MacAdam Color Difference Equation

n A color difference equation developed by David MacAdam which is now used as modified by Hugh Davidson and Fred Simon to incorporate the effect of lightness on the chromaticity differences:

$${{\Delta} \rm E} = {\rm [1/K(g}_{{\rm 11}} \overline {{{\Delta} \rm x}^{\rm 2} } + {\rm 2g}_{{\rm 12}} {{\Delta} x{\Delta} \rm y} + {\rm g}_{{\rm 22}} \overline {{{\Delta} \rm y}^{\rm 2} } + {\rm G}\overline {{{\Delta} \rm Y}^{\rm 2} } {\rm ]}^{{\rm 1/7}} $$

where g₁₁, 2G₁₁, and g₂₂ are constants depending on the chromaticity coordinates, x and y, and K and G are constants depending on the luminous reflectance or transmittance, Y. This color difference is frequently calculated from charts prepared by Simon and Goodwin, which have the required constants built-in.