Psychometric scale values for color differences are correlated with physically measured chromaticity differences by use of a formula which postulates that the scale values are proportional to some power, less than unity, of distance in a subjectively isotropic, projective transformation of the CIE chromaticity diagram. Exponents ranging from 0.38 to 0.80 are reported. Eleven to 37% smaller root-mean-square errors of fit to psychometric scale values are obtained with the nonlinear hypothesis than with a linear hypothesis.
DAVID L. MACADAM, "Nonlinear Relations of Psychometric Scale Values to Chromaticity Differences," J. Opt. Soc. Am. 53, 754-755 (1963)