2 and P3 , accordingly
K1 P1 x()()()max1 y max1 z max1
K2 P2 . (10.7) x()()()max 2 y max 2 z max 2
K3 P3 x()()()max3 y max3 z max3 It should be noted that these calculations are only valid for the narrow-spectrum radiation sources used as primary colors. For the sources with the wide spectra of radiation the assumption (10.1) has no effect.
100
LITERATURE REFERENCES
1 GOST 13088-67 Colorimetry. Terms, symbols. 2 J. Gaudin "Kolorimetria pri video-obrabotke" ("Colorimetry applied in video editing", orig. name "Colorimétrie appliquée à la vidéo"), M.: Technosphera publ., 2008. 3 Nicholls John, Martin Robert, Wallace Bruce, Fuchs Paul, "Ot neyrona k mozgu" (orig. name "From Neuron to Brain"): Transl. of the English version, 2nd ed. – M.: LKI publishers, 2008. – 672 pp., color supplementary sheets. ISBN 978-5-382-00808-0. 4 Gregory Richard Langton, "Razumnyi glaz: Kak my uznaem to, chto nam ne dano v oschuscheniyah" (Orig. name "The Intelligent Eye"). Transl. of the English version, 3rd ed. – M.: LIBROCOM Publishers, 2009. – 240 pp., color supplementary sheets. ISBN 978-5-397-00597-4. 5 Godwin T. (1984) The Biochemistry of the carotenoids, Volume 2, Animals, 2nd ed. NY:Chapman&Hall, p.181. 6 James, T. Fulton, (2002) Processes In Biological Vision. 7 Baylor D.A., Lamb T.D., and Yau K.W. 1979. The membrane current of single rod outer segments. J. Physiol. 288: 589-611. 8 Ye. Yustova Color measurement (Colorimetry). – SPb: St. Petersburg University Publishers, in 2000. – 397 pp. ISBN 5-288-02648-3. 9 Susana Martinez-Conde, Stephen L. Macknik (2007) Windows on the mind. J. Scientific American. August 2007: 56-63. 10 Е. Schrödinger, Gesichtsempfindungen 1 Hand. der Рhysik Müller Pacillet, 1929 г. 11 F. Schubert Light-Emitting Diodes / Translated from English, ed. by A. Younovich. – 2-nd ed. – M.: FIZMATLIT Publishers, 2008. – 496 pp. – ISBN 978-5-9221-0851-5. 12 M. Krivosheyev, A. Kustarev Color measurement. – M.: Energoatomizdat Publishers, 1990. – 240 pages: ill. ISBN 5-283-00545-3. 13 M. Fairchild "Modeli tsvetovogo vospriyatiya" (Color Appearance Models), 2nd ed.: transl. from English – SPb, 2006. 14 S. Kravkov Color vision - published by the Academy of Sciences of the USSR, Moscow, 1951, 175 pages 15 N. Nyuberg "Izmerenie tsveta i tsvetovye standarty" (Color Measurement and Color Standards) - State Publishing House STANDARDIZATION AND RATIONALIZATION, Moscow, 1933, 104 pages 16 Ch. Izmailov, Ye. Sokolov, A. Cheriorizov "Psikhofiziologiya tsvetovogo zreniya" (Psychophysiology of Color Vision). Moscow: MGU Publishing house, 1997. – 206 pp. ISBN 5-211-00228-8.
101
17 G. Agoston Color Theory and its Application in Art and Design: Translated from English – M.: Mir Publishing House, 1982. – 184 pages, illustrated. 18 M. Gurevich "Tsvet i ego izmerenie" (Color and its Measurement) USSR Academy of Sciences Publishing House, Moscow-Leningrad, 1950 19 M. Minnart "Svet i tsvet v prirode" (Light and Color in Nature) Moscow, 1969, 360 pages, illustrated 20 Ye. Kirillov "Tsvetovedenie" (Color Science) Study guide for high schools. – Moscow: Legprombytizdat, 1987 - 128 pages 21 Goethe’s Theory of Colours; Translated from German: with notes by Charles Lock Eastlake, r.a., f.r.s. London: John Murray, Albemarle street. 1840. 22 A. Louizov "Glaz i svet" (Eye and Color). L.: Energoatomizdat. Leningradskoye Otdeleniye, 1983 – 144 pages, illustrated. 23 M. Domasev, S. Gnatyuk "Tsvet, upravlenie tsvetom, tsvetovye raschety i izmereniya" (Color, Color Management, Color Calculations and Measurements) – SPb: Piter Publishing House, 2009. – 224 pages: ill. - ("Training Course" series). ISBN 978-5-388-00341-6. 24 Colorimetry: understanding the CIE system / edited by Janos Schanda. Published by John Willey & Sons, Inc., Hoboken, New Jersey, Canada, 2007. ISBN 978-0-470-04904-4. 25 V. Peshkova, M. Gromova "Prakticheskoe rukovodstvo po spektrofotometrii i kolorimetrii" (Practical Manual on Spectral Photometry and Colorimetry). 2nd Edition, amended translation. Moscow: MGU Publishing House, 1965, 132 pages, ill. 26 D. Judd, G. Vyshetsky, "Tsvet v nauke i tekhnike" (Color in Science and Technology): Translated from English – edited by D.Eng.Sc., Prof. L. Artyushin – Moscow: Mir Publishing House, 1978 – 592 pages, ill. 27 www.brucelindbloom.com website. 28 D. Forsyth, J. Ponce, "Kompyuternoe zrenie. Sovremennyi podkhod" (Computer Vision. A Modern Approach.) : Translated from English – M.: "Williams" Publishing House, 2004 – 928 pages: ill. – Parallel English title, ISBN 5-8459-0542-7. 29 R. W. G. Hunt. "Tsvetovosproizvedenie" (The Reproduction of Colour"), 6th edition: transl. from English – SPb, 2009. 30 A. A. Bergh, P. J. Dean "Svetodiody" ("Light-Emitting Diodes"): Translated from English – M.: "Mir" Publishing House - 1979.
