Abstract

Flicker photometric equivalence is both additive and transitive when the test and standard are alternated upon a relatively more intense colored background. When the balance of red versus green cone excitation from the background is unequal, the contribution of one cone type to flicker photometric spectral sensitivity may be depressed in relation to that of the other by at least 1 order of magnitude more than Weber’s law predicts. The resultant spectral sensitivity is determined predominantly by only one class of cone. The cone spectral sensitivities of normals are then seen to be the same as those of dichromats, although there is some individual variation. A model is developed to explain this surprising phenomenon.

© 1981 Optical Society of America

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  1. W. A. H. Rushton, “From nerves to eyes,” in The Neurosciences: Paths of Discovery, F. G. Worden, J. P. Swazey, and G. Anderson, eds. (MIT, Cambridge, Mass., 1975), pp. 277–292.
  2. W. S. Stiles, Mechanisms of Colour Vision (Academic, New York, 1978).
  3. K. Kranda and P. E. King-Smith, “Detection of coloured stimuli by independent linear systems,” Vision Res. 19, 733–745 (1979).
    [Crossref] [PubMed]
  4. P. E. King-Smith and D. Carden, “Luminance and opponent color contributions to visual detection and adaptation and to temporal and spatial integration,” J. Opt. Soc. Am. 66, 709–717 (1976).
    [Crossref] [PubMed]
  5. S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
    [Crossref] [PubMed]
  6. E. N. Pugh, “The nature of the π1 colour mechanism of W. S. Stiles,” J. Physiol. 257, 713–747 (1976).
  7. E. N. Pugh and J. D. Mollon, “A theory of the π1 and π3 color mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
    [Crossref]
  8. R. M. Boynton and D. N. Whitten, “Visual adaptation in monkey cones: recordings of late receptor potentials,” Science 170, 1423–1425 (1970).
    [Crossref] [PubMed]
  9. D. A. Baylor and A. L. Hodgkin, “Changes in time scale and sensitivity in turtle photo-receptors,” J. Physiol. 242, 729–758 (1974).
  10. H. DeVries, “The luminosity curve of the eye as determined by measurement with the flickerphotometer,” Physica 14, 319–348 (1948).
    [Crossref]
  11. A. Eisner, “The contribution of the different cone types to luminance while the eye is adapted to colored backgrounds,” Ph.D. dissertation (University of California at San Diego, La Jolla, Calif., 1979).
  12. L. Sirovich and I. Abramov, “Photopigments and pseudo-pigments,” Vision Res. 17, 5–16 (1977).
    [Crossref] [PubMed]
  13. For any given background the sensitivities from each session were multiplied by a normalizing factor before the between-sessions SEM were computed. This translation minimizes the small, but almost inevitable, changes in sensitivity that are due to changes in the apparatus and in the subject’s position between sessions. The remaining variance after translation is therefore a more accurate measure of any variation in relative spectral sensitivity.
  14. Thus far we have verified Abney’s law only for lights that do not elicit a blue cone contribution to luminance. But we have shown [A. Eisner and D. I. A. MacLeod, “Blue sensitive cones do not contribute to luminance,” J. Opt. Soc. Am. 70, 121–123 (1980)] that blue cones do not contribute to FPSμ(λ) even with modest midwavelength adapting fields that selectively densitize red and green cones.
    [Crossref] [PubMed]
  15. J. J. Vos and P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
    [Crossref] [PubMed]
  16. Although the brightest backgrounds in Table 1 bleach 5–10% of the visual pigment in the predominating cones, self-screening was not allowed for, since the corrections needed never exceed ±0.005 log unit across the spectral range examined. This assumes peak pigment densities of 0.45 and a half-bleach intensity of 30,000 td for white light [M. Hollins and M. Alpern, “Dark adaptation and visual pigment regeneration in human cones,” J. Gen. Physiol. 62, 430–447 (1973)].
  17. Suitable coefficients for fitting the data by using different values of n were found by constraining the fits to be exact at λ = 540 nm and λ = 620 nm. Subject to this constraint, the least-squares value of n was calculated as the value for which the sum of the deviations of log sensitivity from prediction, each weighted by its derivative with respect to n, was zero; this gave n= 1.03. From the rms errors of prediction, the probability of the observed data could be derived as a function of n. The resulting 95% limits for n were 0.92 and 1.18. It should be stressed that, whereas this implies that the summed time-varying signals from each cone type are nearly linear with test stimulus intensity, the data place no strong constraint on the extent of nonlinearity as a function of total intensity, since the test increments were always small in relation to the steady background.
  18. Despite the small number of observers, the evidence for clustering is statistically significant. In the larger cluster of five observers, relative sensitivity to red and green is so uniform that even if all the observed variation between observers were due to variation in the wavelength of peak absorption in the red cones, the rms interobserver variation in that wavelength would be only 0.3 nm. A good estimate of the standard deviation of peak absorption wavelength between observers in a population of deuteranopes is 2.8 nm [based on the data of M. Alpern and T. Wake, “Cone pigments in human deutan vision defects,” J. Physiol. 266, 595–612 (1977) and Alpern and Pugh (Ref. 19)]. Reference to the chi-square distribution for 4 degrees of freedom shows that the probability of a standard deviation of 0.3 nm or less in a sample of five from a population standard deviation of 2.8 nm is only 0.03%; the probability that at least one group of five in a sample of seven will be as uniform is only 0.6%. The agreement between the remaining two observers is equally striking.
