tristimulus

Tristimulus values are three numbers, X, Y, and Z, used to quantify the color of a light stimulus as perceived by a standard observer. They form the core of the CIE XYZ color space and are derived from the spectral power distribution of the stimulus through a set of color-matching functions. For a given spectral power distribution S(λ), the tristimulus values are defined by X = ∫ S(λ) x̄(λ) dλ, Y = ∫ S(λ) ȳ(λ) dλ, and Z = ∫ S(λ) z̄(λ) dλ, where x̄(λ), ȳ(λ), and z̄(λ) are the CIE color-matching functions for a standard observer.

The Y component is closely related to luminance and correlates with perceived brightness, while X and Z, together with Y, describe the color's chromaticity. From X, Y, and Z one can derive chromaticity coordinates x = X/(X+Y+Z), y = Y/(X+Y+Z), and z = Z/(X+Y+Z) (with x + y + z = 1). The tristimulus values depend on the observer and illumination assumptions; the most common reference uses the CIE 1931 standard observer, with 2° and, later, 10° field-of-view definitions, and various updates have extended to other datasets.

In practice, tristimulus values are obtained by measuring a material’s spectral power distribution with a spectrophotometer or colorimeter and computing the integrals against the appropriate color-matching functions. They enable conversion between color representations (for example, to sRGB, CIELAB, or other color spaces) and facilitate device characterization, color matching, and metamerism analysis, since different spectra can yield the same tristimulus values under a given observer and illuminant.