102
APPENDICES
Appendix 1 – Color match curves for CIE 1931 color space , nm x() y() z () , nm x() y() z () 360 0.000130 0.000004 0.000606 596 1.059794 0.682219 0.000969 361 0.000146 0.000004 0.000681 597 1.061799 0.669472 0.000930 362 0.000164 0.000005 0.000765 598 1.062807 0.656674 0.000887 363 0.000184 0.000006 0.000860 599 1.062910 0.643845 0.000843 364 0.000207 0.000006 0.000967 600 1.062200 0.631000 0.000800 365 0.000232 0.000007 0.001086 601 1.060735 0.618156 0.000761 366 0.000261 0.000008 0.001221 602 1.058444 0.605314 0.000724 367 0.000293 0.000009 0.001373 603 1.055224 0.592476 0.000686 368 0.000329 0.000010 0.001544 604 1.050977 0.579638 0.000645 369 0.000370 0.000011 0.001734 605 1.045600 0.566800 0.000600 370 0.000415 0.000012 0.001946 606 1.039037 0.553961 0.000548 371 0.000464 0.000014 0.002177 607 1.031361 0.541137 0.000492 372 0.000519 0.000016 0.002436 608 1.022666 0.528353 0.000435 373 0.000582 0.000017 0.002732 609 1.013048 0.515632 0.000383 374 0.000655 0.000020 0.003078 610 1.002600 0.503000 0.000340 375 0.000742 0.000022 0.003486 611 0.991368 0.490469 0.000307 376 0.000845 0.000025 0.003975 612 0.979331 0.478030 0.000283 377 0.000965 0.000028 0.004541 613 0.966492 0.465678 0.000265 378 0.001095 0.000032 0.005158 614 0.952848 0.453403 0.000252 379 0.001231 0.000035 0.005803 615 0.938400 0.441200 0.000240 380 0.001368 0.000039 0.006450 616 0.923194 0.429080 0.000230 381 0.001502 0.000043 0.007083 617 0.907244 0.417036 0.000221 382 0.001642 0.000047 0.007745 618 0.890502 0.405032 0.000212 383 0.001802 0.000052 0.008501 619 0.872920 0.393032 0.000202 384 0.001996 0.000057 0.009415 620 0.854450 0.381000 0.000190 385 0.002236 0.000064 0.010550 621 0.835084 0.368918 0.000174 386 0.002535 0.000072 0.011966 622 0.814946 0.356827 0.000156 387 0.002893 0.000082 0.013656 623 0.794186 0.344777 0.000136 388 0.003301 0.000094 0.015588 624 0.772954 0.332818 0.000117 389 0.003753 0.000106 0.017730 625 0.751400 0.321000 0.000100 390 0.004243 0.000120 0.020050 626 0.729584 0.309338 0.000086 391 0.004762 0.000135 0.022511 627 0.707589 0.297850 0.000075 392 0.005330 0.000151 0.025203 628 0.685602 0.286594 0.000065 393 0.005979 0.000170 0.028280 629 0.663810 0.275625 0.000057 394 0.006741 0.000192 0.031897 630 0.642400 0.265000 0.000050 395 0.007650 0.000217 0.036210 631 0.621515 0.254763 0.000044 103
396 0.008751 0.000247 0.041438 632 0.601114 0.244890 0.000039 397 0.010029 0.000281 0.047504 633 0.581105 0.235334 0.000036 398 0.011422 0.000319 0.054120 634 0.561398 0.226053 0.000033 399 0.012869 0.000357 0.060998 635 0.541900 0.217000 0.000030 400 0.014310 0.000396 0.067850 636 0.522600 0.208162 0.000028 401 0.015704 0.000434 0.074486 637 0.503546 0.199549 0.000026 402 0.017147 0.000473 0.081362 638 0.484744 0.191155 0.000024 403 0.018781 0.000518 0.089154 639 0.466194 0.182974 0.000022 404 0.020748 0.000572 0.098540 640 0.447900 0.175000 0.000020 405 0.023190 0.000640 0.110200 641 0.429861 0.167224 0.000018 406 0.026207 0.000725 0.124613 642 0.412098 0.159646 0.000016 407 0.029782 0.000826 0.141702 643 0.394644 0.152278 0.000014 408 0.033881 0.000941 0.161304 644 0.377533 0.145126 0.000012 409 0.038468 0.001070 0.183257 645 0.360800 0.138200 0.000010 410 0.043510 0.001210 0.207400 646 0.344456 0.131500 0.000008 411 0.048996 0.001362 0.233692 647 0.328517 0.125025 0.000005 412 0.055023 0.001531 0.262611 648 0.313019 0.118779 0.000003 413 0.061719 0.001720 0.294775 649 0.298001 0.112769 0.000001 414 0.069212 0.001935 0.330799 650 0.283500 0.107000 0.000000 415 0.077630 0.002180 0.371300 651 0.269545 0.101476 0.000000 416 0.086958 0.002455 0.416209 652 0.256118 0.096189 0.000000 417 0.097177 0.002764 0.465464 653 0.243190 0.091123 0.000000 418 0.108406 0.003118 0.519695 654 0.230727 0.086265 0.000000 419 0.120767 0.003526 0.579530 655 0.218700 0.081600 0.000000 420 0.134380 0.004000 0.645600 656 0.207097 0.077121 0.000000 421 0.149358 0.004546 0.718484 657 0.195923 0.072826 0.000000 422 0.165396 0.005159 0.796713 658 0.185171 0.068710 0.000000 423 0.181983 0.005829 0.877846 659 0.174832 0.064770 0.000000 424 0.198611 0.006546 0.959439 660 0.164900 0.061000 0.000000 425 0.214770 0.007300 1.039050 661 0.155367 0.057396 0.000000 426 0.230187 0.008087 1.115367 662 0.146230 0.053955 0.000000 427 0.244880 0.008909 1.188497 663 0.137490 0.050674 0.000000 428 0.258777 0.009768 1.258123 664 0.129147 0.047550 0.000000 429 0.271808 0.010664 1.323930 665 0.121200 0.044580 0.000000 430 0.283900 0.011600 1.385600 666 0.113640 0.041759 0.000000 431 0.294944 0.012573 1.442635 667 0.106465 0.039085 0.000000 432 0.304897 0.013583 1.494804 668 0.099690 0.036564 0.000000 433 0.313787 0.014630 1.542190 669 0.093331 0.034200 0.000000 434 0.321645 0.015715 1.584881 670 0.087400 0.032000 0.000000 435 0.328500 0.016840 1.622960 671 0.081901 0.029963 0.000000
104
436 0.334351 0.018007 1.656405 672 0.076804 0.028077 0.000000 437 0.339210 0.019214 1.685296 673 0.072077 0.026329 0.000000 438 0.343121 0.020454 1.709875 674 0.067687 0.024708 0.000000 439 0.346130 0.021718 1.730382 675 0.063600 0.023200 0.000000 440 0.348280 0.023000 1.747060 676 0.059807 0.021801 0.000000 441 0.349600 0.024295 1.760045 677 0.056282 0.020501 0.000000 442 0.350147 0.025610 1.769623 678 0.052971 0.019281 0.000000 443 0.350013 0.026959 1.776264 679 0.049819 0.018121 0.000000 444 0.349287 0.028351 1.780433 680 0.046770 0.017000 0.000000 445 0.348060 0.029800 1.782600 681 0.043784 0.015904 0.000000 446 0.346373 0.031311 1.782968 682 0.040875 0.014837 0.000000 447 0.344262 0.032884 1.781700 683 0.038073 0.013811 0.000000 448 0.341809 0.034521 1.779198 684 0.035405 0.012835 0.000000 449 0.339094 0.036226 1.775867 685 0.032900 0.011920 0.000000 450 0.336200 0.03800 1.772110 686 0.030564 0.011068 0.000000 451 0.333198 0.039847 1.768259 687 0.028381 0.010273 