Abstract

The contrast thresholds of equiluminous chromaticity-modulated gratings are measured for various waveforms (sine-, square-, and triangular-wave gratings). The expectation is expressed that only the fundamental Fourier component is of significance in the threshold visibility of colored gratings. In addition, the Fourier transformation is applied to the chromatic spatial-sensitivity curves. The transformed functions illustrate clearly the spatial organization of the contrast mechanisms. For 160 trolands, the summation area of the red-green chromatic activity extends over 10′, whereas the yellow–blue activity integrates over about 25′. A comparison of the Fourier transforms of a luminance- and chromatic-threshold contrast curve shows (1) inhibitory qualities and (2) the greater spatial sensitivity of the luminous function. The assumption is made that the visual resolution for differences of brightness, as well as chromaticity, is limited by the diffraction of light by the pupil. The visual acuity for differences of hue as a function of the background wavelength is thus predicted for a 30-cpd grating and compared with an empirical function. There is good agreement.

© 1969 Optical Society of America

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References

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  1. O. Dupuy, Vision Res. 8, 1507 (1968).
    [Crossref] [PubMed]
  2. J. P. Thomas, Vision Res. 8, 49 (1968).
    [Crossref]
  3. O. H. Schade, J. Soc. Motion Picture Television Engr. 67, 801 (1958).
  4. D. G. Green, J. Physiol. (London) 196, 415 (1968).
  5. H. Schober and H. Munker, Vision Res. 7, 1015 (1967).
    [Crossref] [PubMed]
  6. F. J. J. Clarke, Symposium: Colour Measurement in Industry (the Colour Group, London, 1967), p. 132.
  7. G. J. C. van der Horst and M. A. Bouman, J. Opt. Soc. Am. 59, 1482 (1969).
    [Crossref] [PubMed]
  8. F. W. Campbell and J. J. Kulikowski, J. Physiol. (London) 187, 437 (1966).
  9. F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).
  10. G. J. C. van der Horst, J. Opt. Soc. Am. 59, 1213 (1969).
    [Crossref] [PubMed]
  11. See also Table II in Ref. 7.
  12. We use here the distance between the zero crossings in the plot.
  13. G. J. C. van der Horst, C. M. M. de Weert, and M. A. Bouman, J. Opt. Soc. Am. 57, 1260 (1967).
    [Crossref] [PubMed]
  14. In Ref. 7 and 10. The viewing distance was increased in this particular case from 3.70 to 7.80 m, in order to have a greater range of spatial frequencies. One observer (the author) is used as subject. Pupil diameter was now 1.5 mm.
  15. The chromaticity contrast at the reference color Y is defined as follows: ΔC={(Δx)2+(Δy)2}12={(x−x0)2+(y−y0)2}12, where (x0,y0) are the chromaticity coordinates of the reference point Y.
  16. G. von Békésy, J. Opt. Soc. Am. 50, 1060 (1960).
    [Crossref]
  17. G. von Békésy, Vision Res. 8, 1483 (1968).
    [Crossref]
  18. O. Bryngdahl, Pfüg. Arch. Ges. Physiol. 280, 362 (1964).
    [Crossref]
  19. O. Bryngdahl, Vision Res. 6, 553 (1966).
    [Crossref] [PubMed]
  20. A. S. Patel, J. Opt. Soc. Am. 56, 689 (1966).
    [Crossref] [PubMed]
  21. V. D. Glazer, Vision Res. 5, 497 (1965).
    [Crossref]
  22. A. Marechal and M. Françon, Diffraction, Structure des Images (Ed. Revue d’Optique Théorique et Instrumentale, Paris, 1960).
  23. The reader may be referred to the discussion on this matter in Ref.13.
  24. We now make the important assumption that the perception of a grating is dependent on only the chromatic contrast and not on the grating frequency. Because of the variation of receptive fields with the eccentricity, e.g., a varying ratio of rods and cones, this assumption may be contestable.
  25. W. D. Wright, Researches in Normal and Defective Colour-Vision (Henry Kimpton, London, 1946).
  26. For this transformation, we used Pitt’s fundamental response curves, as revised byP. L. Walraven and M. A. Bouman. [Vision Res. 6, 567 (1966).] Using the 1931 CIE tristimulus values, substantially the same results were obtained as those plotted in Fig. 7.
    [Crossref] [PubMed]
  27. C. R. Cavonius, Science 152, 1276 (1966).In his study Cavonius used an artificial pupil of 1.5 mm. The stimulus size was 1°. Retinal illuminance 42 td. The hue-discrimination data of Wright were obtained for a 2° field, 70 td.
    [Crossref] [PubMed]
  28. A. C. S. van Heel, J. Opt. Soc. Am. 36, 237 (1946).
    [PubMed]

