Planckian locus

In Color theory The Planckian locus is generally the path that the color of a black body would take in a particular color space as the blackbody temperature changes. Generally, a color space is a set of three numbers (e.g. X, Y, and Z) which specify the color and brightness of a particular homogeneous visual stimulus. Sometimes we may only wish to deal with the chromaticity (color) of a visual stimulus. This is a two-dimensional space of two numbers (e.g. x and y) which leave out the brightness information. In this case the Planckian locus is the path that the color of a black body takes in this chromaticity space as the blackbody temperature changes.

Example: The Planckian locus in CIE XYZ space

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

$X = \int_0^\infty X(\lambda)I(\lambda)\,d\lambda$

$Y = \int_0^\infty Y(\lambda)I(\lambda)\,d\lambda$

$Z = \int_0^\infty Z(\lambda)I(\lambda)\,d\lambda$

where I(λ) is the spectral intensity of the light being viewed, and X(λ), Y(λ) and Z(λ) are the CIE standard observer functions shown in the diagram on the right, and λ is the wavelength. The Planckian locus is determined by substituting the Black body intensity into the above equations. The black body intensity is given by:

$I(\lambda) =\frac{2hc^2}{\lambda^5}\frac{1}{\exp\left(\frac{hc/\lambda}{kT}\right)-1}$

where:

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 XYZ space. If these coordinates are X(T), Y(T), Z(T) where T is the temperature, then In the CIE chromaticity coordinates will be

$x(T) = \frac{X(T)}{X(T)+Y(T)+Z(T)}$

$y(T) = \frac{Y(T)}{X(T)+Y(T)+Z(T)}$

The Planckian locus in xy space is shown in the diagram on the left.

Categories: Color