0.000000 452 0.330041 0.041768 1.764039 688 0.026345 0.009533 0.000000 453 0.326636 0.043766 1.758944 689 0.024453 0.008846 0.000000 454 0.322887 0.045843 1.752466 690 0.022700 0.008210 0.000000 455 0.318700 0.048000 1.744100 691 0.021084 0.007624 0.000000 456 0.314025 0.050244 1.733560 692 0.019600 0.007085 0.000000 457 0.308884 0.052573 1.720858 693 0.018237 0.006591 0.000000 458 0.303290 0.054981 1.705937 694 0.016987 0.006138 0.000000 459 0.297258 0.057459 1.688737 695 0.015840 0.005723 0.000000 460 0.290800 0.060000 1.669200 696 0.014791 0.005343 0.000000 461 0.283970 0.062602 1.647529 697 0.013831 0.004996 0.000000 462 0.276721 0.065278 1.623413 698 0.012949 0.004676 0.000000 463 0.268918 0.068042 1.596022 699 0.012129 0.004380 0.000000 464 0.260423 0.070911 1.564528 700 0.011359 0.004102 0.000000 465 0.251100 0.073900 1.528100 701 0.010629 0.003838 0.000000 466 0.240848 0.077016 1.486111 702 0.009939 0.003589 0.000000 467 0.229851 0.080266 1.439522 703 0.009288 0.003354 0.000000 468 0.218407 0.083667 1.389880 704 0.008679 0.003134 0.000000 469 0.206811 0.087233 1.338736 705 0.008111 0.002929 0.000000 470 0.195360 0.090980 1.287640 706 0.007582 0.002738 0.000000 471 0.184214 0.094918 1.237422 707 0.007089 0.002560 0.000000 472 0.173327 0.099046 1.187824 708 0.006627 0.002393 0.000000 473 0.162688 0.103367 1.138761 709 0.006195 0.002237 0.000000 474 0.152283 0.107885 1.090148 710 0.005790 0.002091 0.000000 475 0.142100 0.112600 1.041900 711 0.005410 0.001954 0.000000
105
476 0.132179 0.117532 0.994198 712 0.005053 0.001825 0.000000 477 0.122570 0.122674 0.947347 713 0.004718 0.001704 0.000000 478 0.113275 0.127993 0.901453 714 0.004404 0.001590 0.000000 479 0.104298 0.133453 0.856619 715 0.004109 0.001484 0.000000 480 0.095640 0.139020 0.812950 716 0.003834 0.001384 0.000000 481 0.087300 0.144676 0.770517 717 0.003576 0.001291 0.000000 482 0.079308 0.150469 0.729445 718 0.003334 0.001204 0.000000 483 0.071718 0.156462 0.689914 719 0.003109 0.001123 0.000000 484 0.064581 0.162718 0.652105 720 0.002899 0.001047 0.000000 485 0.057950 0.169300 0.616200 721 0.002704 0.000977 0.000000 486 0.051862 0.176243 0.582329 722 0.002523 0.000311 0.000000 487 0.046282 0.183558 0.550416 723 0.002354 0.000850 0.000000 488 0.041151 0.191274 0.520338 724 0.002197 0.000793 0.000000 489 0.036413 0.199418 0.491967 725 0.002049 0.000740 0.000000 490 0.032010 0.208020 0.465180 726 0.001911 0.000690 0.000000 491 0.027917 0.217120 0.439925 727 0.001781 0.000643 0.000000 492 0.024144 0.226735 0.416184 728 0.001660 0.000690 0.000000 493 0.020687 0.236857 0.393882 729 0.001546 0.000558 0.000000 494 0.017540 0.247481 0.372946 730 0.001440 0.000520 0.000000 495 0.014700 0.258600 0.353300 731 0.001340 0.000484 0.000000 496 0.012162 0.270185 0.334858 732 0.001246 0.000450 0.000000 497 0.009920 0.282294 0.317552 733 0.001158 0.000418 0.000000 498 0.007967 0.295051 0.301338 734 0.001076 0.000389 0.000000 499 0.006296 0.308578 0.286169 735 0.001000 0.000361 0.000000 500 0.004900 0.323000 0.272000 736 0.000929 0.000335 0.000000 501 0.003778 0.338402 0.258817 737 0.000862 0.000311 0.000000 502 0.002945 0.354686 0.246484 738 0.000801 0.000289 0.000000 503 0.002425 0.371699 0.234772 739 0.000743 0.000268 0.000000 504 0.002236 0.389288 0.223453 740 0.000690 0.000249 0.000000 505 0.002400 0.407300 0.212300 741 0.000641 0.000231 0.000000 506 0.002926 0.425630 0.201169 742 0.000595 0.000215 0.000000 507 0.003837 0.444310 0.190120 743 0.000552 0.000199 0.000000 508 0.005175 0.463394 0.179225 744 0.000512 0.000185 0.000000 509 0.006982 0.482940 0.168561 745 0.000476 0.000172 0.000000 510 0.009300 0.503000 0.158200 746 0.000442 0.000160 0.000000 511 0.012149 0.523569 0.148138 747 0.000412 0.000149 0.000000 512 0.015536 0.544512 0.138376 748 0.000383 0.000138 0.000000 513 0.019478 0.565690 0.128994 749 0.000357 0.000129 0.000000 514 0.023993 0.586965 0.120075 750 0.000332 0.000120 0.000000 515 0.029000 0.608200 0.111700 751 0.000310 0.000112 0.000000
106
516 0.034815 0.629346 0.103905 752 0.000289 0.000104 0.000000 517 0.041120 0.650307 0.096667 753 0.000270 0.000097 0.000000 518 0.047985 0.670875 0.089983 754 0.000252 0.000091 0.000000 519 0.055379 0.690842 0.083845 755 0.000235 0.000085 0.000000 520 0.063270 0.710000 0.078250 756 0.000219 0.000079 0.000000 521 0.071635 0.728185 0.073209 757 0.000205 0.000074 0.000000 522 0.080462 0.745464 0.068678 758 0.000191 0.000069 0.000000 523 0.089740 0.761969 0.064568 759 0.000178 0.000064 0.000000 524 0.099456 0.777837 0.060788 760 0.000166 0.000060 0.000000 525 0.109600 0.793200 0.057250 761 0.000155 0.000056 0.000000 526 0.120167 0.808110 0.053904 762 0.000145 0.000052 0.000000 527 0.131115 0.822496 0.050747 763 0.000135 0.000049 0.000000 528 0.142368 0.836307 0.047753 764 0.000126 0.000045 0.000000 529 0.153854 0.849492 0.044899 765 0.000117 0.000042 0.000000 530 0.165500 0.862000 0.042160 766 0.000110 0.000040 0.000000 531 0.177257 0.873811 0.039507 767 0.000102 0.000037 0.000000 532 0.189140 0.884962 0.036936 768 0.000095 0.000034 0.000000 533 0.201169 0.895494 0.034458 769 0.000089 0.000032 0.000000 534 0.213366 0.905443 0.032089 770 0.000083 0.000030 0.000000 535 0.225750 0.914850 0.029840 771 0.000078 0.000028 0.000000 536 0.238321 0.923735 0.028812 772 0.000072 0.000026 0.000000 537 0.251067 0.932092 0.025694 773 0.000067 0.000024 0.000000 538 0.263992 0.939923 0.023787 774 0.000063 0.000023 0.000000 539 0.277102 0.947225 0.021989 775 0.000059 0.000021 0.000000 540 0.290400 0.954000 0.020300 776 0.000055 0.000020 0.000000 541 0.303891 0.960256 0.018718 777 0.000051 0.000018 0.000000 542 0.317573 0.966007 0.017240 778 0.000048 0.000017 0.000000 543 0.331438 0.971261 0.015864 779 0.000044 0.000016 0.000000 544 0.345483 0.976023 0.014585 780 0.000042 0.000015 0.000000 545 0.359700 0.980300 0.013400 781 0.000039 0.000014 0.000000 546 0.374084 0.984092 0.012307 782 0.000036 0.000013 0.000000 547 0.388640 0.987418 0.11302 783 0.000034 0.000012 0.000000 548 0.403378 0.990313 0.010378 784 0.000031 0.000011 0.000000 549 0.418312 0.992812 0.009529 785 0.000029 0.000011 0.000000 550 0.433450 0.994950 0.008750 786 0.000027 0.000010 0.000000 551 0.448795 0.996711 0.008035 787 0.000026 0.000009 0.000000 552 0.464336 0.998098 0.007382 788 0.000024 0.000009 0.000000 553 0.480064 0.999112 0.006785 789 0.000022 0.000008 0.000000 554 0.495971 0.999748 0.006243 790 0.000021 0.000007 0.000000 555 0.512050 1.000000 0.005750 791 0.000019 0.000007 0.000000
