Scale values D 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 W = Y − 33.33p. W is the whiteness, Y is the luminous reflectance of the sample, and p is the ratio of two distances in the 1931 CIE chromaticity diagram, p = <O F>/<O E>. <O F> is the distance between the chromaticity point F of the sample and a point O with the chromaticity coordinates x_{o} = 0.3090, y_{o} = 0.3170. Point O is the center of an ellipse with a major semiaxis a = 0.030 and a minor semiaxis b = 0.009. The angle of inclination of the major axis with respect to the positive direction of the x axis of the chromaticity diagram is θ = 48.0°. <O E> is the distance between point O and the intersection E of the ellipse with the straight line through the points O and F. Good correlation between D and W 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.

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D = visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressions are normally distributed. d = visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressions are uniformly distributed. W_{7} = whiteness, calculated from the Vaeck–Van Lierde formula (see Ref. 15). W = whiteness, calculated from Eq. (7).

D = visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressions are normally distributed. d = visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressions are uniformly distributed. W_{1} = whiteness, calculated from the Berger formula (see Refs. 8 and 10). W_{2} = whiteness, calculated from the Taube formula (see Refs. 8 and 11). W_{3} = whiteness, calculated from the Hunter formula (see Refs. 8 and 11). W_{4} = whiteness, calculated from the Stensby formula (see Refs. 8 and 12). W_{5} = whiteness, calculated from the Stephansen formula (see Refs. 8 and 13). W_{6} = SCAN brightness (see Refs. 8 and 14). W_{7} = whiteness, calculated from the Vaeck–Van Lierde formula (see Ref. 15). W = whiteness, calculated from Eq. (7).

Tables (2)

Table I

Tristimulus values, visually determined scale values of whiteness, and colorimetrically evaluated whiteness.

D = visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressions are normally distributed. d = visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressions are uniformly distributed. W_{7} = whiteness, calculated from the Vaeck–Van Lierde formula (see Ref. 15). W = whiteness, calculated from Eq. (7).

D = visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressions are normally distributed. d = visually determined scale values of whiteness, calculated with the assumption that differences between whiteness impressions are uniformly distributed. W_{1} = whiteness, calculated from the Berger formula (see Refs. 8 and 10). W_{2} = whiteness, calculated from the Taube formula (see Refs. 8 and 11). W_{3} = whiteness, calculated from the Hunter formula (see Refs. 8 and 11). W_{4} = whiteness, calculated from the Stensby formula (see Refs. 8 and 12). W_{5} = whiteness, calculated from the Stephansen formula (see Refs. 8 and 13). W_{6} = SCAN brightness (see Refs. 8 and 14). W_{7} = whiteness, calculated from the Vaeck–Van Lierde formula (see Ref. 15). W = whiteness, calculated from Eq. (7).