A measured spectrum may contain hundreds of wavelength samples. A colorimetric observer reduces that information to three coordinates. This reduction supports reproducible color matching, but it cannot preserve the full spectrum or every aspect of appearance. Choosing the right representation makes those limits visible.
Project a spectrum into three dimensions
LMS coordinates describe responses using a specified set of cone fundamentals. CIE XYZ uses standardized color-matching functions . For a spectral stimulus :
The common factor sets the scale. The CIE 1931 observer assigns photopic luminance information to ; and are not separate cone signals. A matrix conversion between color coordinates requires compatible observer definitions. Arbitrary Gaussian LMS curves cannot be transformed into exact CIE 1931 XYZ values by a universal matrix.
For a monochromatic stimulus with fixed radiant power, changing wavelength traces a parametric curve in response space. Increasing its power moves outward along a ray from the origin. Mixtures add the response vectors. Without a power limit, nonnegative spectra generate a convex cone of accessible responses, rather than filling a bounded cube.
Some mathematical coordinates remain inaccessible: a stimulus cannot excite only M cones while producing exactly zero L response where their sensitivities overlap. This restriction concerns ordinary spectral stimulation, not unusual adaptation experiments. The familiar unit RGB cube instead describes the limited drive range of a specified three-primary system.
Remove the overall scale
Chromaticity divides each tristimulus value by their sum:
This maps a three-dimensional ray to the plane . The two independent coordinates retain chromaticity while discarding magnitude. Add to form when luminance information is needed. At , chromaticity is undefined.
Plot data: CIE (2019), CC BY-SA 4.0. Diagram adapted by Iris Optics under the same license.
The curved spectral locus represents single wavelengths. The straight closing edge joins the extreme spectral ends through purple mixtures. Three non-collinear display primaries span a triangle inside the accessible chromaticity region. A larger triangle does not imply more brightness or more distinguishable code values.
Mix in a linear space
Two additive stimuli mix on the line joining their chromaticities, but equal radiant powers do not generally place the result at the midpoint. First add XYZ, then normalize. The chromaticity weights depend on each stimulus’s contribution.
Why additive mixtures lie on a straight chromaticity line
Let , and . For nonnegative strengths :
The same relation holds for . Both coordinates share the weight , giving a point on the joining segment whenever the denominator is positive. Equal source strengths give the geometric midpoint only when their tristimulus sums are equal.
Different spectra can produce the same XYZ coordinates for one observer: they are metamers. A material pair that matches under one illuminant may separate under another. An RGB photograph or XYZ reading therefore cannot reconstruct a unique spectrum or establish a match under every lighting condition. Retain spectral data when illumination changes are part of the application.