Primary color

 ( Color ) 

Traditional color theory is based on experience with pigments, more than on the science of light. In 1920, Snow and Froehlich explained:

The widespread adoption of teaching of RYB as primary colors in post-secondary art schools in the twentieth century has been attributed to the influence of the Bauhaus, where Johannes Itten developed his ideas on color during his time there in the 1920s, and of his book on color

published in 1961.

The set of pigments available to mix diverse gamuts of color (in various media such as oil paint, watercolor, acrylic paint, gouache, and pastel) is large and has changed throughout history.

The CIE 1931 standard observer is derived from experiments in which participants observe a foveal secondary bipartite field with a dark surround. Half of the field is illuminated with a monochromatic test stimulus (ranging from 380 nm to 780 nm) and the other half is the matching stimulus illuminated with three coincident monochromatic primary lights: 700 nm for red (R), 546.1 nm for green (G), and 435.8 nm for blue (B). These primaries correspond to CIE RGB. The intensities of the primary lights could be adjusted by the participant observer until the matching stimulus matched the test stimulus, as predicted by Grassman's laws of additive mixing. Different standard observers from other color matching experiments have been derived since 1931. The variations in experiments include choices of primary lights, field of view, number of participants etc. but the presentation below is representative of those results.

Matching was performed across many participants in incremental steps along the range of test stimulus wavelengths (380 nm to 780 nm) to ultimately yield the color matching functions: $\backslash overline\{r\}(\backslash lambda)$, $\backslash overline\{g\}(\backslash lambda)$ and $\backslash overline\{b\}(\backslash lambda)$ that represent the relative intensities of red, green, and blue light to match each wavelength ($\backslash lambda$). These functions imply that $C$ units of the test stimulus with any spectral power distribution, $P(\backslash lambda)$, can be matched by , , and units of each primary where:

^{780\text{ nm}} \overline{r}(\lambda) P(\lambda)\,d\lambda \cdot R + \int_{380\text{ nm}}^{780\text{ nm}} \overline{g}(\lambda) P(\lambda)\,d\lambda \cdot G + \int_{380\text{ nm}}^{780\text{ nm}} \overline{b}(\lambda) P(\lambda)\,d\lambda \cdot B.

Each integral term in the above equation is known as a tristimulus value and measures amounts in the adopted units. No set of real primary lights can match another monochromatic light under additive mixing so at least one of the color matching functions is negative for each wavelength. A negative tristimulus value corresponds to that primary being added to the test stimulus instead of the matching stimulus to achieve a match.

The negative tristimulus values made certain types of calculations difficult, so the CIE put forth new color matching functions $\backslash overline\{x\}(\backslash lambda)$, $\backslash overline\{y\}(\backslash lambda)$, and $\backslash overline\{z\}(\backslash lambda)$ defined by the following linear map:

These new color matching functions correspond to imaginary primary lights X, Y, and Z (CIE XYZ). All colors can be matched by finding the amounts , , and analogously to , , and as defined in . The functions $\backslash overline\{x\}(\backslash lambda)$, $\backslash overline\{y\}(\backslash lambda)$, and $\backslash overline\{z\}(\backslash lambda)$ based on the specifications that they should be nonnegative for all wavelengths, $\backslash overline\{y\}(\backslash lambda)$ be equal to photometric luminance, and that $X=Y=Z$ for an equienergy (i.e., a uniform spectral power distribution) test stimulus.

Derivations use the color matching functions, along with data from other experiments, to ultimately yield the cone fundamentals: $\backslash overline\{l\}(\backslash lambda)$, $\backslash overline\{m\}(\backslash lambda)$ and $\backslash overline\{s\}(\backslash lambda)$. These functions correspond to the response curves for the three types of color photoreceptors found in the human retina: long-wavelength (L), medium-wavelength (M), and short-wavelength (S) cone cell. The three cone fundamentals are related to the original color matching functions by the following linear transformation (specific to a 10° field):

LMS color space comprises three primary lights (L, M, and S) that stimulate only the L-, M-, and S-cones respectively. A real primary that stimulates only the M-cone is impossible, and therefore these primaries are imaginary. The LMS color space has significant physiological relevance as these three photoreceptors mediate trichromatic color vision in humans.

Both XYZ and LMS color spaces are complete since all colors in the gamut of the standard observer are contained within their color spaces. Complete color spaces must have imaginary primaries, but color spaces with imaginary primaries are not necessarily complete (e.g. ProPhoto RGB color space).

A color in a color space is defined as a combination of its primaries, where each primary must give a non-negative contribution. Any color space based on a finite number of real primaries is incomplete in that it cannot reproduce every color within the gamut of the standard observer.

Practical color spaces such as sRGB and scRGB are typically (at least partially) defined in terms of linear transformations from CIE XYZ, and color management often uses CIE XYZ as a middle point for transformations between two other color spaces.

Most color spaces in the color-matching context (those defined by their relationship to CIE XYZ) inherit its three-dimensionality. However, more complex color appearance models like CIECAM02 require extra dimensions to describe colors appear under different viewing conditions.