Jim Worthey, Lighting and Color Research
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Jim Worthey • Lighting & Color Research • jim@jimworthey.com • 301-977-3551 • 11 Rye Court, Gaithersburg, MD 20878-1901, USA
Color Rendering Basic Facts


A white light can be made that emits all its power in two narrow bands: one in the blue and one in the yellow region of the spectrum. This graph shows a 2-bands light as used to make Figure 1 of the introductory article. (Here I have broadened the bands a little for a prettier drawing.)


The two bands suffice to make a colorless light because the yellow band by itself stimulates two receptor systems: the red-sensitive cones and the green-sensitive cones. The green and red sensitivities overlap, and any wavelength in the vicinity of 550-580 nanometers will stimulate both types of cone quite well. The blue band stimulates the blue-sensitive cones. Stimulating all three cone systems is just what a normal white light (such as daylight) would do.

The drawing shows human cone sensitivities computed as linear combinations of the color matching functions of the CIE 2° observer. For tabulated cone fundamentals and other data, see http://www.cvrl.org/.


When used to illuminate colorful objects, the two-bands light loses reds and greens, turning them into browns and blacks. Other colors become yellows, whites, and blues. This figure is essentially the same as Figure 1 of the introductory article.


Another good example is a one-band light that is occasionally used for street lighting: the low-pressure sodium light. Under this light, all objects take on the same chromaticity, (x, y) = (0.569, 0.430). This graph shows a transition from daylight at 4002 K to low-pressure sodium light.


Figure 2 in the introductory article displays a basic example, comparing 4 color-matched lights, as follows:

  • One ideal of "normal" lighting is the spectrum of blackbody radiation, which is computed from a formula derived by Max Planck. The single parameter, temperature T, determines if the blackbody radiation is yellowish or bluish; in the figure, T = 4002 K.
  • Daylight, meaning direct sunlight plus light from the sky, is not blackbody radiation, but it is similar to blackbody if the two lights are selected to match up in color. Daylight is certainly a benchmark for normal lighting.
  • A commercial light (filtered tungsten-halogen) that was designed to resemble daylight or blackbody at 4000 K.
  • Finally, there is the spectrum of Cool White Fluorescent, which rises above the others in the yellow and blue, but falls short in the red and the green.

This figure is rich in facts; it shows by a realistic example why color rendering is an issue. The only "theoretical" content is in the textbook colorimetry used to match up the lights in color and illuminance. A few other figures in the two articles present similar color-matched comparisons of light source spectra.


We all know that daytime vision is "trichromatic." The 3 cone types in the retina are echoed in the 3 pigments of color film, the 3 colored inks (plus black) of an inkjet printer or a magazine page, the 3 phosphors of color TV. Research shows that certain ink or phosphor colors work best; they can't be chosen arbitrarily. [See R. W. G. Hunt's book, The reproduction of color. I have the 3rd edition, published in 1975 by The Fountain Press. A sixth edition is forthcoming in 2002 August.] Dr. William Thornton has found a set of 3 "prime colors" that work best in a 3-band light source, and not surprisingly they are similar to the phosphor colors of NTSC television (colored dots). In words of one syllable, Thornton seeks to use the hues with the most punch. I have a similar goal, but start with opponent-color ideas to develop a method not restricted to 3-band lamps.


Most solid objects have reflectances that vary slowly with wavelength, showing one or two smooth transitions between low and high, within the visible spectrum. While this was "discovered" by Jozef Cohen in 1964 in a useful mathematical form, it is often implicitly assumed in color work. Cohen brought the idea out in the open, and I use a version of his formula to bring the spectral smoothness of object colors into my analysis. The objects that you might see are numerous, but here are spectral reflectances of 4 surfaces that Michael Vrhel measured:


Given a single object viewed by the CIE standard observer, the tristimulus values of the object can be computed for any light. Some color scientists feel that if the tristimulus values can be found for any light and object, this is all one needs to know, and there is no color rendering issue. This shows a charming and innocent faith in basic colorimetry, but it is not correct. In daily life, even in daylight, the color of the light varies. A bluer light shifts chromaticities towards blue; a yellower light shifts them towards yellow. (See calculation article, Figure 4.) The eye has an (imperfect) mechanism of "color constancy," so that one sees object colors as stable, even when object chromaticities are shifted. A single object's tristimulus vector, by itself, does not predict the perceived color of the object. A color rendering discussion must in some way deal with color constancy, and the two new articles do this:
  • by comparing lights that have the same chromaticity (exactly or approximately). According to most theories, the light's chromaticity steers the constancy mechanism. Comparing lights of the same chromaticity should keep constancy out of the picture.
  • by plotting colorimetric shifts for large numbers of color chips (64 or 36 in most cases), rather than one or a few object colors. Plotting a large number of colorimetric shifts in one drawing displays "the forest" as well as "the trees," you might say.
  • by referring to color contrast and saturated chromatic colors, not just color shifts.
  • by presenting a calculation based on opponent colors, to keep the issue of saturated chromatic colors in plain view.

Item 8 can be repeated in a simpler way. Again, the issue is that for a single spectral reflectance under a single light, textbook colorimetry enables tristimulus values (X, Y, Z) to be computed, and then chromaticity (x, y). Why then is another discussion and calculation needed for color rendering? For a direct answer, look at the graphs in items 3 and 4 above. Lights can have strong systematic effects. A color rendering calculation is needed to describe and quantify these systematic effects. One tristimulus vector, or even the shift of one tristimulus vector when the light is changed, does not convey the systematic loss or gain of chromatic colors that can occur.


In reviewing drafts of the color rendering articles before publication, various scientists have made suggestions with a common theme. They would like me to project colorimetric shifts into a nonlinear color difference space such as CIELAB, or relate my results to some color appearance model. That is not what this work is about. In everyday life, vision involves 3 actors:
1. The object.
2. The light source.
3. The eye and visual system.
Most studied is the visual system. It is fascinating and complex and the study of the visual system connects to the large occupational communities of optometry and medicine. Objects connect to smaller occupational groups relating to pigments, copy machines and so forth, and objects are studied in a moderately scientific way. What is highly neglected is the light source as an actor in the visual process. For instance, vision scientists occasionally study Color Constancy, in experiments such as that of McCann, McKee and Taylor, discussed in my introductory article. Such studies must vary the light, but most authors say little about how one light differs from another. The scientists are being paid to talk about eyeballs. They may receive money from National Institutes of Health. They don't know about lights and are not being paid to think about that.

My goal from the beginning has been to focus on the neglected issue: how do lights differ from each other and what are the effects of these differences? Above all, the light acts in the linear, physical regime where it shines upon the objects, the object properties interact with light source properties, and the resulting object radiances then interact with the receptors of color vision. I make two assumptions about the eye:
1. All sensation must be mediated by the 3 spectral sensitivities of cones. (Leaving aside scotopic and mesopic vision.)
2. Color vision is stimulated when different retinal areas receive stimuli that are well separated in color space.
If a light causes reds to lose their redness and also causes greens to lose their greenness, it is important to know this. It is important to understand this as an issue in itself, and not to drag in other issues that are well studied already. The introductory article looks at the basic facts of color rendering in a workmanlike way, as no other author has done. (See items 1-5 above.) The mathematics used in the second article is appropriate to the color rendering problem as it actually exists. That should be enough for now.

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Page last modified, 2006 June 17, 12:44