1969 (2)

1968 (5)

O. Dupuy, Vision Res. 8, 1507 (1968).
[Crossref] [PubMed]

J. P. Thomas, Vision Res. 8, 49 (1968).
[Crossref]

D. G. Green, J. Physiol. (London) 196, 415 (1968).

G. von Békésy, Vision Res. 8, 1483 (1968).
[Crossref]

F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).

1967 (2)

1966 (5)

F. W. Campbell and J. J. Kulikowski, J. Physiol. (London) 187, 437 (1966).

For this transformation, we used Pitt’s fundamental response curves, as revised byP. L. Walraven and M. A. Bouman. [Vision Res. 6, 567 (1966).] Using the 1931 CIE tristimulus values, substantially the same results were obtained as those plotted in Fig. 7.
[Crossref] [PubMed]

C. R. Cavonius, Science 152, 1276 (1966).In his study Cavonius used an artificial pupil of 1.5 mm. The stimulus size was 1°. Retinal illuminance 42 td. The hue-discrimination data of Wright were obtained for a 2° field, 70 td.
[Crossref] [PubMed]

O. Bryngdahl, Vision Res. 6, 553 (1966).
[Crossref] [PubMed]

A. S. Patel, J. Opt. Soc. Am. 56, 689 (1966).
[Crossref] [PubMed]

1965 (1)

V. D. Glazer, Vision Res. 5, 497 (1965).
[Crossref]

1964 (1)

O. Bryngdahl, Pfüg. Arch. Ges. Physiol. 280, 362 (1964).
[Crossref]

1960 (1)

1958 (1)

O. H. Schade, J. Soc. Motion Picture Television Engr. 67, 801 (1958).

1946 (1)

Bouman, M. A.

G. J. C. van der Horst and M. A. Bouman, J. Opt. Soc. Am. 59, 1482 (1969).
[Crossref] [PubMed]

G. J. C. van der Horst, C. M. M. de Weert, and M. A. Bouman, J. Opt. Soc. Am. 57, 1260 (1967).
[Crossref] [PubMed]

For this transformation, we used Pitt’s fundamental response curves, as revised byP. L. Walraven and M. A. Bouman. [Vision Res. 6, 567 (1966).] Using the 1931 CIE tristimulus values, substantially the same results were obtained as those plotted in Fig. 7.
[Crossref] [PubMed]

Bryngdahl, O.

O. Bryngdahl, Vision Res. 6, 553 (1966).
[Crossref] [PubMed]

O. Bryngdahl, Pfüg. Arch. Ges. Physiol. 280, 362 (1964).
[Crossref]

Campbell, F. W.

F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).

F. W. Campbell and J. J. Kulikowski, J. Physiol. (London) 187, 437 (1966).

Cavonius, C. R.

C. R. Cavonius, Science 152, 1276 (1966).In his study Cavonius used an artificial pupil of 1.5 mm. The stimulus size was 1°. Retinal illuminance 42 td. The hue-discrimination data of Wright were obtained for a 2° field, 70 td.
[Crossref] [PubMed]

Clarke, F. J. J.

F. J. J. Clarke, Symposium: Colour Measurement in Industry (the Colour Group, London, 1967), p. 132.

de Weert, C. M. M.

Dupuy, O.

