O-Matrix User Stories

Computerizing Color Research

Nowadays, all color scientists have access to computers, but their way of thinking is often anchored in ideas from the pre-computer era. It is the essence of established color theory that colors add as vectors, and yet the old-fashioned methods have no vector diagram. James Worthey's research addresses such basic questions as how the spectrum of a white light affects the colors that you see under that light.

My favorite way of working is to derive simple formulas and apply them with real data, perhaps gain some insight, and continue with similar work. O-Matrix is convenient for this purpose. And, O-Matrix enables me to graph the results.

     - James Worthey, P.E., PhD

2 bands

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. The graph above shows a 2-bands light.

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 above shows human cone sensitivities computed as linear combinations of the color matching functions of the CIE 2 observer.

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.

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). The graph above shows a transition from daylight at 4002 K to low-pressure sodium light.

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]. 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.

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 James Worthey uses a version of Cohen's formula to bring the spectral smoothness of object colors into his analysis. The objects that you might see are numerous, but the plot above are spectral reflectances of 4 surfaces that Michael Vrhel measured.

The image above illustrates colors being added vectorially in the color space invented by Jozef Cohen. The picture is a screen grab from a virtual reality plot generated from VRML (virtual reality modeling language). The VRML code was generated directly by an O-Matrix program and there was no manual adjustment. The 2-D graphs above were generated using the graphing features of O-Matrix, and were then edited in Adobe Illustrator.

This user story was contributed by James Worthey. See his homepage for more information on his color research and how he uses O-Matrix. http://www.jimworthey.com

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