Abstract

Color-discrimination data are compared with the predictions of a generalized fluctuation theory for visual threshold behavior. Our observations for the tritanopic component of vision at low luminances are in good agreement with the expectations from this theory. We measured just-noticeable differences of hue with equiluminous square-wave test objects, which were modulated only in chromaticity. A chromaticity-contrast sensitivity function was introduced for the description of these results, in analogy of the luminance-contrast sensitivity function. Observations were made for different spatial frequencies at four reference wavelengths and at several luminance levels. The results do not show an attenuation of the low frequencies such as appears in the luminance-threshold contrast modulation. We infer from this that spatial interactions are different in the chromaticness and brightness channels of the visual system. Furthermore a decrease of the luminance level causes an increase of the neural integrative interaction of the color signals. We divided the measured chromaticity-contrast sensitivity function into an optical and a nervous component. A calculation for the optical part is given.

© 1967 Optical Society of America

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References

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1967 (1)

1966 (4)

C. R. Cavonius, Science 152, 1276 (1966).
[CrossRef] [PubMed]

P. L. Walraven and M. A. Bouman, Vis. Res. 6, 567 (1966).
[CrossRef]

R. L. DeValois, I. Abramov, and G. H. Jacobs, J. Opt. Soc. Am. 56, 966 (1966).
[CrossRef]

T. N. Wiesel and D. H. Hubel, J. Neurophysiol. 29, 1115 (1966).
[PubMed]

1965 (1)

F. W. Campbell and D. G. Green, J. Physiol. (London) 181, 576 (1965).

1964 (4)

W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).
[CrossRef] [PubMed]

P. K. Brown and G. Wald, Science 144, 45 (1964).
[CrossRef] [PubMed]

P. L. Walraven and M. A. Bouman, Proc. CIE–Congr., Vienna,  18, (1964).

M. A. Bouman, Acta Psychol. 23, 239 (1964).

1963 (1)

1962 (3)

1961 (1)

L. F. C. Friele, Farbe 10, 193 (1961).

1960 (1)

A. Arnulf and O. Dupuy, Compt. Rend. 250, 2757 (1960).

1959 (1)

S. Ooue, J. Appl. Phys. (Japan) 28, 531 (1959).

1958 (1)

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

1956 (1)

1955 (1)

1954 (1)

1953 (1)

1952 (1)

1951 (2)

L. C. Thomson and P. W. Trezona, J. Phys. 114, 98 (1951).

F. B. Fischer, M. A. Bouman, and J. ten Doesschate, Documenta Ophth. 5, 55 (1951).

1948 (1)

1946 (2)

A. C. S. van Heel, J. Opt. Soc. Am. 36, 237 (1946).

W. S. Stiles, Proc. Phys. Soc. (London) 58, 41 (1946).
[CrossRef]

1944 (1)

F. G. H. Pitt, Proc. Phys. Soc. (London) B. 132, 101 (1944).
[CrossRef]

1943 (1)

H. de Vries, Physica 10, 553 (1943).
[CrossRef]

1938 (1)

1920 (1)

E. Schrödinger, Ann. Physik (IV) 63, 481 (1920).
[CrossRef]

Abramov, I.

Ampt, C. G. F.

M. A. Bouman and C. G. F. Ampt, Performances of the Eye at Low Luminances (Excerpta Medica Foundation, Amsterdam, 1966), p. 57.

Arnulf, A.

A. Arnulf and O. Dupuy, Compt. Rend. 250, 2757 (1960).

Bouman, M. A.

F. L. van Nes and M. A. Bouman, J. Opt. Soc. Am. 57, 401 (1967).
[CrossRef]

P. L. Walraven and M. A. Bouman, Vis. Res. 6, 567 (1966).
[CrossRef]

P. L. Walraven and M. A. Bouman, Proc. CIE–Congr., Vienna,  18, (1964).

M. A. Bouman, Acta Psychol. 23, 239 (1964).

M. A. Bouman, J. J. Vos, and P. L. Walraven, J. Opt. Soc. Am. 53, 121 (1963).
[CrossRef] [PubMed]

M. A. Bouman and P. L. Walraven, Vis. Res. 2, 177 (1962).
[CrossRef]

F. B. Fischer, M. A. Bouman, and J. ten Doesschate, Documenta Ophth. 5, 55 (1951).

M. A. Bouman, Physicomathematical Aspects of Biology; (Academic Press Inc., New York, 1961). p. 142.

M. A. Bouman and C. G. F. Ampt, Performances of the Eye at Low Luminances (Excerpta Medica Foundation, Amsterdam, 1966), p. 57.

