Abstract

The purpose of the study is to characterize the excitation of the three cone types and the rods in a colorimetric system. Two representations of photoreceptor activity are developed. In the first, rod activity is characterized within a cone colorimetric system that is based on three known physical primaries. Examples are given that use color CRT phosphor spectra. We illustrate how this representation can be used to evaluate the range of chromaticities over which rod signals may intrude into color-monitor-based investigations of cone function. In the second representation, mixtures of four physical primary lights are used to manipulate the four receptor excitations independently. This method allows specification of sets of lights that isolate or silence up to three receptor classes or any combination of receptor classes. Examples are given that use spectra from four light-emitting diodes. This approach opens a field of research in which rod input to various retinal pathways can be evaluated.

© 1996 Optical Society of America

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References

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  1. M. Schultze, “Zur Anatomie und Physiologie der Retina,” Arch. Mikr. Anat. Entwicklungsmech. 2, 175–286 (1866).
    [Crossref]
  2. S. Hecht, “Rods, cones, and the chemical basis of vision,” Physiol. Rev. 17, 239–290 (1937).
  3. W. A. H. Rushton, “Visual adaptation. The Ferrier lecture,” Proc. R. Soc. London Ser. B 162, 20–46 (1965).
    [Crossref]
  4. R. F. Hess, “Rod mediated vision: role of post-receptoral filters,” in Night Vision, R. F. Hess, L. T. Sharpe, K. Nordby, eds. (Cambridge U. Press, Cambridge, 1990), pp. 3–48.
  5. N. W. Daw, E. J. Jensen, W. J. Bunken, “Rod pathways in the mammalian reinae,” Trends Neurosci. 13(3), 110–115 (1990).
    [Crossref] [PubMed]
  6. H. Wässle, U. Grünert, M. H. Chun, B. B. Boycott, “The rod pathway of the macaque monkey retina: identification of AII-amacrine cells with antibodies against calretinin,” J. Comp. Neurol. 361, 537–551 (1995).
    [Crossref] [PubMed]
  7. P. W. Trezona, “The tetrachromatic colour match as a colorimetric technique,” Vis. Res. 13, 9–25 (1973).
    [Crossref]
  8. M. H. Brill, “Mesopic color matching: some theoretical issues,” J. Opt. Soc. Am. A 7, 2048–2051 (1990).
    [Crossref] [PubMed]
  9. R. W. Rodieck, “Which two lights that match for cones show the greatest ratio for rods?,” Vis. Res. 16, 303–307 (1976).
    [Crossref] [PubMed]
  10. G. Wyszecki, W. S. Stiles, Color Science—Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).
  11. Because the CIE does not define a photopic spectral efficacy factor for the 10° data, we will follow the simplification of W. S. Stiles, G. Wyszecki, “Rod intrusion in large-field color matching,” Acta Chromatica, 2, 155–163 (1973), and use the 2° efficacy factor for the 10° values;hence Km equals 683.002 lm/W. The scotopic efficacy factor, equals km′ 1700.06 lm/W.
  12. H. Anton, Elementary Linear Algebra (Wiley, New York, 1977), pp. 117–118.
  13. D. H. Brainard, “Colorimetry,” in Handbook of Optics, 2nd ed., M. Bass et al., eds. (McGraw-Hill, New York, 1995), pp. 26.1–26.54.
  14. D. I. A. MacLeod, R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli of equal luminance,” J. Opt. Soc. Am. 69, 1183–1185 (1979).