107
556 0.528296 0.999857 0.005304 792 0.000018 0.000006 0.000000 557 0.544692 0.999305 0.004900 793 0.000017 0.000006 0.000000 558 0.561209 0.998326 0.004534 794 0.000016 0.000006 0.000000 559 0.577822 0.996899 0.004202 795 0.000015 0.000005 0.000000 560 0.594500 0.995000 0.003900 796 0.000014 0.000005 0.000000 561 0.611221 0.992601 0.003623 797 0.000013 0.000005 0.000000 562 0.627976 0.989743 0.003371 798 0.000012 0.000004 0.000000 563 0.644760 0.986444 0.003141 799 0.000011 0.000004 0.000000 564 0.661570 0.982724 0.002935 800 0.000010 0.000004 0.000000 565 0.678400 0.978600 0.002750 801 0.000010 0.000003 0.000000 566 0.695239 0.974084 0.002585 802 0.000009 0.000003 0.000000 567 0.712059 0.969171 0.002439 803 0.000008 0.000003 0.000000 568 0.728828 0.963857 0.002309 804 0.000008 0.000003 0.000000 569 0.745549 0.958135 0.002197 805 0.000007 0.000003 0.000000 570 0.762100 0.952000 0.002100 806 0.000007 0.000002 0.000000 571 0.778543 0.945450 0.002018 807 0.000006 0.000002 0.000000 572 0.794826 0.938499 0.001948 808 0.000006 0.000002 0.000000 573 0.810926 0.931163 0.001890 809 0.000005 0.000002 0.000000 574 0.826825 0.923458 0.001841 810 0.000005 0.000002 0.000000 575 0.842500 0.915400 0.001800 811 0.000005 0.000002 0.000000 576 0.857933 0.907006 0.001766 812 0.000004 0.000002 0.000000 577 0.873082 0.898277 0.001738 813 0.000004 0.000001 0.000000 578 0.887894 0.889205 0.001711 814 0.000004 0.000001 0.000000 579 0.902318 0.879782 0.001683 815 0.000004 0.000001 0.000000 580 0.916300 0.870000 0.001650 816 0.000003 0.000001 0.000000 581 0.929800 0.859861 0.001610 817 0.000003 0.000001 0.000000 582 0.942798 0.849392 0.001564 818 0.000003 0.000001 0.000000 583 0.955278 0.838622 0.001514 819 0.000003 0.000001 0.000000 584 0.967218 0.827581 0.001459 820 0.000003 0.000001 0.000000 585 0.978600 0.816300 0.001400 821 0.000002 0.000001 0.000000 586 0.989386 0.804795 0.001337 822 0.000002 0.000001 0.000000 587 0.999549 0.793082 0.001270 823 0.000002 0.000001 0.000000 588 1.009089 0.781192 0.001205 824 0.000002 0.000001 0.000000 589 1.018006 0.769155 0.001147 825 0.000002 0.000001 0.000000 590 1.026300 0.757000 0.001100 826 0.000002 0.000001 0.000000 591 1.033983 0.744754 0.001069 827 0.000001 0.000001 0.000000 592 1.040986 0.732422 0.001049 828 0.000001 0.000000 0.000000 593 1.047188 0.720004 0.001036 829 0.000001 0.000000 0.000000 594 1.052467 0.707497 0.001021 830 0.000001 0.000000 0.000000 595 1.056700 0.694900 0.001000
108
Appendix 2 – Color temperature Tc in Mired ( ), chromaticity coordinates of a
Planck's emitter on the CIE 1976 color diagram (u0 , v0 ) and tangents of the isothermal line inclination (t )
Tc , u0 v0 Tc , u0 v0 0 0.18006 0.26352 -0.24341 250 0.22511 0.33439 -1.4512 10 0.18066 0.26589 -0.25479 275 0.23247 0.33904 -1.7298 20 0.18133 0.26846 -0.26876 300 0.2401 0.34308 -2.0637 30 0.18208 0.27119 -0.28539 325 0.24792 0.34655 -2.4681 40 0.18293 0.27407 -0.3047 350 0.25591 0.34951 -2.9641 50 0.18388 0.27709 -0.32675 375 0.264 0.352 -3.5814 60 0.18494 0.28021 -0.35156 400 0.27218 0.35407 -4.3633 70 0.18611 0.28342 -0.37915 425 0.28039 0.35577 -5.3762 80 0.1874 0.28668 -0.40955 450 0.28863 0.35714 -6.7262 90 0.1888 0.28997 -0.44278 475 0.29685 0.35823 -8.5955 100 0.19032 0.29326 -0.47888 500 0.30505 0.35907 -11.324 125 0.19462 0.30141 -0.58204 525 0.3132 0.35968 -15.628 150 0.19962 0.30921 -0.70471 550 0.32129 0.36011 -23.325 175 0.20525 0.31647 -0.84901 575 0.32931 0.36038 -40.77 200 0.21142 0.32312 -1.0182 600 0.33724 0.36051 -116.45 225 0.21807 0.32909 -1.2168
Appendix 3 – Color coordinates of the primary white color sources
Source xW yW zW A 109.850 100 35.585 B 99.072 100 85.223 C 98.074 100 118.232 D50 96.422 100 82.521 D55 95.682 100 92.149 D65 95.047 100 108.883 D75 94.972 100 122.638 E 100 100 100 F2 99.186 100 67.393 F7 95.041 100 108.747 F11 100.962 100 64.350
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Appendix 4 – Parameters of the various RGB color spaces types
Primary red Primary green Primary blue Type W xr yr yr xg yg yg xb yb yb Lab Gamut - D50 ------Adobe RGB 2.2 D65 0.6400 0.3300 0.297361 0.2100 0.7100 0.627355 0.1500 0.0600 0.075285 (1998) Apple RGB 1.8 D65 0.6250 0.3400 0.244634 0.2800 0.5950 0.672034 0.1550 0.0700 0.083332 Best RGB 2.2 D50 0.7347 0.2653 0.228457 0.2150 0.7750 0.737352 0.1300 0.0350 0.034191 Beta RGB 2.2 D50 0.6888 0.3112 0.303273 0.1986 0.7551 0.663786 0.1265 0.0352 0.032941 Bruce RGB 2.2 D65 0.6400 0.3300 0.240995 0.2800 0.6500 0.683554 0.1500 0.0600 0.075452 CIE RGB 2.2 E 0.7350 0.2650 0.176204 0.2740 0.7170 0.812985 0.1670 0.0090 0.010811 ColorMatch RGB 1.8 D50 0.6300 0.3400 0.274884 0.2950 0.6050 0.658132 0.1500 0.0750 0.066985 Don RGB 4 2.2 D50 0.6960 0.3000 0.278350 0.2150 0.7650 0.687970 0.1300 0.0350 0.033680 ECI RGB v2 L* D50 0.6700 0.3300 0.320250 0.2100 0.7100 0.602071 0.1400 0.0800 0.077679 Ekta Space PS5 2.2 D50 0.6950 0.3050 0.260629 0.2600 0.7000 0.734946 0.1100 0.0050 0.004425 NTSC RGB 2.2 C 0.6700 0.3300 0.298839 0.2100 0.7100 0.586811 0.1400 0.0800 0.114350 PAL/ SECAM 2.2 D65 0.6400 0.3300 0.222021 0.2900 0.6000 0.706645 0.1500 0.0600 0.071334 RGB ProPhoto RGB 1.8 D50 0.7347 0.2653 0.288040 0.1596 0.8404 0.711874 0.0366 0.0001 0.000086 SMPTE-C RGB 2.2 D65 0.6300 0.3400 0.212395 0.3100 0.5950 0.701049 0.1550 0.0700 0.086556 sRGB - D65 0.6400 0.3300 0.212656 0.3000 0.6000 0.715158 0.1500 0.0600 0.072186 Wide Gamut 2.2 D50 0.7350 0.2650 0.258187 0.1150 0.8260 0.724938 0.1570 0.0180 0.016875 RGB