  19. M. Alpern and E. N. Pugh, “Variation in the action spectrum of erythrolabe among deuteranopes,” J. Physiol. 266, 613–646 (1977).
  20. Both JW and RM, the two males whose data form the smaller cluster, have a low density of macular pigment. JW is an experienced observer who has great difficulty in eliciting Maxwell’s spot. For both JW and RM, pure green cone spectral sensitivities derived from FPS656(λ) are broader than G(λ) for 520 nm ≤ λ ≤ 530 nm by the same value as the discrepancies in Fig. 7, which in turn are about proportional to the values for average density of macular pigment tabulated in G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967), p. 219.
  21. V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972).
    [Crossref] [PubMed]
  22. W. A. H. Rushton and H. D. Baker, “Red/green sensitivity in normal vision,” Vision Res. 4, 75–85 (1964).
    [Crossref] [PubMed]
  23. O. Estévez and C. R. Cavonius, “Human color perception and Stiles’ π mechanisms,” Vision Res. 17, 417–422 (1977).
    [Crossref]
  24. J. K. Bowmaker and et al., “The visual pigments of rods and cones in the rhesus monkey,” J. Physiol. 274, 329–348 (1978).
  25. C. Sigel and E. N. Pugh, “Stiles’s π5 color mechanism: tests of field displacement and additivity properties.” J. Opt. Soc. Am. 70, 71–81 (1980).
    [Crossref] [PubMed]
  26. This factor differs from the corresponding entry in Table 1. The difference may reflect random error, which perhaps elevated the estimates in Table 1, or it may reflect small nonlinearities or cone response phase differences. In any case, the suppression of the red cone contribution to FPS619(λ) is profound even for tests at the red end of the spectrum. We used the Kodak specification of 678 nm for the Wratten 70. The exact equivalent wavelength of the particular filter used in the experiment is not at all critical in establishing a profound depression in the red cone contribution, although it may change the precise estimate of this depression. Any wavelength greater than 650 nm would suffice to establish profound depression. Wavelengths shorter than this would imply negative weights.
  27. G. S. Brindley, “The effects on colour vision of adaptation to very bright lights,” J. Physiol. 122, 352–350 (1953).
  28. P. L. Walraven, A. M. van Hout, and H. J. Leebeek, “Fundamental response curves of a normal and a deuteranomalous observer derived from chromatic adaptation data,” J. Opt. Soc. Am. 56, 125–127 (1966).
    [Crossref] [PubMed]
  29. P. Gouras and E. Zrenner, “Enhancement of luminance flicker by color-opponent mechanisms,” Science 205, 587–589 (1979).
    [Crossref] [PubMed]
  30. F. S. Werblin, “Synaptic interactions mediating bipolar response in the retina of the tiger salamander,” in Vertebrate Photoreception, H. B. Barlow and P. Fatt, eds. (Academic, New York, 1977), pp. 205–230.
  31. H. E. Ives, “Studies in the photometry of lights of different colors. III. Distortions in spectral luminosity curves produced by variations in the character of the comparison standard and of the surroundings of the photometric field,” Philos. Mag. 24, 744–751 (1912).
  32. H. Piéron, “Recherches sur la validité de la loi d’Abney impliquant l’addition intégrale des valences luminenses élémentaires dans les flux composites,” Ann. Psychol. 40, 52–83 (1942).
    [Crossref]
  33. F. L. Tufts, “Spectrophotometry of normal and colorblind eyes,” Phys. Rev. 25, 433–452 (1907).
  34. H. E. Ives, “Studies in the photometry of lights of different colours—IV. The addition of luminosities of different colour,” Philos. Mag. 24, 845–853 (1913).
  35. A. Dresler, “The non-additivity of heterochromatic brightness,” Trans. Illum. Eng. Soc. 18, 141–165 (1953).
  36. Y. Legrand, Light, Colour and Vision (Chapman and Hall, London, 1968), pp. 123–125.
  37. G. Wagner and R. M. Boynton, “Comparison of four methods of heterochromatic photometry,” J. Opt. Soc. Am. 62, 1508–1515 (1972).
    [Crossref] [PubMed]
  38. H. G. Sperling, “An experimental investigation of the relationship between colour mixture and luminous efficiency,” in Visual Problems of Colour, National Physical Laboratory Symposium No. 8 (H. M. Stationery Office, London, 1958).
  39. H. E. Ives, “Studies in the photometry of lights of different colours. I. Spectral luminosity curves obtained by the equality of the brightness photometer and the flicker photometer under similar conditions,” Philos. Mag. 24, 149–188 (1912).
  40. C. R. Ingling and et al., “The achromatic channel. I. The nonlinearity of minimum-border and flicker matches,” Vision Res. 18, 379–390 (1978).
    [Crossref]
  41. G. Wald, “Defective color vision and its inheritance,” Proc. Nat. Acad. Sci. USA,  55, 1347–1363 (1966).
  42. M. Ikeda, K. Hukami, and M. Urakubo, “Flicker photometry with chromatic adaptation and defective color vision,” Am. J. Ophthalmol. 73, 270–277 (1972).
    [PubMed]
  43. M. Ikeda and M. Urakubo, “Flicker HTRF as a test of color vision,” J. Opt. Soc. Am. 58, 27–31 (1968).
    [Crossref] [PubMed]
  44. V. C. Smith and J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
    [Crossref] [PubMed]
  45. C. E. Sternheim, C. F. Stromeyer, and M. C. K. Khoo, “Visibility of chromatic flicker upon spectrally mixed adapting fields,” Vision Res. 19, 175–184 (1979).
    [Crossref] [PubMed]
  46. P. E. King-Smith and J. R. Webb, “The use of photopic saturation in determining the fundamental spectral sensitivity curves,” Vision Res. 14, 421–429 (1974).
    [Crossref] [PubMed]

