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 Vλ 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.

© 1973 Optical Society of America

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References

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  1. S. L. Guth, J. Opt. Soc. Am. 55, 718 (1965).
    [Crossref]
  2. S. L. Guth, Vision Res. 7, 319 (1967).
    [Crossref] [PubMed]
  3. S. L. Guth, J. V. Alexander, J. I. Chumbly, C. B. Gillman, and M. M. Patterson, Vision Res. 8, 913 (1968).
    [Crossref] [PubMed]
  4. S. L. Guth, N. J. Donley, and R. T. Marrocco, Vision Res. 9, 537 (1969).
    [Crossref] [PubMed]
  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).
    [Crossref] [PubMed]
  7. W. W. Coblentz and W. B. Emerson, Natl. Bur. Std. (U. S.) Bull. 14, 167 (1917).
    [Crossref]
  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).
    [Crossref] [PubMed]
  12. H. R. Lodge, Dissertation, Indiana University (1971).
  13. W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).
    [Crossref] [PubMed]
  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).
    [Crossref] [PubMed]
  17. H. Helson and W. C. Michels, J. Opt. Soc. Am. 38, 1025 (1948).
    [Crossref] [PubMed]
  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).
    [Crossref] [PubMed]
  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).
    [Crossref]
  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).
    [Crossref] [PubMed]
  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).
    [Crossref] [PubMed]
  29. B. V. Graham and S. L. Guth, J. Opt. Soc. Am. 60, 1573 (1970).

1971 (1)

1970 (3)

1969 (1)

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

1968 (2)

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

R. M. Boynton and P. K. Kaiser, Science 161, 366 (1968).
[Crossref] [PubMed]

1967 (2)

1965 (1)

1964 (1)

W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).
[Crossref] [PubMed]

1960 (2)

1953 (1)

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

1951 (1)

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

1948 (1)

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).
[Crossref]

Alexander, J. V.

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

Boynton, R. M.

R. M. Boynton and P. K. Kaiser, Science 161, 366 (1968).
[Crossref] [PubMed]

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).
[Crossref] [PubMed]

Coblentz, W. W.

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

Donley, N. J.

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

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).
[Crossref]

Gillman, C. B.

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

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).
[Crossref] [PubMed]

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

S. L. Guth, Vision Res. 7, 319 (1967).
[Crossref] [PubMed]

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

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.

Judd, D. B.

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

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

Kaiser, P. K.

P. K. Kaiser, J. Opt. Soc. Am. 61, 966 (1971).
[Crossref] [PubMed]

R. M. Boynton and P. K. Kaiser, Science 161, 366 (1968).
[Crossref] [PubMed]

Kohlrausch, A.

A. Kohlrausch, Licht 5, 259 (1935).

Lewis, W. G.

Lodge, H. R.

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

Luria, S. M.

W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).
[Crossref] [PubMed]

Marrocco, R. T.

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

McCree, K. J.

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

Michels, W. C.

Miller, S.

Nimeroff, I.

Patterson, M. M.

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

Richards, W.

W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).
[Crossref] [PubMed]

Sperling, H. G.

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

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).
[Crossref] [PubMed]

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

J. Opt. Soc. Am. (8)

J. Physiol. (Lond.) (1)

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

Licht (1)

A. Kohlrausch, Licht 5, 259 (1935).

Natl. Bur. Std. (U. S.) Bull. (1)

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

Opt. Acta (1)

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

Science (1)

R. M. Boynton and P. K. Kaiser, Science 161, 366 (1968).
[Crossref] [PubMed]

Trans. Illum. Eng. Soc. (1)

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

Vision Res. (4)

S. L. Guth, Vision Res. 7, 319 (1967).
[Crossref] [PubMed]

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

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

W. Richards and S. M. Luria, Vision Res. 4, 281 (1964).
[Crossref] [PubMed]

Other (11)

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).

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

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

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

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

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

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. 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)].

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Figures (16)

F. 1
F. 1

Cosines of angles between spectral lights as derived from heterochromatic additivity data obtained at near-threshold levels (long dashes with squares), threshold levels (solid lines with circles), and as predicted by the A, T, D threshold model (short dashes). Each set of functions is arbitrarily positioned on the ordinate; the full ordinate values for each set can be reproduced by use of its unity value together with the scale shown on the left. Each function shows the cosine of the angle between the wavelength indicated at unity on the ordinate and the wavelength shown on the abscissa. Theoretical predictions were made at 10-nm intervals; therefore, the predicted functions are always identified by a wavelength that is an integral multiple of ten. If one other identifying wavelength is given, then that wavelength is appropriate for both the threshold and near-threshold functions.

