Analytic approximations for the CIE 1964 ten-degree-field color-matching functions*

Abstract

The similarity of the shapes and relative positions of the peaks and valleys of the first few hydrogen-atom radial probability-density functions to the CIE 1964 x¯,y¯,z¯,10°-field color-matching functions makes the former ideal candidates for analytic approximations to the latter. The hydrogen functions are, therefore, mapped into the wavelength range of the tristimulus coefficients and scaled appropriately. The two sets of curves are compared by looking at their ratios throughout the 380- to 750-nm range. Methods for curve fitting these ratios using a Chebychev-polynomial least-squares-fit procedure are described and approximate analytic expressions for x¯,y¯,z¯ are given for varying degrees of fitting accuracy.