1980 (2)

1979 (4)

P. Gouras and E. Zrenner, “Enhancement of luminance flicker by color-opponent mechanisms,” Science 205, 587–589 (1979).
[Crossref] [PubMed]

K. Kranda and P. E. King-Smith, “Detection of coloured stimuli by independent linear systems,” Vision Res. 19, 733–745 (1979).
[Crossref] [PubMed]

E. N. Pugh and J. D. Mollon, “A theory of the π1 and π3 color mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

C. E. Sternheim, C. F. Stromeyer, and M. C. K. Khoo, “Visibility of chromatic flicker upon spectrally mixed adapting fields,” Vision Res. 19, 175–184 (1979).
[Crossref] [PubMed]

1978 (2)

J. K. Bowmaker and et al., “The visual pigments of rods and cones in the rhesus monkey,” J. Physiol. 274, 329–348 (1978).

C. R. Ingling and et al., “The achromatic channel. I. The nonlinearity of minimum-border and flicker matches,” Vision Res. 18, 379–390 (1978).
[Crossref]

1977 (4)

L. Sirovich and I. Abramov, “Photopigments and pseudo-pigments,” Vision Res. 17, 5–16 (1977).
[Crossref] [PubMed]

O. Estévez and C. R. Cavonius, “Human color perception and Stiles’ π mechanisms,” Vision Res. 17, 417–422 (1977).
[Crossref]

Despite the small number of observers, the evidence for clustering is statistically significant. In the larger cluster of five observers, relative sensitivity to red and green is so uniform that even if all the observed variation between observers were due to variation in the wavelength of peak absorption in the red cones, the rms interobserver variation in that wavelength would be only 0.3 nm. A good estimate of the standard deviation of peak absorption wavelength between observers in a population of deuteranopes is 2.8 nm [based on the data of M. Alpern and T. Wake, “Cone pigments in human deutan vision defects,” J. Physiol. 266, 595–612 (1977) and Alpern and Pugh (Ref. 19)]. Reference to the chi-square distribution for 4 degrees of freedom shows that the probability of a standard deviation of 0.3 nm or less in a sample of five from a population standard deviation of 2.8 nm is only 0.03%; the probability that at least one group of five in a sample of seven will be as uniform is only 0.6%. The agreement between the remaining two observers is equally striking.

M. Alpern and E. N. Pugh, “Variation in the action spectrum of erythrolabe among deuteranopes,” J. Physiol. 266, 613–646 (1977).

1976 (2)

1975 (1)

V. C. Smith and J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

1974 (2)

P. E. King-Smith and J. R. Webb, “The use of photopic saturation in determining the fundamental spectral sensitivity curves,” Vision Res. 14, 421–429 (1974).
[Crossref] [PubMed]

D. A. Baylor and A. L. Hodgkin, “Changes in time scale and sensitivity in turtle photo-receptors,” J. Physiol. 242, 729–758 (1974).

1973 (2)

S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
[Crossref] [PubMed]

Although the brightest backgrounds in Table 1 bleach 5–10% of the visual pigment in the predominating cones, self-screening was not allowed for, since the corrections needed never exceed ±0.005 log unit across the spectral range examined. This assumes peak pigment densities of 0.45 and a half-bleach intensity of 30,000 td for white light [M. Hollins and M. Alpern, “Dark adaptation and visual pigment regeneration in human cones,” J. Gen. Physiol. 62, 430–447 (1973)].

1972 (3)

V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972).
[Crossref] [PubMed]

M. Ikeda, K. Hukami, and M. Urakubo, “Flicker photometry with chromatic adaptation and defective color vision,” Am. J. Ophthalmol. 73, 270–277 (1972).
[PubMed]

G. Wagner and R. M. Boynton, “Comparison of four methods of heterochromatic photometry,” J. Opt. Soc. Am. 62, 1508–1515 (1972).
[Crossref] [PubMed]

1971 (1)

J. J. Vos and P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
[Crossref] [PubMed]

1970 (1)

R. M. Boynton and D. N. Whitten, “Visual adaptation in monkey cones: recordings of late receptor potentials,” Science 170, 1423–1425 (1970).
[Crossref] [PubMed]

1968 (1)

1966 (2)

1964 (1)

W. A. H. Rushton and H. D. Baker, “Red/green sensitivity in normal vision,” Vision Res. 4, 75–85 (1964).
[Crossref] [PubMed]

1953 (2)

G. S. Brindley, “The effects on colour vision of adaptation to very bright lights,” J. Physiol. 122, 352–350 (1953).

A. Dresler, “The non-additivity of heterochromatic brightness,” Trans. Illum. Eng. Soc. 18, 141–165 (1953).

1948 (1)

H. DeVries, “The luminosity curve of the eye as determined by measurement with the flickerphotometer,” Physica 14, 319–348 (1948).
[Crossref]

1942 (1)

H. Piéron, “Recherches sur la validité de la loi d’Abney impliquant l’addition intégrale des valences luminenses élémentaires dans les flux composites,” Ann. Psychol. 40, 52–83 (1942).
[Crossref]

1913 (1)

H. E. Ives, “Studies in the photometry of lights of different colours—IV. The addition of luminosities of different colour,” Philos. Mag. 24, 845–853 (1913).

1912 (2)

H. E. Ives, “Studies in the photometry of lights of different colours. I. Spectral luminosity curves obtained by the equality of the brightness photometer and the flicker photometer under similar conditions,” Philos. Mag. 24, 149–188 (1912).

H. E. Ives, “Studies in the photometry of lights of different colors. III. Distortions in spectral luminosity curves produced by variations in the character of the comparison standard and of the surroundings of the photometric field,” Philos. Mag. 24, 744–751 (1912).

1907 (1)

F. L. Tufts, “Spectrophotometry of normal and colorblind eyes,” Phys. Rev. 25, 433–452 (1907).

Abramov, I.

L. Sirovich and I. Abramov, “Photopigments and pseudo-pigments,” Vision Res. 17, 5–16 (1977).
[Crossref] [PubMed]

Alpern, M.

Despite the small number of observers, the evidence for clustering is statistically significant. In the larger cluster of five observers, relative sensitivity to red and green is so uniform that even if all the observed variation between observers were due to variation in the wavelength of peak absorption in the red cones, the rms interobserver variation in that wavelength would be only 0.3 nm. A good estimate of the standard deviation of peak absorption wavelength between observers in a population of deuteranopes is 2.8 nm [based on the data of M. Alpern and T. Wake, “Cone pigments in human deutan vision defects,” J. Physiol. 266, 595–612 (1977) and Alpern and Pugh (Ref. 19)]. Reference to the chi-square distribution for 4 degrees of freedom shows that the probability of a standard deviation of 0.3 nm or less in a sample of five from a population standard deviation of 2.8 nm is only 0.03%; the probability that at least one group of five in a sample of seven will be as uniform is only 0.6%. The agreement between the remaining two observers is equally striking.

