Propagation of errors in a color matching experiment

Abstract

AbstractWe revisit the problem of propagation of errors in the color matching experiment reported by MacAdam [J. Opt. Soc. Am. 32, 247 (1942)]. The observer made color matchings by tuning the angle of a Rochon prism. The average value and the standard deviations of the angle settings were considered to derive the average tristimulus values and the uncertainty intervals. Here, we use a rigorous statistical method to derive the probability density functions of the tristimulus values assuming a Gaussian distribution for the Rochon prism angle. We analyze how much the actual probability density functions deviate from the Gaussian. We outline two methods to derive the interval of color mismatch and compare their predictions with those derived using the standard procedure.