Brown, P. K.

P. K. Brown and G. Wald, Science 144, 45 (1964).
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell and D. G. Green, J. Physiol. (London) 181, 576 (1965).

Cavonius, C. R.

C. R. Cavonius, Science 152, 1276 (1966).
[CrossRef] [PubMed]

de Lange, H.

de Vries, H.

H. de Vries, Physica 10, 553 (1943).
[CrossRef]

DePalma, J. J.

DeValois, R. L.

Dobelle, W. H.

W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).
[CrossRef] [PubMed]

Dupuy, O.

A. Arnulf and O. Dupuy, Compt. Rend. 250, 2757 (1960).

Fischer, F. B.

F. B. Fischer, M. A. Bouman, and J. ten Doesschate, Documenta Ophth. 5, 55 (1951).

Françon, M

Aλ(ω) = 2/π{θ−sinθ· cosθ} in which cosθ= (180/π) · (λ/p) ν. P is the pupil diameter and ν the spatial frequency in cpd. An extensive treatment on this subject is given in A. Maréchal and M FrançonDiffraction, Structure des Images, (Ed. Revue d’optique théorique et instrumentale, Paris, 1960).

Friele, L. F. C.

L. F. C. Friele, Farbe 10, 193 (1961).

Green, D. G.

F. W. Campbell and D. G. Green, J. Physiol. (London) 181, 576 (1965).

Hubel, D. H.

T. N. Wiesel and D. H. Hubel, J. Neurophysiol. 29, 1115 (1966).
[PubMed]

Jacobs, G. H.

Lowry, E. M.

MacNichol, E. F.

W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).
[CrossRef] [PubMed]

Maréchal, A.

Aλ(ω) = 2/π{θ−sinθ· cosθ} in which cosθ= (180/π) · (λ/p) ν. P is the pupil diameter and ν the spatial frequency in cpd. An extensive treatment on this subject is given in A. Maréchal and M FrançonDiffraction, Structure des Images, (Ed. Revue d’optique théorique et instrumentale, Paris, 1960).

Marks, W. B.

W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).
[CrossRef] [PubMed]

Ooue, S.

S. Ooue, J. Appl. Phys. (Japan) 28, 531 (1959).

Pitt, F. G. H.

F. G. H. Pitt, Proc. Phys. Soc. (London) B. 132, 101 (1944).
[CrossRef]

Ratliff, F.

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden–Day, Inc., San Francisco, 1965), p. 63.

Rose, A.

Schade, O. H.

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

O. H. Schade, J. Opt. Soc. Am. 46, 721 (1956).
[CrossRef] [PubMed]

Schrödinger, E.

E. Schrödinger, Ann. Physik (IV) 63, 481 (1920).
[CrossRef]

Siegel, M. H.

Silberstein, L.

Stiles, W. S.

W. S. Stiles, Proc. Phys. Soc. (London) 58, 41 (1946).
[CrossRef]

ten Doesschate, J.

F. B. Fischer, M. A. Bouman, and J. ten Doesschate, Documenta Ophth. 5, 55 (1951).

Thomson, L. C.

L. C. Thomson and W. D. Wright, J. Opt. Soc. Am. 43, 890 (1953).
[CrossRef] [PubMed]

L. C. Thomson and P. W. Trezona, J. Phys. 114, 98 (1951).

Trezona, P. W.

L. C. Thomson and P. W. Trezona, J. Phys. 114, 98 (1951).

van Heel, A. C. S.

van Nes, F. L.

von Schelling, H.

Vos, J. J.

Wald, G.

P. K. Brown and G. Wald, Science 144, 45 (1964).
[CrossRef] [PubMed]

Walraven, P. L.

P. L. Walraven and M. A. Bouman, Vis. Res. 6, 567 (1966).
[CrossRef]

P. L. Walraven and M. A. Bouman, Proc. CIE–Congr., Vienna,  18, (1964).

M. A. Bouman, J. J. Vos, and P. L. Walraven, J. Opt. Soc. Am. 53, 121 (1963).
[CrossRef] [PubMed]

M. A. Bouman and P. L. Walraven, Vis. Res. 2, 177 (1962).
[CrossRef]

P. L. Walraven, On the Mechanisms of Color Vision. (Thesis, University of Utrecht, 1962).

Wiesel, T. N.

