Abstract

In three separate experiments it is shown that (i) heterochromatic additivity failures for foveally viewed trichromatic lights can be predicted using a vector model derived from bichromatic additivity data, (ii) near-threshold bichromatic additivity failures are not qualitatively different from threshold-level failures, and (iii) foveal spectral sensitivities obtained by direct brightness matching and threshold methods are greater in the long- and short-wavelength ends of the spectrum than sensitivities obtained by flicker photometry. A new opponent-colors model that is appropriate for threshold-level color vision is expressed as a transformation of the CIE standard observer. The model allows the derivation of a light unit that correlates with signal detectability and predicts (a) confusion lines for deuteranopic and tritanopic vision, (b) spectral sensitivity as measured by flicker photometry (i.e., a sensitivity function much like the CIE <i>V</i><sub>λ</sub>function), (c) spectral sensitivity as measured by threshold (or direct-matching) techniques, (d) threshold-level heterochromatic additivity failures, (e) the apparent saturation of a threshold-level spectrum, (f) wavelength discrimination for a near-threshold spectrum, (g) loci of constant lightness-to-luminance ratios Within the CIE chromaticity diagram, and (h) the essential quantitative differences between threshold and near-threshold heterochromatic additivity failures.

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  1. S. L. Guth, J. Opt. Soc. Am. 55, 718 (1965).
  2. S. L. Guth, Vision Res. 7, 319 (1967).
  3. S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
  4. S. L. Guth, N. J. Donley, and R. T. Marrocco, Vision Res. 9, 537 (1969).
  5. S. L. Guth, in Visual Science, edited by J. R. Pierce and J. R. Levene (Indiana U. P., Bloomington, 1971), p. 125.
  6. P. K. Kaiser, J. Opt. Soc. Am. 61, 966 (1971).
  7. W. W. Coblentz and W. B. Emerson, Natl. Bur. Std. (U. S.) Bull. 14, 167 (1917).
  8. A. Dresler, Trans. Illum. Eng. Soc. 18, 141 (1953).
  9. A. Kohlrausch, Licht 5, 259 (1935).
  10. H. G. Sperling, in N. P. L. Symposium No. 8: Visual Problems of Colour (H. M. Stationery Office, London, 1958), p. 251.
  11. H. G. Sperling and W. G. Lewis, J. Opt. Soc. Am. 50, 156 (1960).
  12. H. R. Lodge, Dissertation, Indiana University (1971).
  13. W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).
  14. D. B. Judd, in Handbook of Experimental Psychology, edited by S. S. Stevens (Wiley, New York, 1951).
  15. P. L. Walraven, Dissertation, University of Utrecht (1962).
  16. G. Wyszecki, J. Opt. Soc. Am. 57, 254 (1967).
  17. H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).
  18. G. Wyszecki and W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulas (Wiley, New York, 1967), p. 405.
  19. I. Nimeroff, J. Opt. Soc. Am. 60, 966 (1970).
  20. D. B. Judd, in CIE Proceedings, Vol. I, Part 7 (Bureau Central CIE, 57 Rue Cuvier, Paris 5, 1951).
  21. R. A. Weale, J. Physiol. (Lond.) 113, 115 (1951).
  22. K. J. McCree, Opt. Acta 7, 317 (1960).
  23. R. M. Boynton and G. Wagner, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (AIC/Holland, Soesterberg, 1972).
  24. S. Miller, J. Opt. Soc. Am. 60, 1404 (1970).
  25. S. L. Guth, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (AIC/Holland, Soesterberg, 1972).
  26. For these reasons, the CIE X, Y, Z colorimetric system, which assumes Abney's law to be true, is logically valid. The use of Abney's law in deriving the distribution coefficients amounts to saying that the whiteness component on each side of a color match is identical—a statement which is, of course, true.
  27. It is possible that customary luminance values will also remain useful when responses involve temporal resolution (e.g., flicker photometry) or spatial resolution [e.g., border minimization (Refs. 6 and 28) or visual acuity (Ref. 29)].
  28. R. M. Boynton and P. K. Kaiser, Science 161, 366 (1968).
  29. B. V. Graham and S. L. Guth, J. Opt. Soc. Am. 60, 1573 (1970).

