Scale values <i>D</i> of whiteness have been determined visually by the method of paired comparisons of a number of white samples that differed in hue, saturation, and lightness. Each sample was also specified by use of a newly developed whiteness formula <i>W</i> = <i>Y</i> - 33.33<i>p</i>. <i>W</i> is the whiteness, <i>Y</i> is the luminous reflectance of the sample, and <i>p</i> is the ratio of two distances in the 1931 CIE chromaticity diagram, <i>p</i> = <<i>OF</i>>/<<i>OE</i>>. <<i>OF</i>> is the distance between the chromaticity point <i>F</i> of the sample and a point <i>O</i> with the chromaticity coordinates <i>x</i><sub>o</sub> = 0.3090, <i>y</i><sub>o</sub> = 0.3170. Point <i>O</i> is the center of an ellipse with a major semiaxis <i>a</i> = 0.030 and a minor semiaxis <i>b</i> = 0.009. The angle of inclination of the major axis with respect to the positive direction of the <i>x</i> axis of the chromaticity diagram is θ = 48.0 °. <<i>OE</i>> is the distance between point <i>O</i> and the intersection <i>E</i> of the ellipse with the straight line through the points <i>O</i> and <i>F</i>. Good correlation between <i>D</i> and <i>W</i> was obtained in all cases, even if samples were compared that differed considerably in hue. This demonstrates the greater range of validity of the newly developed formula in comparison with current whiteness formulas.
R. Thielert and G. Schliemann, "Visual impression of whiteness and its colorimetric definition," J. Opt. Soc. Am. 63, 1607-1612 (1973)