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Appendix 5 – Direct and inversed correction matrices for the different methods of color correction M 1 Method A M A 1.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 XYZ 0.0000000 1.0000000 0.0000000 0.0000000 1.0000000 0.0000000 Scaling 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 1.0000000 0.8951000 0.2664000 -0.1614000 0.9869929 -0.1470543 0.1599627 Bradford -0.7502000 1.7135000 0.0367000 0.4323053 0.5183603 0.0492912 0.0389000 -0.0685000 1.0296000 -0.0085287 0.0400428 0.9684867 0.4002400 0.7076000 -0.0808100 1.8599364 -1.1293816 0.2198974 Von -0.2263000 1.1653200 0.0457000 0.3611914 0.6388125 -0.0000064 Kries 0.0000000 0.0000000 0.9182200 0.0000000 0.0000000 1.0890636
Appendix 6 – Reflectivity of eight CIE reference color surfaces
, nm R1() R2 () R3() R4 () R5() R6 () R7 () R8() 360 0.116 0.053 0.058 0.057 0.143 0.079 0.150 0.075 365 0.136 0.055 0.059 0.059 0.187 0.081 0.177 0.078 370 0.159 0.059 0.061 0.062 0.233 0.089 0.218 0.084 375 0.190 0.064 0.063 0.067 0.269 0.113 0.293 0.090 380 0.219 0.070 0.065 0.074 0.295 0.151 0.378 0.104 385 0.239 0.079 0.068 0.083 0.306 0.203 0.459 0.129 390 0.252 0.089 0.070 0.093 0.310 0.265 0.524 0.170 395 0.256 0.101 0.072 0.105 0.312 0.339 0.546 0.240 400 0.256 0.111 0.073 0.116 0.313 0.410 0.551 0.319 405 0.254 0.116 0.073 0.121 0.315 0.464 0.555 0.416 410 0.252 0.118 0.074 0.124 0.319 0.492 0.559 0.462 415 0.248 0.120 0.074 0.126 0.322 0.508 0.560 0.482 420 0.244 0.121 0.074 0.128 0.326 0.517 0.561 0.490 425 0.240 0.122 0.073 0.131 0.330 0.524 0.558 0.488 430 0.237 0.122 0.073 0.135 0.334 0.531 0.556 0.482 435 0.232 0.122 0.073 0.139 0.339 0.538 0.551 0.473 440 0.230 0.123 0.073 0.144 0.346 0.544 0.544 0.462 445 0.226 0.124 0.073 0.151 0.352 0.551 0.535 0.450 450 0.225 0.127 0.074 0.161 0.360 0.556 0.522 0.439 455 0.222 0.128 0.075 0.172 0.369 0.556 0.506 0.426 460 0.220 0.131 0.077 0.186 0.381 0.554 0.488 0.413 465 0.218 0.134 0.080 0.205 0.394 0.549 0.469 0.397 470 0.216 0.138 0.085 0.229 0.403 0.541 0.448 0.382 111
475 0.214 0.143 0.094 0.254 0.410 0.531 0.429 0.366 480 0.214 0.150 0.109 0.281 0.415 0.519 0.408 0.352 485 0.214 0.159 0.126 0.308 0.418 0.504 0.385 0.337 490 0.216 0.174 0.148 0.332 0.419 0.488 0.363 0.325 495 0.218 0.190 0.172 0.352 0.417 0.469 0.341 0.310 500 0.223 0.207 0.198 0.370 0.413 0.450 0.324 0.299 505 0.225 0.225 0.221 0.383 0.409 0.431 0.311 0.289 510 0.226 0.242 0.241 0.390 0.403 0.414 0.301 0.283 515 0.226 0.253 0.260 0.394 0.396 0.395 0.291 0.276 520 0.225 0.260 0.278 0.395 0.389 0.377 0.283 0.270 525 0.225 0.264 0.302 0.392 0.381 0.358 0.273 0.262 530 0.227 0.267 0.339 0.385 0.372 0.341 0.265 0.256 535 0.230 0.269 0.370 0.377 0.363 0.325 0.260 0.251 540 0.236 0.272 0.392 0.367 0.353 0.309 0.257 0.250 545 0.245 0.276 0.399 0.354 0.342 0.293 0.257 0.251 550 0.253 0.282 0.400 0.341 0.331 0.279 0.259 0.254 555 0.262 0.289 0.393 0.327 0.320 0.265 0.260 0.258 560 0.272 0.299 0.380 0.312 0.308 0.253 0.260 0.264 565 0.283 0.309 0.365 0.296 0.296 0.241 0.258 0.269 570 0.298 0.322 0.349 0.280 0.284 0.234 0.256 0.272 575 0.318 0.329 0.332 0.263 0.271 0.227 0.254 0.274 580 0.341 0.335 0.315 0.247 0.260 0.225 0.254 0.278 585 0.367 0.339 0.299 0.299 0.247 0.222 0.259 0.284 590 0.390 0.341 0.285 0.214 0.232 0.221 0.270 0.295 595 0.409 0.341 0.272 0.198 0.220 0.220 0.284 0.316 600 0.424 0.342 0.264 0.185 0.210 0.220 0.302 0.348 605 0.435 0.342 0.257 0.175 0.200 0.220 0.324 0.384 610 0.442 0.342 0.252 0.169 0.194 0.220 0.344 0.434 615 0.448 0.341 0.247 0.164 0.189 0.220 0.362 0.482 620 0.450 0.341 0.241 0.160 0.185 0.223 0.377 0.528 625 0.451 0.339 0.235 0.156 0.183 0.227 0.389 0.568 630 0.451 0.339 0.229 0.154 0.180 0.233 0.400 0.604 635 0.451 0.338 0.224 0.152 0.177 0.239 0.410 0.629 640 0.451 0.338 0.220 0.151 0.176 0.244 0.420 0.648 645 0.451 0.337 0.217 0.149 0.175 0.251 0.429 0.663 650 0.450 0.336 0.216 0.148 0.175 0.258 0.438 0.676 655 0.450 0.335 0.216 0.148 0.175 0.263 0.445 0.685 660 0.451 0.334 0.219 0.148 0.175 0.268 0.452 0.693 665 0.451 0.332 0.224 0.149 0.177 0.273 0.457 0.700 670 0.453 0.332 0.230 0.151 0.180 0.278 0.462 0.705 675 0.454 0.331 0.238 0.154 0.183 0.281 0.466 0.709 680 0.455 0.331 0.251 0.158 0.186 0.283 0.468 0.712 112
685 0.457 0.330 0.269 0.162 0.189 0.286 0.470 0.715 690 0.458 0.329 0.288 0.165 0.192 0.291 0.473 0.717 695 0.460 0.328 0.312 0.168 0.195 0.296 0.477 0.719 700 0.462 0.328 0.340 0.170 0.199 0.302 0.483 0.721 705 0.463 0.327 0.366 0.171 0.200 0.313 0.489 0.720 710 0.464 0.326 0.390 0.170 0.199 0.325 0.496 0.719 715 0.465 0.325 0.412 0.168 0.198 0.338 0.503 0.722 720 0.466 0.324 0.431 0.166 0.196 0.351 0.511 0.725 725 0.466 0.324 0.447 0.164 0.195 0.364 0.518 0.727 730 0.466 0.624 0.460 0.164 0.195 0.376 0.525 0.729 735 0.466 0.323 0.472 0.165 0.196 0.389 0.532 0.730 740 0.467 0.322 0.481 0.168 0.197 0.401 0.539 0.730 745 0.467 0.321 0.488 0.172 0.200 0.413 0.546 0.730 750 0.467 0.320 0.493 0.177 0.203 0.425 0.553 0.730 755 0.467 0.318 0.497 0.181 0.205 0.436 0.559 0.730 760 0.467 0.316 0.500 0.185 0.208 0.447 0.565 0.730 765 0.467 0.315 0.502 0.189 0.212 0.458 0.570 0.730 770 0.467 0.315 0.505 0.192 0.215 0.469 0.575 0.730 775 0.467 0.314 0.510 0.194 0.217 0.477 0.578 0.730 780 0.467 0.314 0.516 0.197 0.219 0.485 0.581 0.730 785 0.467 0.313 0.520 0.200 0.222 0.493 0.583 0.730 790 0.467 0.313 0.524 0.204 0.226 0.500 0.585 0.731 795 0.466 0.312 0.527 0.210 0.231 0.506 0.587 0.731 800 0.466 0.312 0.531 0.218 0.237 0.512 0.588 0.731 805 0.466 0.311 0.535 0.225 0.243 0.517 0.589 0.731 810 0.466 0.311 0.539 0.233 0.249 0.521 0.590 0.731 815 0.466 0.311 0.544 0.243 0.257 0.525 0.590 0.731 820 0.465 0.311 0.548 0.254 0.265 0.529 0.590 0.731 825 0.464 0.311 0.552 0.264 0.273 0.532 0.591 0.731 830 0.464 0.310 0.555 0.274 0.280 0.535 0.592 0.731
