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Color Theory - Introduction, Physiology, CIE Color Spaces

light spectral cones blue

Rochester Institute of Technology


What are they playing?" asked Tock, looking up inquisitively at Alec. “The sunset, of course. They play it every evening about this time … and they also play morning, noon and night, when, of course, it’s morning, noon, or night. Why, there wouldn’t be any color in the world unless they played it. Each instrument plays a different one,” he explained .

Norton Juster , The Phantom Tollbooth.

In the children’s fantasy The Phantom Tollbooth , Chroma is conductor of an orchestra that “plays” the colors of the world. Tones emitted by a collection of instruments do make a good metaphor for the complex properties of a scene’s spectral radiance. Like the intricate combination of sound frequencies that comprise an orchestral piece, spectral radiance from any point in a scene consists of a rich mixture of photon frequencies.

Newton’s prism experiments, such as the one illustrated in Figure 74, explained how light and its interaction with matter give rise to the conditions in which color may be seen:

From all which it is manifest that if the Sun’s light consisted of but one sort of rays, there would be but one colour in the whole world … and by consequence, that the variety of colours depends upon the composition of light…. Colours in the object are nothing but a disposition to reflect this or that sort of rays more copiously than the rest .

For a given material and an encountered photon of a certain wavelength, there are certain events that may happen. The photon may be transmitted, reflected, or absorbed. Absorption may lead to, among other things, reconversion back to visible radiation through fluorescence or phosphorescence. All these processes are stochastic. The result is a spectral power distribution emitted from an illuminated object.

Philosophers may argue metaphysical questions about whether or not a color belongs to an object, but it is scientifically accepted that the appearance of color requires a mental process: “There may be light of different wavelengths independent of an observer, but there is no color independent of an observer, because color is a psychological phenomenon that arises only within an observer.” Thus, the spectral power distribution encountered by an eye when focused from an object in a given environment gives rise to the viewer’s idea of the object’s color.

In 1802, Thomas Young presented to the Royal Society his conclusion that human perception of color is based on three primaries. “It is almost impossible to conceive each sensitive point of the retina to contain an infinite number of particles, each capable of vibrating in perfect unison with every possible undulation, it becomes necessary to suppose the number limited, for instance, to the three principal colors, red, yellow, and blue.” The mid-19th century saw much work in the refinement and verification of Young’s hypothesis with the participation of James Clerk Maxwell, Hermann von Helmholtz, and Arthur König. Proof of trichromacy was supposed to have occurred in 1861 with Maxwell’s successful public demonstration of the first three-channel full-color photography. Although the theory Maxwell was pursuing was correct, Maxwell’s experiment itself was flawed. 1

The strange thing about the success of the experiment was that spectral sensitization dyes for film would not be invented for another 12 years. In contradiction, it would have seemed that Maxwell’s experiment relied on emulsions sensitive to green and red light. The material he was working with should only have had intrinsic blue and ultraviolet sensitivities. Thus, the red and green filtered records should have been blank.

Evans, in a 1961 article, explained that Maxwell was probably helped by a series of happy coincidences. Blues and greens from a ribbon he imaged were separated because the transmittance of the green filter used by Maxwell leaked slightly into the blue region and the strong green on his ribbon had slight reflectance in the blue. He employed a relatively high exposure time for the green photograph correcting for the low level of reflectance. For the red separation, Maxwell’s red filter happened to have a secondary transmission in the ultraviolet and synthetic red dyes like those likely on the ribbon tend to have, coin-cidentally, secondary reflectances in that same spectral range (Evans, 1961).

Ewald Hering came soon afterward and found that trichromacy was insufficient to explain all color phenomena. For one thing, he noted, after images required a more complex solution. How, for example, are yellow and blue related, as each is the other’s after image. Hering promoted the concept of an opponency platform where certain color sensations are at polar odds with others. Although this new theory appeared to be in direct conflict with Young’s theory, it would eventually be proven that the two ideas are indeed compatible and represent different stages in the physiology of color vision.

Other important innovations in color science also took place in the mid-1800s. For example, the inventor of linear algebra, Hermann Grassmann. applied his new tool to color vision. He determined several laws concerning metamers formed through the additive mixing of lights. His first law is that of additivity: By equally adding to each of a pair of metamers the same additional light, the match will not be broken. Second is Grassmann’s scalar law: A metameric match is not broken by equally increasing or decreasing the intensity of each of a pair of meta-mers. Finally, Grassmann described the associative law: If a and b make a metameric pair and c and d are also metameric, then a + c and b + d is also a metameric pair.

The breakthroughs in color science of the 19th century were necessary to the successes of color reproduction in the 20th century. These fundamental understandings of color vision provided engineers with means to create trade-offs based on minimizing their visual impact. Further, it laid the foundation for modern color-matching experiments leading to the specification of the standard observer and the definition of standard colorimetry.


