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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 4 — Apr. 1, 1980
  • pp: 411–417

Visual impression of whiteness and its colorimetric definition. II.

R. Thielert and G. Schliemann  »View Author Affiliations

JOSA, Vol. 70, Issue 4, pp. 411-417 (1980)

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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)

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  1. J. Lanter, "Prüfung und Bewertung von optischen Aufhellern," SVF Fachorgan Textilveredl. 19, 469–480 (1964).
  2. A. Räuchle and W. Schramm, "Allgemeine Betrachtungen zur visuellen und farbmetrischen Beurteilung von gebleichten und mit Aufhellern behandelten textilen Geweben," Textilveredlung 2, 719–729 (1967).
  3. J. Lanter, "Die Bewertung des Aufhelleffektes und die Bestimmung der Echtheiten optisch aufgehellter Textilien," Ciba Rundsch. 152, 26–32 (1960).
  4. Anonymous, "Visuelle Weissbewertung," Ciba-Geigy Rundsch. 1973/1, 10–13 (1973).
  5. R. Thielert and G. Schliemann, "Visual impression of whiteness and its colorimetric definition," J. Opt. Soc. Am. 63, 1607–1612 (1973).
  6. R. Griesser (private communication).
  7. G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967), p. 289.
  8. K. Honjyo and M. Nonaka, "Perception of white in a 10° field," J. Opt. Soc. Am. 60, 1690–1694 (1970).
  9. A. Hald, Statistical Theory with Engineering Applications (Wiley, New York, 1967), p. 608.
  10. The correlation coefficients of the samples F 1-F 12 and H 1-H 10 that are listed in Table II of our previous paper5 deviate slightly from those listed in Table II of this paper. This is because the whiteness values W calculated previously5 for these samples (see Table I of our previous paper) were slightly incorrect, presumably due to computational errors. The correlation coefficients r¯ (D, W) listed in Table II of this paper are the correct ones.

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