M. Alpern and E. N. Pugh, “Variation in the action spectrum of erythrolabe among deuteranopes,” J. Physiol. 266, 613–646 (1977).

Although the brightest backgrounds in Table 1 bleach 5–10% of the visual pigment in the predominating cones, self-screening was not allowed for, since the corrections needed never exceed ±0.005 log unit across the spectral range examined. This assumes peak pigment densities of 0.45 and a half-bleach intensity of 30,000 td for white light [M. Hollins and M. Alpern, “Dark adaptation and visual pigment regeneration in human cones,” J. Gen. Physiol. 62, 430–447 (1973)].

Baker, H. D.

W. A. H. Rushton and H. D. Baker, “Red/green sensitivity in normal vision,” Vision Res. 4, 75–85 (1964).
[Crossref] [PubMed]

Baylor, D. A.

D. A. Baylor and A. L. Hodgkin, “Changes in time scale and sensitivity in turtle photo-receptors,” J. Physiol. 242, 729–758 (1974).

Bowmaker, J. K.

J. K. Bowmaker and et al., “The visual pigments of rods and cones in the rhesus monkey,” J. Physiol. 274, 329–348 (1978).

Boynton, R. M.

G. Wagner and R. M. Boynton, “Comparison of four methods of heterochromatic photometry,” J. Opt. Soc. Am. 62, 1508–1515 (1972).
[Crossref] [PubMed]

R. M. Boynton and D. N. Whitten, “Visual adaptation in monkey cones: recordings of late receptor potentials,” Science 170, 1423–1425 (1970).
[Crossref] [PubMed]

Brindley, G. S.

G. S. Brindley, “The effects on colour vision of adaptation to very bright lights,” J. Physiol. 122, 352–350 (1953).

Carden, D.

Cavonius, C. R.

O. Estévez and C. R. Cavonius, “Human color perception and Stiles’ π mechanisms,” Vision Res. 17, 417–422 (1977).
[Crossref]

DeVries, H.

H. DeVries, “The luminosity curve of the eye as determined by measurement with the flickerphotometer,” Physica 14, 319–348 (1948).
[Crossref]

Dresler, A.

A. Dresler, “The non-additivity of heterochromatic brightness,” Trans. Illum. Eng. Soc. 18, 141–165 (1953).

Eisner, A.

Estévez, O.

O. Estévez and C. R. Cavonius, “Human color perception and Stiles’ π mechanisms,” Vision Res. 17, 417–422 (1977).
[Crossref]

Gouras, P.

P. Gouras and E. Zrenner, “Enhancement of luminance flicker by color-opponent mechanisms,” Science 205, 587–589 (1979).
[Crossref] [PubMed]

Guth, S. L.

Hodgkin, A. L.

D. A. Baylor and A. L. Hodgkin, “Changes in time scale and sensitivity in turtle photo-receptors,” J. Physiol. 242, 729–758 (1974).

Hollins, M.

Although the brightest backgrounds in Table 1 bleach 5–10% of the visual pigment in the predominating cones, self-screening was not allowed for, since the corrections needed never exceed ±0.005 log unit across the spectral range examined. This assumes peak pigment densities of 0.45 and a half-bleach intensity of 30,000 td for white light [M. Hollins and M. Alpern, “Dark adaptation and visual pigment regeneration in human cones,” J. Gen. Physiol. 62, 430–447 (1973)].

Hukami, K.

M. Ikeda, K. Hukami, and M. Urakubo, “Flicker photometry with chromatic adaptation and defective color vision,” Am. J. Ophthalmol. 73, 270–277 (1972).
[PubMed]

Ikeda, M.

M. Ikeda, K. Hukami, and M. Urakubo, “Flicker photometry with chromatic adaptation and defective color vision,” Am. J. Ophthalmol. 73, 270–277 (1972).
[PubMed]

M. Ikeda and M. Urakubo, “Flicker HTRF as a test of color vision,” J. Opt. Soc. Am. 58, 27–31 (1968).
[Crossref] [PubMed]

Ingling, C. R.

C. R. Ingling and et al., “The achromatic channel. I. The nonlinearity of minimum-border and flicker matches,” Vision Res. 18, 379–390 (1978).
[Crossref]

Ives, H. E.

H. E. Ives, “Studies in the photometry of lights of different colours—IV. The addition of luminosities of different colour,” Philos. Mag. 24, 845–853 (1913).

H. E. Ives, “Studies in the photometry of lights of different colours. I. Spectral luminosity curves obtained by the equality of the brightness photometer and the flicker photometer under similar conditions,” Philos. Mag. 24, 149–188 (1912).

H. E. Ives, “Studies in the photometry of lights of different colors. III. Distortions in spectral luminosity curves produced by variations in the character of the comparison standard and of the surroundings of the photometric field,” Philos. Mag. 24, 744–751 (1912).

Khoo, M. C. K.

C. E. Sternheim, C. F. Stromeyer, and M. C. K. Khoo, “Visibility of chromatic flicker upon spectrally mixed adapting fields,” Vision Res. 19, 175–184 (1979).
[Crossref] [PubMed]

King-Smith, P. E.

K. Kranda and P. E. King-Smith, “Detection of coloured stimuli by independent linear systems,” Vision Res. 19, 733–745 (1979).
[Crossref] [PubMed]

P. E. King-Smith and D. Carden, “Luminance and opponent color contributions to visual detection and adaptation and to temporal and spatial integration,” J. Opt. Soc. Am. 66, 709–717 (1976).
[Crossref] [PubMed]

P. E. King-Smith and J. R. Webb, “The use of photopic saturation in determining the fundamental spectral sensitivity curves,” Vision Res. 14, 421–429 (1974).
[Crossref] [PubMed]

Kranda, K.

K. Kranda and P. E. King-Smith, “Detection of coloured stimuli by independent linear systems,” Vision Res. 19, 733–745 (1979).
[Crossref] [PubMed]

Leebeek, H. J.

