The correlated color temperature (CCT, Tcp) is defined as "the temperature of the Planckian radiator whose perceived color most closely resembles that of a given stimulus at the same brightness and under specified viewing conditions
Motivation
Black-body radiators are the reference by which the whiteness of light sources is judged. A black body can be described by its temperature and produces light of a particular hue, as depicted above. This set of colors is called color temperature. By analogy, nearly Planckian light sources such as certain fluorescent or high-intensity discharge lamps can be judged by their correlated color temperature (CCT), the temperature of the Planckian radiator whose color best approximates them. For light source spectra that are not Planckian, matching them to that of a black body is not well defined; the concept of correlated color temperature was extended to map such sources as well as possible onto the one-dimensional scale of color temperature, where "as well as possible" is defined in the context of an objective color space.
Background
The notion of using Planckian radiators as a yardstick against which to judge other light sources is not new. In 1923, writing about "grading of illuminants with reference to quality of color ... the temperature of the source as an index of the quality of color", Priest essentially described CCT as we understand it today, going so far as to use the term "apparent color temperature", and astutely recognized three cases: "Those for which the spectral distribution of energy is identical with that given by the Planckian formula." "Those for which the spectral distribution of energy is not identical with that given by the Planckian formula, but still is of such a form that the quality of the color evoked is the same as would be evoked by the energy from a Planckian radiator at the given color temperature." "Those for which the spectral distribution of energy is such that the color can be matched only approximately by a stimulus of the Planckian form of spectral distribution."
Several important developments occurred in 1931. In chronological order:
Raymond Davis published a paper on "correlated color temperature" (his term). Referring to the Planckian locus on the r-g diagram, he defined the CCT as the average of the "primary component temperatures" (RGB CCTs), using trilinear coordinates. The CIE announced the XYZ color space. Deane B. Judd published a paper on the nature of "least perceptible differences" with respect to chromatic stimuli. By empirical means he determined that the difference in sensation, which he termed ΔE for a "discriminatory step between colors ... Empfindung" (German for sensation) was proportional to the distance of the colors on the chromaticity diagram. Referring to the (r,g) chromaticity diagram depicted aside, he hypothesized that
KΔE = |c1 − c2| = max(|r1 − r2|, |g1 − g2|).
These developments paved the way for the development of new chromaticity spaces that are more suited to estimating correlated color temperatures and chromaticity differences. Bridging the concepts of color difference and color temperature, Priest made the observation that the eye is sensitive to constant differences in "reciprocal" temperature:
Priest proposed to use "the scale of temperature as a scale for arranging the chromaticities of the several illuminants in a serial order". Over the next few years, Judd published three more significant papers:
The first verified the findings of Priest, Davis, and Judd, with a paper on sensitivity to change in color temperature.
The second proposed a new chromaticity space, guided by a principle that has become the holy grail of color spaces: perceptual uniformity (chromaticity distance should be commensurate with perceptual difference). By means of a projective transformation, Judd found a more "uniform chromaticity space" (UCS) in which to find the CCT. Judd determined the "nearest color temperature" by simply finding the point on the Planckian locus nearest to the chromaticity of the stimulus on Maxwell's color triangle, depicted aside. The transformation matrix he used to convert X,Y,Z tristimulus values to R,G,B coordinates was:
From this, one can find these chromaticities:
The third depicted the locus of the isothermal chromaticities on the CIE 1931 x,y chromaticity diagram. Since the isothermal points formed normals on his UCS diagram, transformation back into the xy plane revealed them still to be lines, but no longer perpendicular to the locus.