T. N. Wiesel and D. H. Hubel, J. Neurophysiol. 29, 1115 (1966).
[PubMed]

Wright, W. D.

Acta Psychol. (1)

M. A. Bouman, Acta Psychol. 23, 239 (1964).

Ann. Physik (IV) (1)

E. Schrödinger, Ann. Physik (IV) 63, 481 (1920).
[CrossRef]

Compt. Rend. (1)

A. Arnulf and O. Dupuy, Compt. Rend. 250, 2757 (1960).

Documenta Ophth. (1)

F. B. Fischer, M. A. Bouman, and J. ten Doesschate, Documenta Ophth. 5, 55 (1951).

Farbe (1)

L. F. C. Friele, Farbe 10, 193 (1961).

J. Appl. Phys. (Japan) (1)

S. Ooue, J. Appl. Phys. (Japan) 28, 531 (1959).

J. Neurophysiol. (1)

T. N. Wiesel and D. H. Hubel, J. Neurophysiol. 29, 1115 (1966).
[PubMed]

J. Opt. Soc. Am. (13)

J. Phys. (1)

L. C. Thomson and P. W. Trezona, J. Phys. 114, 98 (1951).

J. Physiol. (London) (1)

F. W. Campbell and D. G. Green, J. Physiol. (London) 181, 576 (1965).

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

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

Physica (1)

H. de Vries, Physica 10, 553 (1943).
[CrossRef]

Proc. CIE–Congr., Vienna (1)

P. L. Walraven and M. A. Bouman, Proc. CIE–Congr., Vienna,  18, (1964).

Proc. Phys. Soc. (London) (1)

W. S. Stiles, Proc. Phys. Soc. (London) 58, 41 (1946).
[CrossRef]

Proc. Phys. Soc. (London) B. (1)

F. G. H. Pitt, Proc. Phys. Soc. (London) B. 132, 101 (1944).
[CrossRef]

Science (3)

C. R. Cavonius, Science 152, 1276 (1966).
[CrossRef] [PubMed]

W. B. Marks, W. H. Dobelle, and E. F. MacNichol, Science 143, 1181 (1964).
[CrossRef] [PubMed]

P. K. Brown and G. Wald, Science 144, 45 (1964).
[CrossRef] [PubMed]

Vis. Res. (2)

M. A. Bouman and P. L. Walraven, Vis. Res. 2, 177 (1962).
[CrossRef]

P. L. Walraven and M. A. Bouman, Vis. Res. 6, 567 (1966).
[CrossRef]

Other (6)

M. A. Bouman, Physicomathematical Aspects of Biology; (Academic Press Inc., New York, 1961). p. 142.

M. A. Bouman and C. G. F. Ampt, Performances of the Eye at Low Luminances (Excerpta Medica Foundation, Amsterdam, 1966), p. 57.

P. L. Walraven, On the Mechanisms of Color Vision. (Thesis, University of Utrecht, 1962).

F. Ratliff, Mach Bands: Quantitative Studies on Neural Networks in the Retina (Holden–Day, Inc., San Francisco, 1965), p. 63.

Aλ(ω) = 2/π{θ−sinθ· cosθ} in which cosθ= (180/π) · (λ/p) ν. P is the pupil diameter and ν the spatial frequency in cpd. An extensive treatment on this subject is given in A. Maréchal and M FrançonDiffraction, Structure des Images, (Ed. Revue d’optique théorique et instrumentale, Paris, 1960).

Reflection of the light from the lamp L0 on the transparent parts of the grating was eliminated by polarization of the light with the Polaroid sheet P0.

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Figures (13)

Fig. 1
Fig. 1

Schematic view of the experimental setup.

Fig. 2
Fig. 2

Chromaticity-contrast threshold data for two observers at λ = 625 nm. Retinal illuminances 3500 and 19 td. Pupil diameter 2 mm. Circles represent the measurements of observer H, triangles those of observer W.

Fig. 3
Fig. 3

Chromaticity-contrast threshold data for observer H (circles) and observer W (triangles) at λ = 598 nm. Retinal illuminances 3500 and 19 td, and an additional measurement of observer H at 1.5 td. Pupil diameter 2 mm.

Fig. 4
Fig. 4

Chromaticity-contrast threshold data for observer H at λ = 567 nm. Four different illuminances: 3500, 19, 1.5, and 0.1 td. Pupil diameter 2 mm.