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Appendix 7 – Reflectivity of six CIE additional reference color surfaces
, nm R9 () R10 () R11() R12 () R13() R14 () 360 0.069 0.042 0.074 0.189 0.071 0.036 365 0.072 0.043 0.079 0.175 0.076 0.036 370 0.073 0.045 0.086 0.158 0.082 0.036 375 0.070 0.047 0.098 0.139 0.090 0.036 380 0.066 0.050 0.111 0.120 0.104 0.036 385 0.062 0.054 0.121 0.103 0.127 0.036 390 0.058 0.059 0.127 0.090 0.161 0.037 395 0.055 0.063 0.129 0.082 0.211 0.038 400 0.052 0.066 0.127 0.076 0.264 0.039 405 0.052 0.067 0.121 0.068 0.313 0.039 410 0.051 0.068 0.116 0.064 0.341 0.040 415 0.050 0.069 0.112 0.065 0.352 0.041 420 0.050 0.069 0.108 0.075 0.359 0.042 425 0.049 0.070 0.105 0.093 0.361 0.042 430 0.048 0.072 0.104 0.123 0.364 0.043 435 0.047 0.073 0.104 0.160 0.365 0.044 440 0.046 0.076 0.105 0.207 0.367 0.044 445 0.044 0.078 0.106 0.256 0.369 0.045 450 0.042 0.083 0.110 0.300 0.372 0.045 455 0.041 0.088 0.115 0.331 0.374 0.046 460 0.038 0.095 0.123 0.346 0.376 0.047 465 0.035 0.103 0.134 0.347 0.379 0.048 470 0.033 0.113 0.148 0.341 0.384 0.050 475 0.031 0.125 0.167 0.328 0.389 0.052 480 0.030 0.142 0.192 0.307 0.397 0.055 485 0.029 0.162 0.219 0.282 0.405 0.057 490 0.028 0.189 0.252 0.257 0.416 0.062 495 0.028 0.219 0.291 0.230 0.429 0.067 500 0.028 0.262 0.325 0.204 0.443 0.075 505 0.029 0.305 0.347 0.178 0.454 0.083 510 0.030 0.365 0.356 0.154 0.461 0.092 515 0.030 0.416 0.353 0.129 0.466 0.100 520 0.031 0.465 0.346 0.109 0.469 0.108 525 0.031 0.509 0.333 0.090 0.471 0.121 530 0.032 0.546 0.314 0.075 0.474 0.133 535 0.032 0.581 0.294 0.062 0.476 0.142 540 0.033 0.610 0.271 0.051 0.483 0.150 545 0.034 0.634 0.248 0.041 0.490 0.154 550 0.035 0.653 0.227 0.035 0.506 0.155 114
555 0.037 0.666 0.206 0.029 0.526 0.152 560 0.041 0.678 0.188 0.025 0.553 0.147 565 0.044 0.687 0.170 0.022 0.582 0.140 570 0.048 0.693 0.153 0.019 0.618 0.133 575 0.052 0.698 0.138 0.017 0.651 0.125 580 0.060 0.701 0.125 0.017 0.680 0.118 585 0.076 0.704 0.114 0.017 0.701 0.112 590 0.102 0.705 0.106 0.016 0.717 0.106 595 0.136 0.705 0.100 0.016 0.729 0.101 600 0.190 0.706 0.096 0.016 0.736 0.098 605 0.256 0.707 0.092 0.016 0.742 0.095 610 0.336 0.707 0.090 0.016 0.745 0.093 615 0.418 0.707 0.087 0.016 0.747 0.090 620 0.505 0.708 0.085 0.016 0.748 0.089 625 0.581 0.708 0.082 0.016 0.748 0.087 630 0.641 0.710 0.080 0.018 0.748 0.086 635 0.682 0.711 0.079 0.018 0.748 0.085 640 0.717 0.712 0.078 0.018 0.748 0.084 645 0.740 0.714 0.078 0.018 0.748 0.084 650 0.758 0.716 0.078 0.019 0.748 0.084 655 0.770 0.718 0.078 0.020 0.748 0.084 660 0.781 0.720 0.081 0.023 0.747 0.085 665 0.790 0.722 0.083 0.024 0.747 0.087 670 0.797 0.725 0.088 0.026 0.747 0.092 675 0.803 0.729 0.093 0.030 0.747 0.096 680 0.809 0.731 0.102 0.035 0.747 0.102 685 0.814 0.735 0.112 0.043 0.747 0.110 690 0.819 0.739 0.125 0.056 0.747 0.123 695 0.824 0.742 0.141 0.074 0.746 0.137 700 0.828 0.746 0.161 0.097 0.746 0.152 705 0.830 0.748 0.182 0.128 0.746 0.169 710 0.831 0.749 0.203 0.166 0.745 0.188 715 0.833 0.751 0.223 0.210 0.744 0.207 720 0.835 0.753 0.242 0.257 0.743 0.226 725 0.836 0.754 0.257 0.305 0.744 0.243 730 0.836 0.755 0.270 0.354 0.745 0.260 735 0.837 0.755 0.282 0.401 0.748 0.277 740 0.838 0.755 0.292 0.446 0.750 0.294 745 0.839 0.755 0.302 0.485 0.750 0.310 750 0.839 0.756 0.310 0.520 0.749 0.325 755 0.839 0.757 0.314 0.551 0.748 0.339 760 0.839 0.758 0.317 0.577 0.748 0.353 115
765 0.839 0.759 0.323 0.599 0.747 0.366 770 0.839 0.759 0.330 0.618 0.747 0.379 775 0.839 0.759 0.334 0.633 0.747 0.390 780 0.839 0.759 0.338 0.645 0.747 0.399 785 0.839 0.759 0.343 0.656 0.746 0.408 790 0.839 0.759 0.348 0.666 0.746 0.416 795 0.839 0.759 0.353 0.674 0.746 0.422 800 0.839 0.759 0.359 0.680 0.746 0.428 805 0.839 0.759 0.365 0.686 0.745 0.434 810 0.838 0.758 0.372 0.691 0.745 0.439 815 0.837 0.757 0.380 0.694 0.745 0.444 820 0.837 0.757 0.388 0.697 0.745 0.448 825 0.836 0.756 0.396 0.700 0.745 0.451 830 0.836 0.756 0.403 0.702 0.745 0.454
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University mission is to generate cutting-edge knowledge, implement innovative findings and prepare an elite workforce capable of working in a fast-paced world and ensuring progress in science, technology and other areas in order to contribute to the solution of topical issues.
DEPARTMENT OF OPTICAL-ELECTRONIC DEVICES AND SYSTEMS AND ITS SCIENTIFIC AND PEDAGOGICAL SCHOOL OF THOUGHT
The department was set up in 1937-38 and has existed under the following names since then: 1938 - 1958 - Department of military optical devices; 1958 - 1967 - Department of special optical devices; 1967 - 1992 - Department of optical-electronic devices; Since 1992 - Department of optical-electronic devices and systems. The department was chaired by: 1938 - 1942 - Professor K. Solodilov; 1942 - 1945 Professor A. Zakharievsky (part-time); 1945 - 1946 - Professor M. Rezunov; 1947 - 1972 - Professor S. Zukkerman; 1972 - 1992 - Honoured master of sciences and engineering of the Russian Soviet Federative Socialist Republic, Professor L. Porfiriev; 1992 - 2007 - Honoured master of sciences of the Russian Federation, Professor E. Pankov. from 2007 until the present - Honorary worker of higher professional education, Professor V. Korotayev. In the years 1938 to 1970 the department was part of the Optical Faculty. In the 1970 the department became part of the Faculty of optical-electronic engineering which was renamed into Engineering-physical faculty in 1976. In 1998, the department became part of the Faculty of optical-information systems and technologies. In 2015, the department became part of the Faculty of laser and light engineering. The history of the department originated in 1937-38 with the formation of the Department of military optical devices in Leningrad Institute of Fine Mechanics and Optics (LITMO). The first Chair of the department was K. Solodilov, previously heading the Central Design Bureau of the All-Union Association of optical-mechanical industry. In early 1947 the department was chaired by Porfessor S. Zukkerman, who headed it until 1972. 117
