Some years ago a formula W = Y - c (l00p) for calculating the whiteness W of object colors was suggested. In this formula Y is the luminous reflectance of the sample, c is a constant, and p = 〈OF〉/〈OE〉 is the ratio of two distances in the 1931 CIE chromaticity diagram. 〈OF〉 is the distance between the chromaticity point F of the sample and a point O with the chromaticity coordinates x0, y0. Point O is the center of an ellipse with a semimajor axis a and a semiminor axis b. The angle of inclination of a with respect to the positive direction of the x axis of the chromaticity diagram is Θ. 〈OE〉 is the distance between point O and the intersection E of the ellipse with the straight line through the points O and F. Originally the numerical values of the parameters x0, y0, Θ, a, b, and c were chosen in such a way that a good correlation between W and visually determined scale values of whiteness D was obtained for all samples that were investigated. In the meantime, however, it became apparent that there was some discrepancy between the calculated whiteness W and the visual impression of whiteness with very light bluish samples. Therefore, a systematic gradual optimization of the parameters x0, y0, Θ, a, and b was carried out. This resulted in a statistically significant improvement of the correlation between D and W even with very light bluish samples. The numerical values of the optimized parameters are x0opt = 0.3060, y0opt =, 0.3130, Θopt = 54°. The numerical values of a, b, and the constant c remained unchanged, i.e., a = 0.030, b = 0.009, and c = 1/3.
© 1980 Optical Society of America
R. Thielert and G. Schliemann, "Visual impression of whiteness and its colorimetric definition. II.," J. Opt. Soc. Am. 70, 411-417 (1980)