    [Crossref] [PubMed]
  15. V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigments between 400 and 500 nm,” Vis. Res. 15, 161–171 (1975).
    [Crossref] [PubMed]
  16. A. Stockman, D. M. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
    [Crossref]
  17. R. M. Boynton, N. Kambe, “Chromatic difference steps of moderate size measured along theoretically critical axes,” Color Res. Appl. 5, 13–23 (1980).
    [Crossref]
  18. V. C. Smith, J. Pokorny, “The design and use of a cone chromaticity space,” Color Res. Appl. 21, 375–383 (1996).
    [Crossref]
  19. E. Schrödinger, “Ueber das Verhaltnis der Vierfarben zur Dreifarbentheorie,” Sitzungber. Kaiseerl. Wien. Akad. Wiss. Math.-naturwiss. Kl. 134, Abt. Ila, 471–190 (1925);Commentary by Qasim Zaid and translation by the National Translation Center, “On the relationship of four-color theory to three-color theory,” Color Res. Appl. 19, 37–47 (1994).
  20. W. S. Stiles, “Adaptation, chromatic adaptation, colour transformation,” Annales d.t. Real. Soc. Espanola d. Fis. Y. Quinn. 57, 149–175 (1961).
  21. M. Aguilar, W. S. Stiles, “Saturation of the rod mechanism of the retina at high levels of illumination,” Opt. Acta 1, 59–65 (1954).
    [Crossref]
  22. L. T. Sharpe, C. Fach, K. Nordby, A. Stockman, “The incremental threshold of the rod visual system and Weber’s law,” Science 244, 354–356 (1989).
    [Crossref] [PubMed]
  23. L. T. Sharpe, C. Fach, A. Stockman, “The field adaptation of the human rod visual system,” J. Physiol. (London) 445, 319–343 (1992).
  24. A. G. Shapiro, J. Pokorny, V. C. Smith, “An investigation of scotopic threshold-versus-illuminance curves for the analysis of color-matching data,” Color Res. Appl. 21, 80–86 (1996).
    [Crossref]
  25. Y. LeGrand, Light, Colour and Vision, 2nd ed. (Chapman & Hall, London, 1968), p. 106.
  26. I. E. Loewenfeld, The Pupil: Anatomy, Physiology, and Clinical Applications (Iowa State U. Press, Ames, Iowa, 1993), Vols. I and II.
  27. J. Pokorny, V. Smith, “How much light reaches the retina?” Doc. Ophthalmol. Proc. Ser. (to be published).
  28. K. Knoblach, “Duel bases in dichromatic color space,” in Colour Vision Deficiencies XII, B. Drum, ed., (Kluwer, Dordrecht, The Netherlands, 1995), pp. 165–176.
    [Crossref]
  29. In all our examples pupil area is assumed to be equal to π mm2.
  30. J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space” Vision Res. 22, 1123–1131 (1982).
    [Crossref] [PubMed]
  31. A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).
  32. In our illustrationA=Cp,Km×[4.23×1034.58×1025.41×1022.68×1039.40×1024.60×1025.39×1022.31×1031.153.42×1026.58×1024.02×1028.00×10−27.66×109.23×1029.46],a value determined from Eq. (8b).
  33. J. Pokorny, V. C. Smith, “Colorimetry and color discrimination,” in Handbook of Perception and Human Performance, Vol I: Sensory Processes and Perception, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986) pp. 8-1–8-51.
  34. Q. Zaidi, A. Shapiro, D. Hood, “The effect of adaptation on the differential sensitivity of the S-cone color system,” Vision Res. 32, 1297–1318 (1992).
    [Crossref] [PubMed]
  35. A. Shapiro, Q. Zaidi, “The effects of prolonged temporal modulation on the differential response of color mechanisms,” Vision Res. 32, 2065–2075 (1992).
    [Crossref] [PubMed]