F. 2
F. 2

Mean foveal spectral sensitivities obtained from five normal subjects using flicker-photometric (small dashes), direct-brightness-matching (solid line), and threshold (long dashes) techniques. Normalization is at 560 nm.

F. 3
F. 3

Foveal spectral sensitivities expressed relative to those from flicker photometry for direct brightness matching (solid line) and threshold (dashes with filled circles) as shown in Fig. 2, and for direct brightness matching as found by Coblentz and Emerson (Ref. 7) (unconnected crosses) and by Kaiser (Ref. 6) (dashes with no data points). Normalization is at 560 nm.

F. 4
F. 4

Direct-brightness-matching spectral sensitivities relative to those from flicker photometry, for each of five normal subjects. Normalization is at 560 nm.

F. 5
F. 5

Foveal-threshold spectral sensitivities relative to those from flicker photometry, for each of five normal subjects. Normalization is at 560 nm.

F. 6
F. 6

Equal-radiance response functions of the A, T, D threshold model. Shown are the achromatic (filled circles), yellowish-red vs bluish-green (hexagons), and greenish-yellow vs violet (open circles) systems.

F. 7
F. 7

Relative spectral sensitivities of the achromatic system (solid line with filled circles) and achromatic-plus-chromatic systems (open circles) of the A, T, D threshold model. Also shown is Judd’s correction (Ref. 20) of the CIE Vλ function (dashes). Above about 490 nm, the achromatic system has a spectral-sensitivity function that is essentially identical to Judd’s function which, in turn, is identical to the Vλ curve.

F. 8
F. 8

Threshold spectral sensitivities relative to those obtained by flicker photometry. Dashes show the experimental function, which is redrawn from Fig. 3, and the solid line shows the function predicted by the A, T, D threshold model.

F. 9
F. 9

Equal vector-luminance (i.e., equally detectable) response functions of the A, T, D threshold model. Shown are the achromatic (large circles), yellowish-red vs bluish-green (small circles), and greenish-yellow vs violet (triangles) systems.

F. 10
F. 10

Apparent saturation of a threshold-level spectrum as predicted by the A, T, D model.

F. 11
F. 11

Threshold-level wavelength discrimination as predicted by the A, T, D model.

F. 12
F. 12

Chromaticity diagram showing projections of spectral vectors through the unit achromatic plane of the A, T, D threshold model.

F. 13
F. 13

Equal lightness-to-luminance-ratio contours. From Wyszecki (Ref. 16).

F. 14
F. 14

Equal lightness-to-luminance-ratio (i.e., vector-luminance-to-achromaticness) contours for the entire chromaticity space according to the A, T, D threshold model.

F. 15
F. 15

Equal lightness-to-luminance-ratio (i.e., vector-luminance-to-achromaticness) contours for a subset of the chromaticity space according to the A, T, D threshold model.

F. 16
F. 16

Predicted heterochromatic additivity failures according to the threshold (dashes) and near-threshold (solid lines) A, T, D vector models. The figure should be interpreted as explained for Fig. 1.

Tables (2)

Tables Icon

Table I Vector luminances of each component in threshold-level bichromatic and trichromatic mixtures.

Tables Icon

Table II Vector luminancesa and cosinesb for chromatic components in unit-level, near-threshold bichromatic mixtures.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

cos θ i j = ( L r * * ) 2 ( L i * * ) 2 ( L j * * ) 2 2 L i * * L j * * ,
q = cos g b cos r g cos r b ( 1 cos r g 2 ) 1 2 .
L * * = [ ( Σ D i L i * * ) 2 + ( Σ E i L i * * ) 2 + ( Σ F i L i * * ) 2 ] 1 2 , i = r , g , b .
ā = 0.000 x ¯ + 0.954 y ¯ + 0.010 z ¯ , t ¯ = 0.799 x ¯ 0.646 y ¯ 0.167 z ¯ , d ¯ = 0.000 x ¯ 0.058 y ¯ + 0.030 z ¯ .
x ¯ = 1.244 ā + 1.251 t ¯ + 6.548 d ¯ , y ¯ = 1.027 ā + 0.000 t ¯ 0.342 d ¯ , z ¯ = 1.986 ā + 0.000 t ¯ + 32.693 d ¯ .
cos θ i , j = ( A L i * * ) ( A L j * * ) + ( T L i * * ) ( T L j * * ) + ( D L i * * ) ( D L j * * ) .
L * * = ( A 2 + T 2 + D 2 ) 1 2 .
ā = 0.000 x ¯ + 0.893 y ¯ + 0.0094 z ¯ , t ¯ = 1.070 x ¯ 0.864 y ¯ 0.223 z ¯ , d ¯ = 0.000 x ¯ 0.078 y ¯ + 0.400 z ¯ .