The ability to see color occurs in the brain. When light enters the eye under normal illumination conditions it will interact with specialized neurons. There, photonic energy is converted into electrical and chemical signals that are relayed to the rest of the brain by way of the optic nerve. Neural connections made both within the eye and extending into the bulk of the brain create psychological attributes of the scene, some of which are interpreted by the observer as color. Under normal illumination levels, the set of photoreceptors in the retina known as cones are functional. Figure 76 illustrates a cone photoreceptor. There are actually three types of cones that are differentiated by their sensitivity to ranges of visible light wavelengths creating the trichromacy of human vision. In low light situations, cones are unable to gather enough light to be effective, but the very sensitive rods are active. See Figure 75 for an illustration of a rod photoreceptor. All rods have essentially the same wavelength sensitivity profile, relatively broad in comparison to that of cones. This ensures maximal use of light since rods are used when photons are at a premium, but this comes at the cost of color being unrecognizable in dark viewing environments since trichromacy is necessary for color vision. More details on the physiology of vision can be found in the Human Vision section of this book.

Low light conditions, such as experienced in a dark room at night, are known as scotopic environments. Scotopic vision is without color sensation. A normal illumination environment, one that is sufficiently photon-rich that all the rods have been bleached and are no longer able to respond to further stimulation, is called photopic. Here three types of cones work in unison and their differential response to spectral power distributions give rise to the experience of color. Mesopic vision takes place at illumination levels that are high enough so cones respond but dim enough so rods are not fully bleached. Thus, both rods and cones are active in mesopic environments that might be found at dusk.

The three types of cones are distinguished by their relative sensitivity differences to light wavelengths. Those most sensitive to the longer visible wavelengths, the reds, are called L-cones. Their peak sensitivity is around 610nm. The S-cones, so called for their response to the shorter visible wavelengths such as the blues, have peak sensitivity at approximately
430 nm. The M-cones have middle or green sensitivity with a peak at about 560nm. Sensitivity curves for a typical set of cones are displayed in Figure 77.

As Hering had noted, colors seem to have their opposites in human color vision. This is noted in after images. For example, staring at a blue field for 10 or 20 seconds will cause the appearance of yellow if the observer turns to a white field afterward. Green will have a magenta after image and red will show cyan. The reverse is also true as yellow has a blue after image, magenta has a green one, and cyan has a red after image. Further, Hering sought to explain why there were certain color concepts that were unavailable to the human imagination such as a yellowish-blue. Hering theorized an opponency system where yellow and blue were at odds as were red and green.

Neural wiring in the human visual pathway can easily be used to explain the visual phenomena that Hering observed. This is not at the expense of Young’s trichromacy because color begins with the red-, green-, and blue-sensitive cones. In the human eye, the S-cones antagonize with a combination of M- and L-cones. When both the M- and L-cones are stimulated, the human response is that of yellow; thus, Hering’s blue/yellow opponency. The other opponent channel can also be shown through additional opponency wiring of the S-, M-, and L-cone. A third channel, that of luminance, is created by combining the responses from all three cone signals into a synergistic relationship.

The brain creates color. Starting with the trichromatic system of L-, M-, and S-cones—or red, green, and blue sensitivities—the signals are then transformed into two opponent
channels and one luminance channel. This is accomplished through neurons applying simple algebraic sums to the cone signals. As the information moves into the brain, additional processing yields other visual sensations such as those of hue, saturation, and lightness.

CIE Color Spaces

In the 1920s a series of experiments by Wright and Guild were undertaken to determine the psychophysical response of humans to individual spectral colors. These involved a now famous experimental setup using a method of adjustment where a round bipartite field was presented to a subject; one-half of the field was illuminated with a particular spectral light and the other half was illuminated by the combination of three primary light sources. The experiment participant was given the task of adjusting the three primaries to create a metameric match (see Figure 78). The intensity levels assigned to each of the primaries for each of the spectral colors became the color matching functions for that individual for those primaries.

It was found that for some of the spectral colors, particularly in the green region of the spectrum, no combination of the primaries was sufficient to match the color. To solve this problem, one of the primaries, usually red, was allowed to be added to the spectral color to desaturate it and then a match was possible. Adding a primary to the spectral color was the equivalent of a negative sensitivity and thus, some of the color-matching functions went negative in certain regions of the spectrum.

A very important year for color was 1931. It was then that Kodak released its Kodacolor process, the first color photographic product for the masses. Another landmark in the world of color technology was also underway. The Commission International de l’Eclairage (CIE) released its first attempt at standardizing a system describing human color response. This system is now known as the 1931 Standard Colorimetric Observer. A set of color matching functions referred to as x¯(?), y¯ (?) and z¯ (?) were defined. These were a linear transformation away from the combined results of Wright and Guild. This special transformation yielded color-matching functions based on theoretical primaries where there were no negative responses and where the y¯(?) response was taken as V (?), the earlier derived human luminance response function.