O. Dupuy, Vision Res. 8, 1507 (1968).
[Crossref] [PubMed]

Françon, M.

A. Marechal and M. Françon, Diffraction, Structure des Images (Ed. Revue d’Optique Théorique et Instrumentale, Paris, 1960).

Glazer, V. D.

V. D. Glazer, Vision Res. 5, 497 (1965).
[Crossref]

Green, D. G.

D. G. Green, J. Physiol. (London) 196, 415 (1968).

Kulikowski, J. J.

F. W. Campbell and J. J. Kulikowski, J. Physiol. (London) 187, 437 (1966).

Marechal, A.

A. Marechal and M. Françon, Diffraction, Structure des Images (Ed. Revue d’Optique Théorique et Instrumentale, Paris, 1960).

Munker, H.

H. Schober and H. Munker, Vision Res. 7, 1015 (1967).
[Crossref] [PubMed]

Patel, A. S.

Robson, J. G.

F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).

Schade, O. H.

O. H. Schade, J. Soc. Motion Picture Television Engr. 67, 801 (1958).

Schober, H.

H. Schober and H. Munker, Vision Res. 7, 1015 (1967).
[Crossref] [PubMed]

Thomas, J. P.

J. P. Thomas, Vision Res. 8, 49 (1968).
[Crossref]

van der Horst, G. J. C.

van Heel, A. C. S.

von Békésy, G.

Walraven, P. L.

For this transformation, we used Pitt’s fundamental response curves, as revised byP. L. Walraven and M. A. Bouman. [Vision Res. 6, 567 (1966).] Using the 1931 CIE tristimulus values, substantially the same results were obtained as those plotted in Fig. 7.
[Crossref] [PubMed]

Wright, W. D.

W. D. Wright, Researches in Normal and Defective Colour-Vision (Henry Kimpton, London, 1946).

J. Opt. Soc. Am. (6)

J. Physiol. (London) (3)

D. G. Green, J. Physiol. (London) 196, 415 (1968).

F. W. Campbell and J. J. Kulikowski, J. Physiol. (London) 187, 437 (1966).

F. W. Campbell and J. G. Robson, J. Physiol. (London) 197, 551 (1968).

J. Soc. Motion Picture Television Engr. (1)

O. H. Schade, J. Soc. Motion Picture Television Engr. 67, 801 (1958).

Pfüg. Arch. Ges. Physiol. (1)

O. Bryngdahl, Pfüg. Arch. Ges. Physiol. 280, 362 (1964).
[Crossref]

Science (1)

C. R. Cavonius, Science 152, 1276 (1966).In his study Cavonius used an artificial pupil of 1.5 mm. The stimulus size was 1°. Retinal illuminance 42 td. The hue-discrimination data of Wright were obtained for a 2° field, 70 td.
[Crossref] [PubMed]

Vision Res. (7)

G. von Békésy, Vision Res. 8, 1483 (1968).
[Crossref]

For this transformation, we used Pitt’s fundamental response curves, as revised byP. L. Walraven and M. A. Bouman. [Vision Res. 6, 567 (1966).] Using the 1931 CIE tristimulus values, substantially the same results were obtained as those plotted in Fig. 7.
[Crossref] [PubMed]

V. D. Glazer, Vision Res. 5, 497 (1965).
[Crossref]

H. Schober and H. Munker, Vision Res. 7, 1015 (1967).
[Crossref] [PubMed]

O. Dupuy, Vision Res. 8, 1507 (1968).
[Crossref] [PubMed]

J. P. Thomas, Vision Res. 8, 49 (1968).
[Crossref]

O. Bryngdahl, Vision Res. 6, 553 (1966).
[Crossref] [PubMed]

Other (9)

In Ref. 7 and 10. The viewing distance was increased in this particular case from 3.70 to 7.80 m, in order to have a greater range of spatial frequencies. One observer (the author) is used as subject. Pupil diameter was now 1.5 mm.

The chromaticity contrast at the reference color Y is defined as follows: ΔC={(Δx)2+(Δy)2}12={(x−x0)2+(y−y0)2}12, where (x0,y0) are the chromaticity coordinates of the reference point Y.