1971 (2)

P. K. Kaiser, J. Opt. Soc. Am. 61, 966 (1971).

H. R. Lodge, Dissertation, Indiana University (1971).

1970 (3)

I. Nimeroff, J. Opt. Soc. Am. 60, 966 (1970).

S. Miller, J. Opt. Soc. Am. 60, 1404 (1970).

B. V. Graham and S. L. Guth, J. Opt. Soc. Am. 60, 1573 (1970).

1969 (1)

S. L. Guth, N. J. Donley, and R. T. Marrocco, Vision Res. 9, 537 (1969).

1968 (2)

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).

R. M. Boynton and P. K. Kaiser, Science 161, 366 (1968).

1967 (2)

S. L. Guth, Vision Res. 7, 319 (1967).

G. Wyszecki, J. Opt. Soc. Am. 57, 254 (1967).

1965 (1)

S. L. Guth, J. Opt. Soc. Am. 55, 718 (1965).

1964 (1)

W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).

1962 (1)

P. L. Walraven, Dissertation, University of Utrecht (1962).

1960 (2)

H. G. Sperling and W. G. Lewis, J. Opt. Soc. Am. 50, 156 (1960).

K. J. McCree, Opt. Acta 7, 317 (1960).

1953 (1)

A. Dresler, Trans. Illum. Eng. Soc. 18, 141 (1953).

1951 (2)

D. B. Judd, in CIE Proceedings, Vol. I, Part 7 (Bureau Central CIE, 57 Rue Cuvier, Paris 5, 1951).

R. A. Weale, J. Physiol. (Lond.) 113, 115 (1951).

1948 (1)

H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).

1935 (1)

A. Kohlrausch, Licht 5, 259 (1935).

1917 (1)

W. W. Coblentz and W. B. Emerson, Natl. Bur. Std. (U. S.) Bull. 14, 167 (1917).

Alexander, J. V.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).

Boynton, R. M.

R. M. Boynton and P. K. Kaiser, Science 161, 366 (1968).

R. M. Boynton and G. Wagner, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (AIC/Holland, Soesterberg, 1972).

Chumbly, J. I.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).

Coblentz, W. W.

W. W. Coblentz and W. B. Emerson, Natl. Bur. Std. (U. S.) Bull. 14, 167 (1917).

Donley, N. J.

S. L. Guth, N. J. Donley, and R. T. Marrocco, Vision Res. 9, 537 (1969).

Dresler, A.

A. Dresler, Trans. Illum. Eng. Soc. 18, 141 (1953).

Emerson, W. B.

W. W. Coblentz and W. B. Emerson, Natl. Bur. Std. (U. S.) Bull. 14, 167 (1917).

Gillman, C. B.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).

Graham, B. V.

B. V. Graham and S. L. Guth, J. Opt. Soc. Am. 60, 1573 (1970).

Guth, S. L.

B. V. Graham and S. L. Guth, J. Opt. Soc. Am. 60, 1573 (1970).

S. L. Guth, N. J. Donley, and R. T. Marrocco, Vision Res. 9, 537 (1969).

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).

S. L. Guth, Vision Res. 7, 319 (1967).

S. L. Guth, J. Opt. Soc. Am. 55, 718 (1965).

S. L. Guth, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (AIC/Holland, Soesterberg, 1972).

S. L. Guth, in Visual Science, edited by J. R. Pierce and J. R. Levene (Indiana U. P., Bloomington, 1971), p. 125.

Helson, H.

H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).

Judd, D. B.

D. B. Judd, in CIE Proceedings, Vol. I, Part 7 (Bureau Central CIE, 57 Rue Cuvier, Paris 5, 1951).

D. B. Judd, in Handbook of Experimental Psychology, edited by S. S. Stevens (Wiley, New York, 1951).

Kaiser, P. K.

P. K. Kaiser, J. Opt. Soc. Am. 61, 966 (1971).

R. M. Boynton and P. K. Kaiser, Science 161, 366 (1968).

Kohlrausch, A.

A. Kohlrausch, Licht 5, 259 (1935).

Lewis, W. G.

H. G. Sperling and W. G. Lewis, J. Opt. Soc. Am. 50, 156 (1960).

Lodge, H. R.

H. R. Lodge, Dissertation, Indiana University (1971).

Luria, S. M.

W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).

Marrocco, R. T.