In 1958, an applied research laboratory "Special optical devices" was formed under the auspices of the department, having quite a strong team of designers and developers. In 1959 G. Ishanin started to work in the laboratory, being the acting Chair of the laboratory in 1966-1972. In 1965 G. Ishanin began to develop theories, calculation methods of calculation and design, as well as technology and design solutions for receivers based on thermoelastic effect in crystalline quartz. The receivers based on thermoelastic effect were introduced into serial production. Based on these industrial-purpose receivers measuring instruments for pulse and continuous laser radiation parameters in a large dynamic range were developed. Research conducted in this area formed the basis of the academic discipline "Optical radiation sources and receivers". Significant impact on the content of specialist training and scientific research of the Department of optical-electronic devices and systems is attributed to the involvement into the work at the department of an outstanding specialist in the field of optical-electronic engineering Professor M. Miroshnikov (Director of the State Optical Institute named after S. Vavilov in 1966-1989, corresponding member of the Russian Academy of Sciences (1984), Hero of Socialist Labor (1976), laureate of Lenin Prize (1981). An important methodological aspect of training engineers which was introduced and promoted by Professor S. Zukkerman and Professor M. Miroshnikov was training engineers according to the nature of their future activities (research engineer, design engineer, engineer-technologist), rather than to the type of devices. Nowadays this is called a competency-based approach to training. From 1972 to 1992 год the department was chaired by the Honoured master of sciences and engineering of the Russian Soviet Federative Socialist Republic, Professor L. Porfiriev, a prominent expert in the field of automatic optical-electronic devices and systems in navigation and control complexes for aviation and space technology. Accordingly, the subject matter for the research work at the department acquired new directions, the number of fundamental and exploratory research works as well as R&D works increased significantly. A new curriculum and training disciplines programs were developed. G. Gryazin, who joined the department in the late 60-ies after working at the Radiotechnical Department, continued his research in the field of applied television, in particular, concerning the development of surveillance systems for fast moving objects and high-speed processes. During this period, E. Pankov led the group research on developing new optical-electronic systems for measuring mutual spatial position of objects. (V. Musiakov, V. Korotayev, I. Koniakhin). From 1975 the applied research laboratory was headed by the senior researcher A. Timofeyev, who continued the research on the development of methods and tools for monitoring the spatial position of objects using 118 optical-electronic devices with optical equisignal sector for mechanical engineering, power engineering, construction, shipbuilding and railway transport. Since 1992, the department is chaired by the Honoured master of sciences of the Russian Federation, Professor E. Pankov. In 1992 the department was renamed into the Department of optical-electronic devices and systems. Under the leadership of E. Pankov in the 1970-1990-ies a number of special-purpose and civil optical-electronic devices were developed, finding their practical implementation and contributing to scientific and technological progress and strengthening the defense capability of the Soviet Union (and later Russia). Implementing the results of scientific research the staff of the Department of optical-electronic devices and systems published 16 monographs, 12 textbooks and manuals. The department has prepared 14 Doctors of Sciences, as well as over 110 PhDs. More than 200 inventions by the staff of the department received copyright certificates of the USSR and patents of the Russian Federation. The greatest contribution in the inventive activity was made by E. Pankov, authoring 123 inventions, of which 33 found industrial implementation. Following the announcement of setting up the scientific pedagogical school «Optical-electronic engineering» in 2009 the following scientific and technical results achieved in 1938-2009 were formulated: construction principles for military optical and mechanical devices developed; principles of precision mechanisms developed; principles of construction of optical-electronic devices with optical equisignal sector developed; theoretical fundamentals and principles of construction of optical-electronic devices systematized; impulse signals description methods, objects identification and classification methods for the system of non-standard laser locations developed; theory, construction principles and calculation methods for impulse TV surveillance systems for fast moving objects developed; thermoelastic effect detected in crystalline quartz, new type of optical radiation receivers created; the theory of constructing autocollimating systems with non-standard configuration components developed; analysis methodology for polarization properties of optical systems with changing the orientation of the elements developed; theoretical fundamentals and principles of construction of measuring systems based on matrix photoconverters systematized; basics of building optical-electronic systems for harmonization of reference bases on the .... nonstationary deformable objects developed.