F. J. J. Clarke, Symposium: Colour Measurement in Industry (the Colour Group, London, 1967), p. 132.

See also Table II in Ref. 7.

We use here the distance between the zero crossings in the plot.

A. Marechal and M. Françon, Diffraction, Structure des Images (Ed. Revue d’Optique Théorique et Instrumentale, Paris, 1960).

The reader may be referred to the discussion on this matter in Ref.13.

We now make the important assumption that the perception of a grating is dependent on only the chromatic contrast and not on the grating frequency. Because of the variation of receptive fields with the eccentricity, e.g., a varying ratio of rods and cones, this assumption may be contestable.

W. D. Wright, Researches in Normal and Defective Colour-Vision (Henry Kimpton, London, 1946).

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Figures (7)

F. 1
F. 1

Square-wave and triangular-wave luminance distributions. The average luminance I0 is indicated by a dotted line.

F. 2
F. 2

CIE chromaticity diagram. R, G, and B are the chromaticity coordinates of the color-television phosphors. The chromatic threshold contrast was measured at standard white E and yellow Y.

F. 3
F. 3

Chromatic threshold-contrast modulation for square-wave (□), sine-wave (0), and triangular-wave (△) gratings. Reference color is white E, with red-bluish-green chromatic modulation. Purity is expressed in percent for a dominant wavelength of 492 nm. Retinal illuminance 160 td. The ratios of sine wave to square wave (0) and sine wave to triangular wave (●) are plotted at the bottom of the figure. The bars show the standard deviations. Solid horizontal lines are drawn corresponding to the ratios 1.27 and 0.81. Pupil diameter 2 mm.

F. 4
F. 4

Fourier cosine transforms of red–bluish-green (solid line) and yellow–blue (dashed line) chromatic-sensitivity functions. The curves are plotted linearly. Reference color is standard E, at 160 td. The threshold-contrast modulation curves were taken from Figs. 2 and 6 from Ref. 7.

F. 5
F. 5

Luminance threshold-contrast modulation (x) for reference color G, 29 td. The luminance contrast is plotted along the right ordinate. Chromatic threshold-contrast modulation (0) for reference color Y, 33 td. Color contrast is plotted along the left ordinate. The grating had a square waveform. Pupil diameter 1.5 mm.

F. 6
F. 6

Fourier cosine transforms of the reciprocal-contrast modulation curves of Fig. 5. The solid line represents the luminous function, the dotted line the chromatic function.

F. 7
F. 7

Experimental hue-discrimination curve of Wright for bipartite fields (0 cpd) together with the calculated hue-discrimination functions for gratings of 20, 30, and 40 cpd. – – – empirical curve of Cavonius.

Equations (8)

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f ( x ) = 4 / π ( sin x + sin 3 x 3 + sin 5 x 5 ) 4 / π = 1.27 .
f ( x ) = 8 / π 2 ( cos x + cos 3 x 9 + cos 5 x 25 ) 8 / π 2 = 0.81 .
I o · 0 1 / ( 2 ) f s ( 1 + M sin 2 π f s x d x ) = I 0 ( 1 2 + M / π ) / f s ,
1 : 1 / 1 2 π : 1 / 1 4 π = 1 : 1 / 1.57 : 1 / 0.78 .
f ( x ) = 2 0 T ( f s ) cos 2 π f s x d f s .
A λ ( f s ) = 2 / π ( θ sin θ cos θ ) ,
{ ( n r / n g ) 1 ( n r / n g ) 2 } 1 2 { A 1 ( f s ) + A 2 ( f s ) } = Δ ( n r / n g ) .
1 2 { ( n r / n g ) 1 ( n r / n g ) 0 } { A 1 ( f s ) + A 0 ( f s ) } = Δ 1 ( n r / n g ) 1 2 { ( n r / n g ) 0 ( n r / n g ) 2 } { A 2 ( f s ) + A 0 ( f s ) } = Δ s ( n r / n g ) ;