S. L. Guth, N. J. Donley, and R. T. Marrocco, Vision Res. 9, 537 (1969).

McCree, K. J.

K. J. McCree, Opt. Acta 7, 317 (1960).

Michels, W. C.

H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).

Miller, S.

S. Miller, J. Opt. Soc. Am. 60, 1404 (1970).

Nimeroff, I.

I. Nimeroff, J. Opt. Soc. Am. 60, 966 (1970).

Patterson, M. M.

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).

Richards, W.

W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).

Sperling, H. G.

H. G. Sperling and W. G. Lewis, J. Opt. Soc. Am. 50, 156 (1960).

H. G. Sperling, in N. P. L. Symposium No. 8: Visual Problems of Colour (H. M. Stationery Office, London, 1958), p. 251.

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulas (Wiley, New York, 1967), p. 405.

Wagner, G.

R. M. Boynton and G. Wagner, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (AIC/Holland, Soesterberg, 1972).

Walraven, P. L.

P. L. Walraven, Dissertation, University of Utrecht (1962).

Weale, R. A.

R. A. Weale, J. Physiol. (Lond.) 113, 115 (1951).

Wyszecki, G.

G. Wyszecki, J. Opt. Soc. Am. 57, 254 (1967).

G. Wyszecki and W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulas (Wiley, New York, 1967), p. 405.

Other (29)

S. L. Guth, J. Opt. Soc. Am. 55, 718 (1965).

S. L. Guth, Vision Res. 7, 319 (1967).

S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).

S. L. Guth, N. J. Donley, and R. T. Marrocco, Vision Res. 9, 537 (1969).

S. L. Guth, in Visual Science, edited by J. R. Pierce and J. R. Levene (Indiana U. P., Bloomington, 1971), p. 125.

P. K. Kaiser, J. Opt. Soc. Am. 61, 966 (1971).

W. W. Coblentz and W. B. Emerson, Natl. Bur. Std. (U. S.) Bull. 14, 167 (1917).

A. Dresler, Trans. Illum. Eng. Soc. 18, 141 (1953).

A. Kohlrausch, Licht 5, 259 (1935).

H. G. Sperling, in N. P. L. Symposium No. 8: Visual Problems of Colour (H. M. Stationery Office, London, 1958), p. 251.

H. G. Sperling and W. G. Lewis, J. Opt. Soc. Am. 50, 156 (1960).

H. R. Lodge, Dissertation, Indiana University (1971).

W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).

D. B. Judd, in Handbook of Experimental Psychology, edited by S. S. Stevens (Wiley, New York, 1951).

P. L. Walraven, Dissertation, University of Utrecht (1962).

G. Wyszecki, J. Opt. Soc. Am. 57, 254 (1967).

H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).

G. Wyszecki and W. S. Stiles, Color Science. Concepts and Methods, Quantitative Data and Formulas (Wiley, New York, 1967), p. 405.

I. Nimeroff, J. Opt. Soc. Am. 60, 966 (1970).

D. B. Judd, in CIE Proceedings, Vol. I, Part 7 (Bureau Central CIE, 57 Rue Cuvier, Paris 5, 1951).

R. A. Weale, J. Physiol. (Lond.) 113, 115 (1951).

K. J. McCree, Opt. Acta 7, 317 (1960).

R. M. Boynton and G. Wagner, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (AIC/Holland, Soesterberg, 1972).

S. Miller, J. Opt. Soc. Am. 60, 1404 (1970).

S. L. Guth, in Color Metrics, edited by J. J. Vos, L. F. C. Friele, and P. L. Walraven (AIC/Holland, Soesterberg, 1972).

For these reasons, the CIE X, Y, Z colorimetric system, which assumes Abney's law to be true, is logically valid. The use of Abney's law in deriving the distribution coefficients amounts to saying that the whiteness component on each side of a color match is identical—a statement which is, of course, true.

It is possible that customary luminance values will also remain useful when responses involve temporal resolution (e.g., flicker photometry) or spatial resolution [e.g., border minimization (Refs. 6 and 28) or visual acuity (Ref. 29)].

R. M. Boynton and P. K. Kaiser, Science 161, 366 (1968).

B. V. Graham and S. L. Guth, J. Opt. Soc. Am. 60, 1573 (1970).

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