Planckian locus

The Planckian locus, the path that the color of a black body takes as the blackbody temperature changes, is often shown in this standard chromaticity space.

The Planckian locus is determined by substituting into the above equations the black body spectral radiant exitance, which is given by Planck's law: where: and This will give the Planckian locus in CIE XYZ color space.

If these coordinates are XT, YT, ZT where T is the temperature, then the CIE chromaticity coordinates will be Note that in the above formula for Planck's Law, you might as well use c1L = 2hc2 (the first radiation constant for spectral radiance) instead of c1 (the “regular” first radiation constant), in which case the formula would give the spectral radiance L(λ,T) of the black body instead of the spectral radiant exitance M(λ,T).

The Planckian locus in xy space is depicted as a curve in the chromaticity diagram above.

Alternatively, one can use the chromaticity (x, y) coordinates estimated from above to derive the corresponding (u, v), if a larger range of temperatures is required.

The correlated color temperature (Tcp) is the temperature of the Planckian radiator whose perceived colour most closely resembles that of a given stimulus at the same brightness and under specified viewing conditionsThe mathematical procedure for determining the correlated color temperature involves finding the closest point to the light source's white point on the Planckian locus.

[6] Today, the CIE 1960 color space is deprecated for other purposes:[7] The 1960 UCS diagram and 1964 Uniform Space are declared obsolete recommendation in CIE 15.2 (1986), but have been retained for the time being for calculating colour rendering indices and correlated colour temperature.Owing to the perceptual inaccuracy inherent to the concept, it suffices to calculate to within 2 K at lower CCTs and 10 K at higher CCTs to reach the threshold of imperceptibility.

As measuring techniques have improved, the General Conference on Weights and Measures has revised its estimate of this constant, with the International Temperature Scale (and briefly, the International Practical Temperature Scale).

These successive revisions caused a shift in the Planckian locus and, as a result, the correlated color temperature scale.

Before ceasing publication of standard illuminants, the CIE worked around this problem by explicitly specifying the form of the SPD, rather than making references to black bodies and a color temperature.

Nevertheless, it is useful to be aware of previous revisions in order to be able to verify calculations made in older texts:[9][10]