Intervals of color mismatch in chromaticity coordinates and in cone-fundamental-based (LMS) space

Abstract

We discuss the uncertainties in chromaticity coordinates in the color matching experiment reported by MacAdam [J. Opt. Soc. Am 32, 247 (1942)]. We also derive the uncertainties in cone-pigments based excitation space. The observer made color matchings by tuning the angle of a Rochon prism. The intervals of color mismatch were obtained using the average value and the standard deviations of the angle settings. We use in this work a rigorous statistical method to derive the probability density functions of chromaticity coordinates assuming a Gaussian distribution for the Rochon prism angle. We also derive the probability density functions of the L-, M-, and S- tristimulus values. We analyze how much the actual probability density functions deviate from the Gaussian. Finally, we determine the bounds of the intervals of color mismatch assuming that the areas of the tails of each probability density function are equal. The so derived intervals are compared to those reported in the original investigation due to MacAdam. We show that color-differences for a certain confidence level cannot be obtained as a simple common scaling factor of the color differences computed for a lower confidence level. The results obtained in LMS space at corneal level exhibit asymmetries between increment and decrement thresholds.