page_title: Color temperature
section_title: Background
hierarchical_section_title: Color temperature / Correlated color temperature / Background
caption_attribution_description: Judd's UCS using the 1931 standard observer and second radiation constant c2=1.4388
context_page_description: The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of a color comparable to that of the light source. Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, horticulture, and other fields. In practice, color temperature is meaningful only for light sources that do in fact correspond somewhat closely to the radiation of some black body, i.e., light in a range going from red to orange to yellow to white to blueish white; it does not make sense to speak of the color temperature of, e.g., a green or a purple light. Color temperature is conventionally expressed in kelvins, using the symbol K, a unit of measure for absolute temperature.
  Color temperatures over 5000 K are called "cool colors", while lower color temperatures are called "warm colors". "Warm" in this context is an analogy to radiated heat flux of traditional incandescent lighting rather than temperature. The spectral peak of warm-coloured light is closer to infrared, and most natural warm-coloured light sources emit significant infrared radiation.
context_section_description: 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:
  A difference of one micro-reciprocal-degree (μrd) is fairly representative of the doubtfully perceptible difference under the most favorable conditions of observation.
  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.
caption: Judd's uniform chromaticity space (UCS), with the Planckian locus and the isotherms from 1000 K to 10000 K, perpendicular to the locus. Judd calculated the isotherms in this space before translating them back into the (x,y) chromaticity space, as depicted in the diagram at the top of the article.
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