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The founders of the scientific school of thought: Konstantin Solodilov, Chair of the Department from 1938 to 1942, Professor; Semen Zukkerman, Chair of the Department from 1947 to 1972, Professor; Mikhail Miroshnikov, Director of the State Optical Institute, Prof. Dr.-Ing., professor at the Department of optical-electronic devices from 1967 г. to 1978; corresponding member of the Russian Academy of Sciences, Hero of Socialist Labor, laureate of Lenin Prize. Leonid Porfiriev, Chair of the Department from 1972 to 1992, Prof. Dr.-Ing., Honoured master of sciences and engineering of the Russian Soviet Federative Socialist Republic. Since 2007 the department has been chaired by the Honorary worker of higher professional education of the Russian Federation, Professor V. Korotayev. The department introduced training for the new engineering specialization "Optical-electronic devices and video information processing systems", as well as the new Master training program "Optical-electronic methods and means of video information processing" In 2007 the academic center of optical-electronic engineering was created. The academic center of optical-electronic engineering performs research and development as well as design and experimental works on the construction of video information and multi-purpose gauging instruments, high-precision instruments for measuring linear, angular and other physical values in industry, power production, transport, as well as artificial vision systems and video information processing systems. Students, graduate students, young professionals, young PhDs are actively involved in the implementation of research and development as well as design and experimental works. The academic center is an active member of the Federal Target Program "Scientific and scholar human resources of innovative Russia" for 2009-2013. Topics of research performed at the Department of optical-electronic devices and systems and academic center of optical-electronic engineering in 2007-2015. Research and development in the field of designing multi-purpose optical-electronic devices and systems, including: image analysis and processing; optical inspection methods and computer processing of optical inspection data; video information gauging systems video information surveillance systems; video information surveillance systems for fast moving objects; complex television-thermal imaging surveillance systems; optical-electronic devices and systems in the field of technosphere safety;
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optical-electronic devices and systems in the field of harmonization of reference bases on the nonstationary deformable objects. autocollimating systems optical-electronic devices and systems in the field of color and spectral analysis of objects.
Department of optical-electronic devices and systems is engaged in the development of optical-electronic devices and systems in general: systems engineering design, development (selection) of the optical system, design development, development (selection) of electronics and information processing means, Software development, assembly, adjustment, tuning and testing. Department of optical-electronic devices and systems delivers the finished product to its customers.
Educational programs implemented in the Department of optical-electronic devices and systems Training areas and specialization areas implemented by the Department of optical-electronic devices and systems of ITMO University in the field of optical engineering and optical-electronic instrumentation. Training area "12.03.02 - Optical engineering". Bachelor preparation profiles: Optical-electronic devices and systems; Video information systems. Duration of training is 4 years. Master programs: «12.04.02 - Optical engineering» Optical-electronic methods and means of video information processing; Optical-electronic devices and security systems; Duration of training is 2 years. Training area "27.04.05 - Innovation studies". Master Program: Innovation studies in optical engineering. Duration of training is 2 years. Specialization area: 12.05.01 - Optical-electronic gauging instruments and systems. Educational program: Optical-electronic gauging instruments and systems. Duration of training is 5.5 years.
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Post graduate department 05.11.07 Optical and optical-electronic devices and systems
As of 2015, the department employs 6 Doctors of sciences. In the period from 2007 to 2014 22 theses for the PhD degree were defended at the department. There is an active replenishment of the faculty with the young PhDs. Currently, the department employs 7 PhDs under the age of 35 years.
Detailed information about the department is available on the department website: http://oeps.ifmo.ru/
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Elena Gorbunova Alexander Chertov
COLORIMETRY OF RADIATION SOURCES
Textbook
Author's Edition Editorial-publishing department of ITMO University Chair of the editorial-publishing department N. Gusarova Authorized for printing Order no. Number of copies Printed on a risograph
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Editorial-publishing department of ITMO University St. Petersburg, Kronverksky pr., 49, 197101
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