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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 70, Iss. 12 — Dec. 1, 1980
  • pp: 1471–1476

Equations for chromatic discrimination models

Robert M. Boynton and John J. Wisowaty  »View Author Affiliations

JOSA, Vol. 70, Issue 12, pp. 1471-1476 (1980)

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Equations are derived to fit the cone sensitivity values of Smith and Pokorny, which are based mainly upon Judd’s modified color matching functions and the spectral sensitivities of normal and dichromatic observers. The equations, which fit Smith and Pokorny’s values to within 1 to 3%, are smooth and differentiable. Derivatives of cone sensitivities for an equal luminance spectrum, which are of particular importance for models of chromatic discrimination, have been calculated and are shown graphically.

© 1980 Optical Society of America

Robert M. Boynton and John J. Wisowaty, "Equations for chromatic discrimination models," J. Opt. Soc. Am. 70, 1471-1476 (1980)

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  1. A. König and C. Dieterici, "Die Grünempfindungen in normalen und anomalen Farbensystemen und ihre Intensitätsverteilung im Spektrum," Z. Psychol. Physiol. Sinnesorg. 4, 241–347 (1893).
  2. J. J. Vos and P. L. Walraven, "On the derivation of the foveal receptor primaries," Vis. Res. 11, 799–818 (1971).
  3. V. C. Smith and J. Pokorny, "Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm," Vis. Res. 15, 161–171 (1975).
  4. A. Eisner and D. I. A. MacLeod, "Blue cones do not contribute to luminance," J. Opt. Soc. Am. 70, 121–123 (1980).
  5. Smith and Pokorny do not give tabled values, but rather present the transformation equations from which they may be calculated. We thank V. Smith for furnishing tabled sensitivity values.
  6. The most convenient source for Judd's values is in G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967), p. 436.
  7. Curves similar to these are given in R. M. Boynton, Human Color Vision, (Holt, New York, 1979), p. 262, where a chromatic discrimination model is discussed.
  8. Transformation equations have been developed that now make it possible to compute Judd's values from CIE values [J. J. Vos, "Colorimetric and photometric properties of a 2° fundamental observer," Color Res. Appl. 3, 125–128, (1978)]. Since the CIE data are readily available in 1-nm intervals, values based on Judd's equations can also be determined for these smaller steps.
  9. This additional information is available as AIP document No. PAPS JOSAA-70-1471-27. Order by PAPS number and journal reference from American Institute of Physics, Auxiliary Publication Service, 335 East 45 St., New York, N.Y. 10017. The price is $5.00. Make remittances payable to the American Institute of Physics.

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