Legrand, Y.

Y. Legrand, Light, Colour and Vision (Chapman and Hall, London, 1968), pp. 123–125.

Lodge, H. R.

MacLeod, D. I. A.

Mollon, J. D.

E. N. Pugh and J. D. Mollon, “A theory of the π1 and π3 color mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

Piéron, H.

H. Piéron, “Recherches sur la validité de la loi d’Abney impliquant l’addition intégrale des valences luminenses élémentaires dans les flux composites,” Ann. Psychol. 40, 52–83 (1942).
[Crossref]

Pokorny, J.

V. C. Smith and J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972).
[Crossref] [PubMed]

Pugh, E. N.

C. Sigel and E. N. Pugh, “Stiles’s π5 color mechanism: tests of field displacement and additivity properties.” J. Opt. Soc. Am. 70, 71–81 (1980).
[Crossref] [PubMed]

E. N. Pugh and J. D. Mollon, “A theory of the π1 and π3 color mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

M. Alpern and E. N. Pugh, “Variation in the action spectrum of erythrolabe among deuteranopes,” J. Physiol. 266, 613–646 (1977).

E. N. Pugh, “The nature of the π1 colour mechanism of W. S. Stiles,” J. Physiol. 257, 713–747 (1976).

Rushton, W. A. H.

W. A. H. Rushton and H. D. Baker, “Red/green sensitivity in normal vision,” Vision Res. 4, 75–85 (1964).
[Crossref] [PubMed]

W. A. H. Rushton, “From nerves to eyes,” in The Neurosciences: Paths of Discovery, F. G. Worden, J. P. Swazey, and G. Anderson, eds. (MIT, Cambridge, Mass., 1975), pp. 277–292.

Sigel, C.

Sirovich, L.

L. Sirovich and I. Abramov, “Photopigments and pseudo-pigments,” Vision Res. 17, 5–16 (1977).
[Crossref] [PubMed]

Smith, V. C.

V. C. Smith and J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972).
[Crossref] [PubMed]

Sperling, H. G.

H. G. Sperling, “An experimental investigation of the relationship between colour mixture and luminous efficiency,” in Visual Problems of Colour, National Physical Laboratory Symposium No. 8 (H. M. Stationery Office, London, 1958).

Sternheim, C. E.

C. E. Sternheim, C. F. Stromeyer, and M. C. K. Khoo, “Visibility of chromatic flicker upon spectrally mixed adapting fields,” Vision Res. 19, 175–184 (1979).
[Crossref] [PubMed]

Stiles, W. S.

W. S. Stiles, Mechanisms of Colour Vision (Academic, New York, 1978).

Both JW and RM, the two males whose data form the smaller cluster, have a low density of macular pigment. JW is an experienced observer who has great difficulty in eliciting Maxwell’s spot. For both JW and RM, pure green cone spectral sensitivities derived from FPS656(λ) are broader than G(λ) for 520 nm ≤ λ ≤ 530 nm by the same value as the discrepancies in Fig. 7, which in turn are about proportional to the values for average density of macular pigment tabulated in G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967), p. 219.

Stromeyer, C. F.

C. E. Sternheim, C. F. Stromeyer, and M. C. K. Khoo, “Visibility of chromatic flicker upon spectrally mixed adapting fields,” Vision Res. 19, 175–184 (1979).
[Crossref] [PubMed]

Tufts, F. L.

F. L. Tufts, “Spectrophotometry of normal and colorblind eyes,” Phys. Rev. 25, 433–452 (1907).

Urakubo, M.

M. Ikeda, K. Hukami, and M. Urakubo, “Flicker photometry with chromatic adaptation and defective color vision,” Am. J. Ophthalmol. 73, 270–277 (1972).
[PubMed]

M. Ikeda and M. Urakubo, “Flicker HTRF as a test of color vision,” J. Opt. Soc. Am. 58, 27–31 (1968).
[Crossref] [PubMed]

van Hout, A. M.

Vos, J. J.

J. J. Vos and P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
[Crossref] [PubMed]

Wagner, G.

Wake, T.

Despite the small number of observers, the evidence for clustering is statistically significant. In the larger cluster of five observers, relative sensitivity to red and green is so uniform that even if all the observed variation between observers were due to variation in the wavelength of peak absorption in the red cones, the rms interobserver variation in that wavelength would be only 0.3 nm. A good estimate of the standard deviation of peak absorption wavelength between observers in a population of deuteranopes is 2.8 nm [based on the data of M. Alpern and T. Wake, “Cone pigments in human deutan vision defects,” J. Physiol. 266, 595–612 (1977) and Alpern and Pugh (Ref. 19)]. Reference to the chi-square distribution for 4 degrees of freedom shows that the probability of a standard deviation of 0.3 nm or less in a sample of five from a population standard deviation of 2.8 nm is only 0.03%; the probability that at least one group of five in a sample of seven will be as uniform is only 0.6%. The agreement between the remaining two observers is equally striking.

Wald, G.

G. Wald, “Defective color vision and its inheritance,” Proc. Nat. Acad. Sci. USA,  55, 1347–1363 (1966).

Walraven, P. L.

Webb, J. R.

P. E. King-Smith and J. R. Webb, “The use of photopic saturation in determining the fundamental spectral sensitivity curves,” Vision Res. 14, 421–429 (1974).
[Crossref] [PubMed]

Werblin, F. S.

F. S. Werblin, “Synaptic interactions mediating bipolar response in the retina of the tiger salamander,” in Vertebrate Photoreception, H. B. Barlow and P. Fatt, eds. (Academic, New York, 1977), pp. 205–230.

Whitten, D. N.

R. M. Boynton and D. N. Whitten, “Visual adaptation in monkey cones: recordings of late receptor potentials,” Science 170, 1423–1425 (1970).
[Crossref] [PubMed]

Wyszecki, G.