Fig. 5
Fig. 5

Chromaticity-contrast threshold data for observer W at λ = 567 nm. Four different illuminance levels: 3500, 19, 1.5, and 0.1 td. Pupil diameter 2 mm.

Fig. 6
Fig. 6

Blue-chromaticity-contrast threshold data for observer H (circles) and observer W (triangles) at λ = 491 nm. Retinal illuminances 900 and 5 td; pupil diameter 2 mm.

Fig. 7
Fig. 7

The fundamental response curves as used in this paper, according to the curves from Pitt and Thomson–Wright,8 in the form R/G vs λ and (R+G)/B vs λ.

Fig. 8
Fig. 8

Luminance modulation percentages for threshold behavior at λ = 580 nm. Retinal illuminance 3500 and 1.5 td. Observer H. M = (BmaxBmin)/(Bmax+Bmin).

Fig. 9
Fig. 9

Hue discrimination in dependence on retinal illuminance at λ = 567 nm for a spatial frequency of 0.5 cpd.

Fig. 10
Fig. 10

Hue-discrimination data at low retinal-illuminance levels represented in a square-root diagram. Lines of constant illuminance are represented by the concentric circles. Circle 1 corresponds with 1.5 td, circle 2 with 0.1 td, circle 3 with 0.045 td, circle 4 with 0.025 td and circle 5 with 0.007 td.

Fig. 11
Fig. 11

Illuminance distribution on the grating G.

Fig. 12
Fig. 12

Diffraction chromaticity-contrast attenuation curve at λ = 567 nm (upper curve) and the deduced retina-brain chromaticness-contrast transfer function. Observer H: circles; observer W: triangles. Retinal illuminance 560 td, pupil diameter 0.8 mm.

Fig. 13
Fig. 13

Diffraction chromaticity-contrast attenuation curve at λ = 491 nm (upper curve) and the deduced retina-brain chromaticness-contrast transfer function. Observer H: circles and observer W: triangles. Retinal illuminance 140 td; pupil diameter 0.8 mm.

Equations (11)

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Δ ( n 1 2 ) = [ d ( n 1 2 ) / d n ] Δ ( n ) = 1 2 n - 1 2 · n 1 2 = const ,
R / G color contrast : Δ ( n ¯ r / n ¯ g ) n ¯ r / n ¯ g Y / B color contrast : Δ [ ( n ¯ r + n ¯ g ) / n ¯ b ] ( n ¯ r + n ¯ g ) / n ¯ b .
Δ R / G R 0 / G 0 = G 0 R 0 [ R α G α - R β G β ]
R α / G α = ( R 1 sin 2 α + R 2 cos 2 α ) / ( G 1 sin 2 α + G 2 cos 2 α )
L 1 = B 0 + B 0 sin ω x L 1 = B 1 - B 1 sin ω x L 2 = B 2 - B 2 sin ω x .
L 0 = B 0 + A 0 ( ω ) B 0 sin ω x L 1 = B 1 - A 1 ( ω ) B 1 sin ω x L 2 = B 2 - A 2 ( ω ) B 2 sin ω x ;
( R G ) diff = Σ R i L i Σ G i L i = Σ R i B i + { 2 R 0 A 0 ( ω ) B 0 - Σ R i A i ( ω ) B i } sin ω x Σ G i B i + { 2 G 0 A 0 ( ω ) B 0 - Σ G i A i ( ω ) B i } sin ω x Σ R i B i Σ G i B i + { Σ A i ( ω ) B i } ( 2 R 0 B 0 - Σ R i B i ) ( Σ G i B i ) 2 sin ω x + · · · · · .
R / G Σ R i B i / Σ G i B i + [ ( Σ B i ) ( 2 R 0 B 0 - Σ R i B i ) / ( Σ G i B i ) 2 ] · sin ω x .
A color ( ω ) Σ A i ( ω ) B i / Σ B i = 1 2 [ A 0 ( ω ) + ( B 1 / B 0 ) A 1 ( ω ) + ( B 2 / B 0 ) A 2 ( ω ) ] .
A color ( ω ) 1 2 { A 0 ( ω ) + sin 2 α . A 1 ( ω ) + cos 2 α . A 2 ( ω ) } .
[ 2 A 0 ( ω ) B 0 - Σ A i B i ] / Σ B i .