Jim Worthey, Lighting and Color Research
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30 (approximately) New Ideas in the Two Color Rendering Articles


Lighting has a purpose, which is to render object properties into black-white and color contrasts. Black-white rendering tends to be in the artistic vocabulary, while color rendering is treated as a nuisance engineering issue. The idea that both kinds of rendering are quantifiable and part of the basic functionality of lighting is at odds with the hidden assumptions that many people make.


Objects that are shiny or transparent image the contrasts of their environment. While this is well understood in computer graphics circles, it is seldom acknowledged in the lighting discussion.


Everyday speech puts trust in the light and does not acknowledge its role. A purpose of these articles is to ask the question, to find the right words to talk about color rendering.


The focus is on the linear, physical, interaction of the object, the light, and the eye. My approach is that of a physicist or lighting inventor who is interested in the "inner workings" of things.


"Color rendering" includes loss or gain of chroma. Some in the lighting industry have understood that "poor color rendering" usually equates to "dull colors," but the issue is seldom stated in clear language (apart from my prior work). 2-bands light loses contrast
6 When chroma is lost in a systematic way, so is color contrast.
7 The two-band light is a prototype for bad color rendering. Thornton and others have noted this fact, but it remains as a simple insight that is seldom mentioned. Render Ask, Fig. 1, shows a detailed example.


The practical reality of color rendering is illustrated by a comparison of four lights that are equated for illuminance, and approximately equated for chromaticity, Render Ask, Fig. 2. spectra of 4 lights


Within the apparatus and experimental design of the famous Quantitative Retinex Experiment is a color rendering example. experiment of McCann et al.


In the universe of color technologies, lighting is similar to television. Chromaticity diagram, lighting & television


Thornton's Prime Color ideas can be approximately explained in terms of an opponent color theory. opponent color sensitivities


The reader is reminded of the connection between prime colors and the diagonal of Matrix R. Jozef Cohen did point out this relationship.


Neodymium glass offers a critical test of Thornton's Prime Color theory.


Color Rendering and Object Metamerism are separate issues. While I believe that this distinction was seen intuitively by past experts including the original authors of the Color Rendering Index, it is sometimes overlooked.


What permits the two-bands light to be seen as white is the great overlap in spectral sensitivities of the red and green receptors. (Going beyond what is said in the color rendering articles, it seems clear that Bill Thornton's Prime Colors, and Jozef Cohen's Matrix R are both methods for dealing with the overlap of red and green sensitivities. Jozef Cohen wrote about "the structure of color space." If the color receptors had three narrow-band and non-overlapping sensitivities, those sensitivities would jump out of color-matching data. The sensitivities would be orthogonal functions with little need for transformation of primaries, opponent color models, Matrix R or Prime Colors.) cone sensitivities, rgb-bar


Guth's opponent model has practical utility because of its simplicity. Opponent colors as a method for color engineering was used in the invention of color television. opponent colors again


Since opponent-color sensitivities look like orthogonal functions, it might be useful to orthogonalize them.


Color matching functions can be used as basis functions of spectral reflectance. Jozef Cohen made this innovation, but it is taken a little further here.


The new color rendering model predicts colorimetric shifts. The numbers that make the prediction are the same numbers that can be used for overall assessment of a lighting substitution.


Within the color rendering model, objects are characterized by their tristimulus values under a pivotal light. The pivotal light can very well be some familiar light such as D65 (6500 K daylight). Therefore, the model incorporates the familiar assumption that if you know an object's tristimulus value under D65, you know a lot about the object.


Thanks to the opponent-color formulation, the illuminant change is represented by a matrix whose elements have intuitive meaning.


The smoothness assumption is used explicitly in deriving the color rendering method.


The opponent-color basis functions are made orthonormal, with an added feature. They are orthonormal with the pivotal light as a weighting function.


Bra and ket notation is used to emphasize the role of inner products and orthogonal functions.


The traditional CRI emphasized summing up the vector magnitudes of colorimetric shifts. By looking at the inner workings (idea 4 above), we see that even if the colorimetric shifts are graphed, the CRI's pastel chips give a non-revealing result. It is saturated reds and greens that are in greatest jeopardy from poor color rendering.


Figs. 5 and 6 of Render Calc permit a grand comparison of many diverse lights in a way that speaks to the need for red-green and blue-yellow contrasts.


The neodymium-filtered light stands out because it enhances both red-green and blue-yellow contrasts, relative to the same source without the filter.


An explicit challenge to the usual lighting discussion: "lighting discussions often operate on the peculiar assumption that what is most obvious need not be studied."


Some common lighting systems cause stimulus deprivation.


The reader is reminded of Guth's take on what the y-bar function is. It is the response of one "second stage" subsystem within the visual system. The achromatic and opponent systems combine vectorially.


The unity or projection operator is presented as a means to derive useful formulas. unity operator


The unity operator that I construct with orthonormalized basis functions equals Jozef Cohen's Matrix R. Rather than emphasize the unity operator as a large square matrix, I allow it to fade away in the derivation of the illuminant substitution matrix. Unity operator same as Matrix R
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