Both JW and RM, the two males whose data form the smaller cluster, have a low density of macular pigment. JW is an experienced observer who has great difficulty in eliciting Maxwell’s spot. For both JW and RM, pure green cone spectral sensitivities derived from FPS656(λ) are broader than G(λ) for 520 nm ≤ λ ≤ 530 nm by the same value as the discrepancies in Fig. 7, which in turn are about proportional to the values for average density of macular pigment tabulated in G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967), p. 219.

Zrenner, E.

P. Gouras and E. Zrenner, “Enhancement of luminance flicker by color-opponent mechanisms,” Science 205, 587–589 (1979).
[Crossref] [PubMed]

Am. J. Ophthalmol. (1)

M. Ikeda, K. Hukami, and M. Urakubo, “Flicker photometry with chromatic adaptation and defective color vision,” Am. J. Ophthalmol. 73, 270–277 (1972).
[PubMed]

Ann. Psychol. (1)

H. Piéron, “Recherches sur la validité de la loi d’Abney impliquant l’addition intégrale des valences luminenses élémentaires dans les flux composites,” Ann. Psychol. 40, 52–83 (1942).
[Crossref]

J. Gen. Physiol. (1)

Although the brightest backgrounds in Table 1 bleach 5–10% of the visual pigment in the predominating cones, self-screening was not allowed for, since the corrections needed never exceed ±0.005 log unit across the spectral range examined. This assumes peak pigment densities of 0.45 and a half-bleach intensity of 30,000 td for white light [M. Hollins and M. Alpern, “Dark adaptation and visual pigment regeneration in human cones,” J. Gen. Physiol. 62, 430–447 (1973)].

J. Opt. Soc. Am. (7)

M. Ikeda and M. Urakubo, “Flicker HTRF as a test of color vision,” J. Opt. Soc. Am. 58, 27–31 (1968).
[Crossref] [PubMed]

G. Wagner and R. M. Boynton, “Comparison of four methods of heterochromatic photometry,” J. Opt. Soc. Am. 62, 1508–1515 (1972).
[Crossref] [PubMed]

S. L. Guth and H. R. Lodge, “Heterochromatic additivity, foveal spectral sensitivity and a new color model,” J. Opt. Soc. Am. 63, 450–462 (1973).
[Crossref] [PubMed]

P. E. King-Smith and D. Carden, “Luminance and opponent color contributions to visual detection and adaptation and to temporal and spatial integration,” J. Opt. Soc. Am. 66, 709–717 (1976).
[Crossref] [PubMed]

C. Sigel and E. N. Pugh, “Stiles’s π5 color mechanism: tests of field displacement and additivity properties.” J. Opt. Soc. Am. 70, 71–81 (1980).
[Crossref] [PubMed]

Thus far we have verified Abney’s law only for lights that do not elicit a blue cone contribution to luminance. But we have shown [A. Eisner and D. I. A. MacLeod, “Blue sensitive cones do not contribute to luminance,” J. Opt. Soc. Am. 70, 121–123 (1980)] that blue cones do not contribute to FPSμ(λ) even with modest midwavelength adapting fields that selectively densitize red and green cones.
[Crossref] [PubMed]

P. L. Walraven, A. M. van Hout, and H. J. Leebeek, “Fundamental response curves of a normal and a deuteranomalous observer derived from chromatic adaptation data,” J. Opt. Soc. Am. 56, 125–127 (1966).
[Crossref] [PubMed]

J. Physiol. (6)

Despite the small number of observers, the evidence for clustering is statistically significant. In the larger cluster of five observers, relative sensitivity to red and green is so uniform that even if all the observed variation between observers were due to variation in the wavelength of peak absorption in the red cones, the rms interobserver variation in that wavelength would be only 0.3 nm. A good estimate of the standard deviation of peak absorption wavelength between observers in a population of deuteranopes is 2.8 nm [based on the data of M. Alpern and T. Wake, “Cone pigments in human deutan vision defects,” J. Physiol. 266, 595–612 (1977) and Alpern and Pugh (Ref. 19)]. Reference to the chi-square distribution for 4 degrees of freedom shows that the probability of a standard deviation of 0.3 nm or less in a sample of five from a population standard deviation of 2.8 nm is only 0.03%; the probability that at least one group of five in a sample of seven will be as uniform is only 0.6%. The agreement between the remaining two observers is equally striking.

M. Alpern and E. N. Pugh, “Variation in the action spectrum of erythrolabe among deuteranopes,” J. Physiol. 266, 613–646 (1977).

J. K. Bowmaker and et al., “The visual pigments of rods and cones in the rhesus monkey,” J. Physiol. 274, 329–348 (1978).

E. N. Pugh, “The nature of the π1 colour mechanism of W. S. Stiles,” J. Physiol. 257, 713–747 (1976).

D. A. Baylor and A. L. Hodgkin, “Changes in time scale and sensitivity in turtle photo-receptors,” J. Physiol. 242, 729–758 (1974).

G. S. Brindley, “The effects on colour vision of adaptation to very bright lights,” J. Physiol. 122, 352–350 (1953).

Philos. Mag. (3)

H. E. Ives, “Studies in the photometry of lights of different colours. I. Spectral luminosity curves obtained by the equality of the brightness photometer and the flicker photometer under similar conditions,” Philos. Mag. 24, 149–188 (1912).

H. E. Ives, “Studies in the photometry of lights of different colors. III. Distortions in spectral luminosity curves produced by variations in the character of the comparison standard and of the surroundings of the photometric field,” Philos. Mag. 24, 744–751 (1912).

H. E. Ives, “Studies in the photometry of lights of different colours—IV. The addition of luminosities of different colour,” Philos. Mag. 24, 845–853 (1913).