The 1931 Standard Observer provided the world, for the first time, with unambiguous color specification. A color sample described by its XYZ tristimulus values, the scalars derived by multiplying a spectral radiance vector by the three color-matching functions and integrating each, should visually match another sample described by the same XYZ tristimulus values under identical viewing conditions. The ability to measure colors by means of a spectrophotometer and to transform measurements to XYZ values created a “universal and fundamental language of color.” The 1931 Standard Observer was important for the growth of color science. As Hardy’s 1936 Handbook of Colorimetry pointed out, “Students of history agree that man’s progress was slow until he had developed a language that enabled him to impart to others the experience that he had just acquired.”

The formula for calculating XYZ from the spectral reflectance factor of an object, R(?) viewed under a light source with spectral radiance described by S(?) is as follows:

X = k ? S(?) R (?) x ¯(?) d ?

Y = k ? S(?) R (?) y ¯(?) d ?

Z = k ? S(?) R (?) z ¯(?) d ?

where constant k is calculated to guarantee that the perfect reflecting diffuser under the light source returns a value of 100 as follows:

The Wright and Guild matching experiments illuminated only the fovea. During the 1950s, Stiles showed that such experiments were not completely accurate for larger fields. Stiles and Burch went on to reinvestigate the color matching functions for a larger 10° field of view, versus the original foveal 2° field of view. Their new color-matching functions were adopted as the 1964 Standard Colorimetric Observer. Both colorimetric systems are still widely used. In the graphic arts industry and, by extension, in color management, the 1931 2°, Standard Colorimetric Observer is usually utilized.

By 1934, transformations of the XYZ system were developed for superior correlation between calculated distances within a color space and human visual perception of color difference. Known as uniform color spaces or uniform color scales, many XYZ transformations were offered. Earliest attempts at improving the non-visually-uniform nature of the XYZ space concentrated on the two-dimensional projection known as the chromaticity diagram (see Figure 79).

MacAdam, one of the original researchers in this area, reminisced in 1985:

Analogous to Mercator charts and other kinds of maps of the world that misrepresent the ratios of distances, the chro-maticity diagram does not represent perceptually equal color differences by equal distances between points that represent equally luminous colors. The noticeability of color differences was not considered—very few data were available—when the chromaticity diagram was devised and adopted. However, as soon as it came into use, anomalies were encountered in interpreting the configurations of points on the diagram. Inconsistencies between distances and perceived magnitudes of color differences were evident .

Many uniform color spaces have been offered between 1931 and today. In 1976, the CIE recommended the use of either of the two-color difference formulae. One of these color difference formulae was based on the 1976 CIELAB space. The color difference associated with this space and its subsequent derivatives have become the dominant ways of specifying color and color difference throughout many industries.

CIELAB is a defined as having one luminance channel (L*) and two opponency channels (a* and b*). The L* channel has a luminance response with a log-like fall off as the brightness of the color increases. The a* channel describes antagonism between green and magenta appearance where negative a* indicates greenness and a positive a* indicates magentaness. The b* channel describes antagonism between blue and yellow appearance whereas negative b* indicates blueness and positive b* indicates yellowness (see Figure 80).

The formula for converting from XYZ to CIELAB is as follows:

L* = 116[f(Y/Yn)] – 16

a* = 500[f(X/Xn) – f(Y/Yn)]

b* = 200[f(Y/Yn) – f(Z/Zn)]

where Xn, Yn, and Zn are the tristimulus values of a perfect reflecting diffuser under the viewing environment and where

f(X/Xn) = (X/Xn)1/3; for (X/Xn) > 0.008856


f(X/Xn) = 7.787 × (X/Xn) + 16/116; otherwise,

f(Y/Yn) = (Y/Yn)1/3; for (Y/Yn) > 0.008856


f(Y/Yn) = 7.787 × (Y/Yn) + 16/116; otherwise,

f(Z/Zn) = (Z/Zn)1/3; for (Z/Zn) > 0.008856


f(Z/Zn) = 7.787 × (Z/Zn) + 16/116; otherwise.

The CIE color difference formula based on the CIELAB color space was originally specified as the Euclidean distance in that space. This was called AE*ab. In 1994 and again in 2000, the CIE published updates to the color difference. The first was named ?E*94 and the latter CIEDE2000. The equation for CIEDE2000 is as follows:

Colorimetry - Trichromatic Theory of Color Vision, Color Matching Functions, Cone fundamentals, CIE [next] [back] Color Spaces, Color Encodings, and Color Image Encodings - Color Spaces, Color space encodings, Color image encodings, Digital color image workflow, Raw sensor response coordinates

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