1996 (2)

V. C. Smith, J. Pokorny, “The design and use of a cone chromaticity space,” Color Res. Appl. 21, 375–383 (1996).
[Crossref]

A. G. Shapiro, J. Pokorny, V. C. Smith, “An investigation of scotopic threshold-versus-illuminance curves for the analysis of color-matching data,” Color Res. Appl. 21, 80–86 (1996).
[Crossref]

1995 (1)

H. Wässle, U. Grünert, M. H. Chun, B. B. Boycott, “The rod pathway of the macaque monkey retina: identification of AII-amacrine cells with antibodies against calretinin,” J. Comp. Neurol. 361, 537–551 (1995).
[Crossref] [PubMed]

1993 (1)

1992 (3)

L. T. Sharpe, C. Fach, A. Stockman, “The field adaptation of the human rod visual system,” J. Physiol. (London) 445, 319–343 (1992).

Q. Zaidi, A. Shapiro, D. Hood, “The effect of adaptation on the differential sensitivity of the S-cone color system,” Vision Res. 32, 1297–1318 (1992).
[Crossref] [PubMed]

A. Shapiro, Q. Zaidi, “The effects of prolonged temporal modulation on the differential response of color mechanisms,” Vision Res. 32, 2065–2075 (1992).
[Crossref] [PubMed]

1990 (2)

M. H. Brill, “Mesopic color matching: some theoretical issues,” J. Opt. Soc. Am. A 7, 2048–2051 (1990).
[Crossref] [PubMed]

N. W. Daw, E. J. Jensen, W. J. Bunken, “Rod pathways in the mammalian reinae,” Trends Neurosci. 13(3), 110–115 (1990).
[Crossref] [PubMed]

1989 (1)

L. T. Sharpe, C. Fach, K. Nordby, A. Stockman, “The incremental threshold of the rod visual system and Weber’s law,” Science 244, 354–356 (1989).
[Crossref] [PubMed]

1984 (1)

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

1982 (1)

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space” Vision Res. 22, 1123–1131 (1982).
[Crossref] [PubMed]

1980 (1)

R. M. Boynton, N. Kambe, “Chromatic difference steps of moderate size measured along theoretically critical axes,” Color Res. Appl. 5, 13–23 (1980).
[Crossref]

1979 (1)

1976 (1)

R. W. Rodieck, “Which two lights that match for cones show the greatest ratio for rods?,” Vis. Res. 16, 303–307 (1976).
[Crossref] [PubMed]

1975 (1)

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

1973 (2)

Because the CIE does not define a photopic spectral efficacy factor for the 10° data, we will follow the simplification of W. S. Stiles, G. Wyszecki, “Rod intrusion in large-field color matching,” Acta Chromatica, 2, 155–163 (1973), and use the 2° efficacy factor for the 10° values;hence Km equals 683.002 lm/W. The scotopic efficacy factor, equals km′ 1700.06 lm/W.

P. W. Trezona, “The tetrachromatic colour match as a colorimetric technique,” Vis. Res. 13, 9–25 (1973).
[Crossref]

1965 (1)

W. A. H. Rushton, “Visual adaptation. The Ferrier lecture,” Proc. R. Soc. London Ser. B 162, 20–46 (1965).
[Crossref]

1961 (1)

W. S. Stiles, “Adaptation, chromatic adaptation, colour transformation,” Annales d.t. Real. Soc. Espanola d. Fis. Y. Quinn. 57, 149–175 (1961).

1954 (1)

M. Aguilar, W. S. Stiles, “Saturation of the rod mechanism of the retina at high levels of illumination,” Opt. Acta 1, 59–65 (1954).
[Crossref]

1937 (1)

S. Hecht, “Rods, cones, and the chemical basis of vision,” Physiol. Rev. 17, 239–290 (1937).

1925 (1)

E. Schrödinger, “Ueber das Verhaltnis der Vierfarben zur Dreifarbentheorie,” Sitzungber. Kaiseerl. Wien. Akad. Wiss. Math.-naturwiss. Kl. 134, Abt. Ila, 471–190 (1925);Commentary by Qasim Zaid and translation by the National Translation Center, “On the relationship of four-color theory to three-color theory,” Color Res. Appl. 19, 37–47 (1994).

1866 (1)

M. Schultze, “Zur Anatomie und Physiologie der Retina,” Arch. Mikr. Anat. Entwicklungsmech. 2, 175–286 (1866).
[Crossref]

Aguilar, M.

M. Aguilar, W. S. Stiles, “Saturation of the rod mechanism of the retina at high levels of illumination,” Opt. Acta 1, 59–65 (1954).
[Crossref]

Anton, H.

H. Anton, Elementary Linear Algebra (Wiley, New York, 1977), pp. 117–118.

Boycott, B. B.

H. Wässle, U. Grünert, M. H. Chun, B. B. Boycott, “The rod pathway of the macaque monkey retina: identification of AII-amacrine cells with antibodies against calretinin,” J. Comp. Neurol. 361, 537–551 (1995).
[Crossref] [PubMed]

Boynton, R. M.

