von Kries coefficients

In 1905 von Kries said that if we accept the Young-Helmholtz theory of trichromatic vision the postulation can be madee that while the three cone mechanisms are affected differently by chromatic adaption their relative spectral sensitivities are not. That is, constant factors dependent upon the colour of the light can be used to describe the adaption provided they are different for the three mechanisms.

R¹ = aR

G¹ = bG

V¹ = gV

where R, G and V are the observer tristimulus values specifying the colour in the original adapting light and R¹, G¹ and V¹ are the tristimulus values of the same patch of light but with the observer now adapted to a different light. a b and g are the von Kries coefficients corresponding to the change in sensitivity of the cone mechanisms due to the adaption.

The exact relationship between the CIE system and the retinal cone mechanism is uncertain but if those suggested by Judd (1945) are adopted then the following equation also suggested by Judd expresses the changes in cone mechanism sensitivity in CIE terms incorporating the von Kries coefficients

X¹ = bX + 2.954(a - b)Y + 0.220(g - b)Z

Y¹ = Y

 Z¹ = gZ

where X, Y and Z are the CIE tristimulus values of a colour in one illuminant and X¹, Y¹ and Z¹ are the tristimulus values of a colour which appears the same under a different illuminant.

To use the equation to adapt from say 'A' to 'D₆₅' we must determine the coefficients a, b and g from: