# Standard Colorimetric Observer Color-Matching Functions

Standard Colorimetric Observer Color-Matching Functions

This Demonstration studies the functions of the form (λ)+(λ)+(1--)(λ), where and are real numbers and , , are the color-matching functions of the CIE 1931 Standard Colorimetric Observer. The main reason for being interested in these functions is that among them there are the spectral responses of electronic cameras that "see colors just like normal humans," meaning that two spectral distributions of radiant energy are indistinguishable for the camera if and only if they are indistinguishable for a normal human observer. Since spectral responses of photo detectors are always positive, the functions of interest are the positive ones. Since the , , are positive by definition, trivially positive linear combinations result if , , and are positive. There are, however, also cases where one of these three coefficients is negative. These were determined in [1].

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This Demonstration lets you inspect all relevant linear combinations by placing the point in the display area with the same coordinate system as the CIE chromaticity diagram. The curve associated with this point is displayed as a colored curve. The display area is structured by a bundle of lines, each belonging to the spectral color in which it is drawn. For any visible wavelength , the corresponding line is drawn such that to on this line there belongs a linear combination of color-matching functions that vanishes at . There is a convex region that is free of these colored lines. The points of this region belong to positive functions and the points on the boundary correspond to functions that touch their axis. The boundary of the line-free area shows a striking similarity to the spectral locus, which is displayed as a colored line. You can use a second point (named instead of ) to compare the two situations.

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