R. M. Boynton, N. Kambe, “Chromatic difference steps of moderate size measured along theoretically critical axes,” Color Res. Appl. 5, 13–23 (1980).
[Crossref]

D. I. A. MacLeod, R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli of equal luminance,” J. Opt. Soc. Am. 69, 1183–1185 (1979).
[Crossref] [PubMed]

Brainard, D. H.

D. H. Brainard, “Colorimetry,” in Handbook of Optics, 2nd ed., M. Bass et al., eds. (McGraw-Hill, New York, 1995), pp. 26.1–26.54.

Brill, M. H.

Bunken, W. J.

N. W. Daw, E. J. Jensen, W. J. Bunken, “Rod pathways in the mammalian reinae,” Trends Neurosci. 13(3), 110–115 (1990).
[Crossref] [PubMed]

Chun, M. H.

H. Wässle, U. Grünert, M. H. Chun, B. B. Boycott, “The rod pathway of the macaque monkey retina: identification of AII-amacrine cells with antibodies against calretinin,” J. Comp. Neurol. 361, 537–551 (1995).
[Crossref] [PubMed]

Daw, N. W.

N. W. Daw, E. J. Jensen, W. J. Bunken, “Rod pathways in the mammalian reinae,” Trends Neurosci. 13(3), 110–115 (1990).
[Crossref] [PubMed]

Derrington, A. M.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Fach, C.

L. T. Sharpe, C. Fach, A. Stockman, “The field adaptation of the human rod visual system,” J. Physiol. (London) 445, 319–343 (1992).

L. T. Sharpe, C. Fach, K. Nordby, A. Stockman, “The incremental threshold of the rod visual system and Weber’s law,” Science 244, 354–356 (1989).
[Crossref] [PubMed]

Grünert, U.

H. Wässle, U. Grünert, M. H. Chun, B. B. Boycott, “The rod pathway of the macaque monkey retina: identification of AII-amacrine cells with antibodies against calretinin,” J. Comp. Neurol. 361, 537–551 (1995).
[Crossref] [PubMed]

Hecht, S.

S. Hecht, “Rods, cones, and the chemical basis of vision,” Physiol. Rev. 17, 239–290 (1937).

Heeley, D. W.

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space” Vision Res. 22, 1123–1131 (1982).
[Crossref] [PubMed]

Hess, R. F.

R. F. Hess, “Rod mediated vision: role of post-receptoral filters,” in Night Vision, R. F. Hess, L. T. Sharpe, K. Nordby, eds. (Cambridge U. Press, Cambridge, 1990), pp. 3–48.

Hood, D.

Q. Zaidi, A. Shapiro, D. Hood, “The effect of adaptation on the differential sensitivity of the S-cone color system,” Vision Res. 32, 1297–1318 (1992).
[Crossref] [PubMed]

Jensen, E. J.

N. W. Daw, E. J. Jensen, W. J. Bunken, “Rod pathways in the mammalian reinae,” Trends Neurosci. 13(3), 110–115 (1990).
[Crossref] [PubMed]

Johnson, N. E.

Kambe, N.

R. M. Boynton, N. Kambe, “Chromatic difference steps of moderate size measured along theoretically critical axes,” Color Res. Appl. 5, 13–23 (1980).
[Crossref]

Knoblach, K.

K. Knoblach, “Duel bases in dichromatic color space,” in Colour Vision Deficiencies XII, B. Drum, ed., (Kluwer, Dordrecht, The Netherlands, 1995), pp. 165–176.
[Crossref]

Krauskopf, J.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space” Vision Res. 22, 1123–1131 (1982).
[Crossref] [PubMed]

LeGrand, Y.

Y. LeGrand, Light, Colour and Vision, 2nd ed. (Chapman & Hall, London, 1968), p. 106.

Lennie, P.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Loewenfeld, I. E.

I. E. Loewenfeld, The Pupil: Anatomy, Physiology, and Clinical Applications (Iowa State U. Press, Ames, Iowa, 1993), Vols. I and II.

MacLeod, D. I. A.

MacLeod, D. M.

Nordby, K.

