Planckian Locus - The Planckian Locus in The XYZ Color Space

The Planckian Locus in The XYZ Color Space

In the CIE XYZ color space, the three coordinates defining a color are given by X, Y, and Z:

where I(λ,T) is the spectral radiance of the light being viewed, and X(λ), Y(λ) and Z(λ) are the color matching functions of the CIE standard colorimetric observer, shown in the diagram on the right, and λ is the wavelength. The Planckian locus is determined by substituting into the above equations the black body spectral radiance, which is given by Planck's law:

where:

I is the black body spectral radiance (power per unit area per unit solid angle per unit wavelength)

T is the temperature of the black body

h is Planck's constant

c is the speed of light

k is Boltzmann's constant

This will give the Planckian locus in CIE XYZ color space. If these coordinates are X_T, Y_T, Z_T where T is the temperature, then in the CIE chromaticity coordinates will be