Phys. Rev. (1)

F. L. Tufts, “Spectrophotometry of normal and colorblind eyes,” Phys. Rev. 25, 433–452 (1907).

Physica (1)

H. DeVries, “The luminosity curve of the eye as determined by measurement with the flickerphotometer,” Physica 14, 319–348 (1948).
[Crossref]

Proc. Nat. Acad. Sci. USA (1)

G. Wald, “Defective color vision and its inheritance,” Proc. Nat. Acad. Sci. USA,  55, 1347–1363 (1966).

Science (2)

R. M. Boynton and D. N. Whitten, “Visual adaptation in monkey cones: recordings of late receptor potentials,” Science 170, 1423–1425 (1970).
[Crossref] [PubMed]

P. Gouras and E. Zrenner, “Enhancement of luminance flicker by color-opponent mechanisms,” Science 205, 587–589 (1979).
[Crossref] [PubMed]

Trans. Illum. Eng. Soc. (1)

A. Dresler, “The non-additivity of heterochromatic brightness,” Trans. Illum. Eng. Soc. 18, 141–165 (1953).

Vision Res. (11)

K. Kranda and P. E. King-Smith, “Detection of coloured stimuli by independent linear systems,” Vision Res. 19, 733–745 (1979).
[Crossref] [PubMed]

C. R. Ingling and et al., “The achromatic channel. I. The nonlinearity of minimum-border and flicker matches,” Vision Res. 18, 379–390 (1978).
[Crossref]

V. C. Smith and J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

C. E. Sternheim, C. F. Stromeyer, and M. C. K. Khoo, “Visibility of chromatic flicker upon spectrally mixed adapting fields,” Vision Res. 19, 175–184 (1979).
[Crossref] [PubMed]

P. E. King-Smith and J. R. Webb, “The use of photopic saturation in determining the fundamental spectral sensitivity curves,” Vision Res. 14, 421–429 (1974).
[Crossref] [PubMed]

V. C. Smith and J. Pokorny, “Spectral sensitivity of color-blind observers and the cone photopigments,” Vision Res. 12, 2059–2071 (1972).
[Crossref] [PubMed]

W. A. H. Rushton and H. D. Baker, “Red/green sensitivity in normal vision,” Vision Res. 4, 75–85 (1964).
[Crossref] [PubMed]

O. Estévez and C. R. Cavonius, “Human color perception and Stiles’ π mechanisms,” Vision Res. 17, 417–422 (1977).
[Crossref]

J. J. Vos and P. L. Walraven, “On the derivation of the foveal receptor primaries,” Vision Res. 11, 799–818 (1971).
[Crossref] [PubMed]

L. Sirovich and I. Abramov, “Photopigments and pseudo-pigments,” Vision Res. 17, 5–16 (1977).
[Crossref] [PubMed]

E. N. Pugh and J. D. Mollon, “A theory of the π1 and π3 color mechanisms of Stiles,” Vision Res. 19, 293–312 (1979).
[Crossref]

Other (10)

A. Eisner, “The contribution of the different cone types to luminance while the eye is adapted to colored backgrounds,” Ph.D. dissertation (University of California at San Diego, La Jolla, Calif., 1979).

For any given background the sensitivities from each session were multiplied by a normalizing factor before the between-sessions SEM were computed. This translation minimizes the small, but almost inevitable, changes in sensitivity that are due to changes in the apparatus and in the subject’s position between sessions. The remaining variance after translation is therefore a more accurate measure of any variation in relative spectral sensitivity.

F. S. Werblin, “Synaptic interactions mediating bipolar response in the retina of the tiger salamander,” in Vertebrate Photoreception, H. B. Barlow and P. Fatt, eds. (Academic, New York, 1977), pp. 205–230.

Both JW and RM, the two males whose data form the smaller cluster, have a low density of macular pigment. JW is an experienced observer who has great difficulty in eliciting Maxwell’s spot. For both JW and RM, pure green cone spectral sensitivities derived from FPS656(λ) are broader than G(λ) for 520 nm ≤ λ ≤ 530 nm by the same value as the discrepancies in Fig. 7, which in turn are about proportional to the values for average density of macular pigment tabulated in G. Wyszecki and W. S. Stiles, Color Science (Wiley, New York, 1967), p. 219.

Suitable coefficients for fitting the data by using different values of n were found by constraining the fits to be exact at λ = 540 nm and λ = 620 nm. Subject to this constraint, the least-squares value of n was calculated as the value for which the sum of the deviations of log sensitivity from prediction, each weighted by its derivative with respect to n, was zero; this gave n= 1.03. From the rms errors of prediction, the probability of the observed data could be derived as a function of n. The resulting 95% limits for n were 0.92 and 1.18. It should be stressed that, whereas this implies that the summed time-varying signals from each cone type are nearly linear with test stimulus intensity, the data place no strong constraint on the extent of nonlinearity as a function of total intensity, since the test increments were always small in relation to the steady background.

H. G. Sperling, “An experimental investigation of the relationship between colour mixture and luminous efficiency,” in Visual Problems of Colour, National Physical Laboratory Symposium No. 8 (H. M. Stationery Office, London, 1958).

Y. Legrand, Light, Colour and Vision (Chapman and Hall, London, 1968), pp. 123–125.

W. A. H. Rushton, “From nerves to eyes,” in The Neurosciences: Paths of Discovery, F. G. Worden, J. P. Swazey, and G. Anderson, eds. (MIT, Cambridge, Mass., 1975), pp. 277–292.

W. S. Stiles, Mechanisms of Colour Vision (Academic, New York, 1978).

This factor differs from the corresponding entry in Table 1. The difference may reflect random error, which perhaps elevated the estimates in Table 1, or it may reflect small nonlinearities or cone response phase differences. In any case, the suppression of the red cone contribution to FPS619(λ) is profound even for tests at the red end of the spectrum. We used the Kodak specification of 678 nm for the Wratten 70. The exact equivalent wavelength of the particular filter used in the experiment is not at all critical in establishing a profound depression in the red cone contribution, although it may change the precise estimate of this depression. Any wavelength greater than 650 nm would suffice to establish profound depression. Wavelengths shorter than this would imply negative weights.

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Figures (14)

Fig. 1
Fig. 1

Ratio of flicker photometric spectral sensitivity obtained by using a 678-nm standard (open squares) or a 541-nm standard (solid circles) to flicker photometric spectral sensitivity obtained by using the usual 589-nm standards. The standard luminance was 75 td for μ = 500 nm (at 700 td) and for μ = 574 nm (at 460 td); it was 300 td for μ = 619 nm (at 3500 td). The data have been vertically translated so that the average deviation is zero.

Fig. 2
Fig. 2

Ratio of flicker photometric spectral sensitivity obtained with a standard of twice the usual radiance to flicker photometric spectral sensitivity obtained by using the usual 589-nm standards (75 td for μ = 656 nm). The rms deviations from invariance are 0.016 log unit for the 500-nm background, 0.014 log unit for the 574-nm background, and 0.013 log unit for the 656-nm background.

Fig. 3
Fig. 3

Top: FPSμ(λ) for μ = 500 nm at 700 td (open circles), for μ = 574 nm at 460 td (solid circles), and for μ = 656 nm at 780 td (open squares) along with the additive combination of FPS656(λ) and FPS574(λ) constrained to coincide with FPS574(λ) at λ = 540 and 630 nm. Here and elsewhere, sensitivities are computed on an energy basis. Bottom: Deviation of additive combination of FPS500(λ) and FPS656(λ) from FPS574(λ).

Fig. 4
Fig. 4

Flicker photometric spectral sensitivity for a 574-nm, 460-td background [FPS574(λ)] along with linear combination of Vos and Walraven’s R(λ) and G(λ) constrained to coincide at λ = 540 and 620 nm.

Fig. 5
Fig. 5

Spectral sensitivity for detection of a steady 1.5° test spot upon a 574-nm, 460-td background, compared with FPS574(λ).

Fig. 6
Fig. 6

FPS500(λ). The mean data for each group of observers are given. The modal cluster (solid circles) is compared with Vos and Walraven’s R(λ) (curve).

Fig. 7
Fig. 7

Same as Fig. 8, but plotted as log quantal sensitivity versus wave number. Open squares have been translated +85 cm−1. No correction for preretinal absorption has been made.

Fig. 8
Fig. 8

FPS500(λ) for red-rich observer, compared with Stiles’s π5 and with Vos and Walraven’s R(λ).

Fig. 9
Fig. 9

FPS619(λ) compared with Vos and Walraven’s G(λ). The background luminance is 3500 td.

Fig. 10
Fig. 10

FPS619(λ) at 11,900 td for observer JW and FPS656(λ) at 2280 td for observer HO compared with Vos and Walraven’s G(λ).

Fig. 11
Fig. 11

Green cone sensitivity during artificial protanopia after bleaching with a 656-nm 25,000-td stimulus. Open squares are the sensitivity measured with color-matching data, and solid circles are that measured with flicker photometry; the curve is Vos and Walraven’s G(λ)

Fig. 12
Fig. 12

Spectral sensitivity for detection of a steady 1.5° test spot upon a 500-nm 700-td background, compared with FPS500(λ).

Fig. 13
Fig. 13

Color discrimination: a 1.5° bipartite test field upon a 7° background field of either 619 nm at 3500 td (solid lines) or 656 nm at 3260 td (dashed line). The ordinate represents the percentage of times a randomly presented variable test was called “different” from a 563-nm standard at a minimally distinct border setting. Mean of two runs.

Fig. 14
Fig. 14

A model for selective suppression of one cone type by colored backgrounds. The luminance signal is formed at the right by additive combination of signals originating in the green and red sensitive cones (upper and lower triangles at left).

Tables (3)

Tables Icon

Table 1 The Ratio wGμ/wRμ for Different Backgrounds, Where FPSμ(λ) is Modeled by wRμR(λ) + wGμG(λ) with Vos and Walraven’s R(λ) and G(λ), Normalized to Reflect the Relative Contributions to the CIE Standard Luminosity Functiona

Tables Icon

Table 2 Flicker Photometric Spectral Sensitivity for All Seven Observers with a 500-nm Background [FPS500(λ)]a

Tables Icon

Table 3 Mean Stimulus Phase Shift Δψ Required by AE in Adjusting Both Test Intensity and Temporal Phase Difference between Test and 589-nm Standard in Order to Eliminate Subjective Flickera

Equations (13)

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w R μ [ R ( λ A ) I A + R ( λ C ) I C ] + w G [ G ( λ A ) I A + G ( λ C ) I C ] = w R μ [ R ( λ B ) I B + R ( λ C ) I C ] + W G μ [ G ( λ B ) I B + G ( λ C ) I C ] .
FPS μ ( λ ) = [ W R μ R p ( λ ) + w G μ G p ( λ ) ] 1 / p = a μ [ w R μ 1 R n ( λ ) + w G μ 1 G n ( λ ) ] 1 / n + b μ [ w R μ 2 R m ( λ ) + w G μ 2 G m ( λ ) ] 1 / m
Δ V G [ Δ I λ G ( λ ) ] / [ I μ G ( μ ) ] ,
( Δ I λ / I μ ) [ k G G ( λ ) / G ( μ ) + k R R ( λ ) / R ( μ ) ] ,
FPS μ ( λ ) = w G μ G ( λ ) + w R μ R ( λ ) ,
w G μ / w R μ = ( k G / k R ) [ R ( μ ) / G ( μ ) ] .
w G 500 / w R 500 w G 619 / w R 619 = R ( 500 ) / G ( 500 ) R ( 619 ) / G ( 619 ) 8.
FPS μ ( λ ) = [ w R μ R n ( λ ) + w G μ G n ( λ ) ] 1 / n .
T = exp ( - V / V 0 ) ,
V R - V f = a ln { 1 + [ I μ R ( μ ) + I λ R ( λ ) ] / i } - V f ,
T R = { 1 + [ I μ R ( μ ) + I λ R ( λ ) ] / i } - a / V 0 exp ( V f / V 0 ) .
exp ( V f / V 0 ) = { [ 1 + I μ G ( μ ) / i ] - a / V 0 + α [ 1 + I μ R ( μ ) / i ] - a / V 0 } - 1 ,
w G / w R = ( 1 / α ) { [ 1 + I μ R ( μ ) / i ] / [ 1 + I μ G ( μ ) / i ] } 1 + a / V 0 .