L. T. Sharpe, C. Fach, K. Nordby, A. Stockman, “The incremental threshold of the rod visual system and Weber’s law,” Science 244, 354–356 (1989).
[Crossref] [PubMed]

Pokorny, J.

A. G. Shapiro, J. Pokorny, V. C. Smith, “An investigation of scotopic threshold-versus-illuminance curves for the analysis of color-matching data,” Color Res. Appl. 21, 80–86 (1996).
[Crossref]

V. C. Smith, J. Pokorny, “The design and use of a cone chromaticity space,” Color Res. Appl. 21, 375–383 (1996).
[Crossref]

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

J. Pokorny, V. Smith, “How much light reaches the retina?” Doc. Ophthalmol. Proc. Ser. (to be published).

J. Pokorny, V. C. Smith, “Colorimetry and color discrimination,” in Handbook of Perception and Human Performance, Vol I: Sensory Processes and Perception, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986) pp. 8-1–8-51.

Rodieck, R. W.

R. W. Rodieck, “Which two lights that match for cones show the greatest ratio for rods?,” Vis. Res. 16, 303–307 (1976).
[Crossref] [PubMed]

Rushton, W. A. H.

W. A. H. Rushton, “Visual adaptation. The Ferrier lecture,” Proc. R. Soc. London Ser. B 162, 20–46 (1965).
[Crossref]

Schrödinger, E.

E. Schrödinger, “Ueber das Verhaltnis der Vierfarben zur Dreifarbentheorie,” Sitzungber. Kaiseerl. Wien. Akad. Wiss. Math.-naturwiss. Kl. 134, Abt. Ila, 471–190 (1925);Commentary by Qasim Zaid and translation by the National Translation Center, “On the relationship of four-color theory to three-color theory,” Color Res. Appl. 19, 37–47 (1994).

Schultze, M.

M. Schultze, “Zur Anatomie und Physiologie der Retina,” Arch. Mikr. Anat. Entwicklungsmech. 2, 175–286 (1866).
[Crossref]

Shapiro, A.

Q. Zaidi, A. Shapiro, D. Hood, “The effect of adaptation on the differential sensitivity of the S-cone color system,” Vision Res. 32, 1297–1318 (1992).
[Crossref] [PubMed]

A. Shapiro, Q. Zaidi, “The effects of prolonged temporal modulation on the differential response of color mechanisms,” Vision Res. 32, 2065–2075 (1992).
[Crossref] [PubMed]

Shapiro, A. G.

A. G. Shapiro, J. Pokorny, V. C. Smith, “An investigation of scotopic threshold-versus-illuminance curves for the analysis of color-matching data,” Color Res. Appl. 21, 80–86 (1996).
[Crossref]

Sharpe, L. T.

L. T. Sharpe, C. Fach, A. Stockman, “The field adaptation of the human rod visual system,” J. Physiol. (London) 445, 319–343 (1992).

L. T. Sharpe, C. Fach, K. Nordby, A. Stockman, “The incremental threshold of the rod visual system and Weber’s law,” Science 244, 354–356 (1989).
[Crossref] [PubMed]

Smith, V.

J. Pokorny, V. Smith, “How much light reaches the retina?” Doc. Ophthalmol. Proc. Ser. (to be published).

Smith, V. C.

A. G. Shapiro, J. Pokorny, V. C. Smith, “An investigation of scotopic threshold-versus-illuminance curves for the analysis of color-matching data,” Color Res. Appl. 21, 80–86 (1996).
[Crossref]

V. C. Smith, J. Pokorny, “The design and use of a cone chromaticity space,” Color Res. Appl. 21, 375–383 (1996).
[Crossref]

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

J. Pokorny, V. C. Smith, “Colorimetry and color discrimination,” in Handbook of Perception and Human Performance, Vol I: Sensory Processes and Perception, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986) pp. 8-1–8-51.

Stiles, W. S.

Because the CIE does not define a photopic spectral efficacy factor for the 10° data, we will follow the simplification of W. S. Stiles, G. Wyszecki, “Rod intrusion in large-field color matching,” Acta Chromatica, 2, 155–163 (1973), and use the 2° efficacy factor for the 10° values;hence Km equals 683.002 lm/W. The scotopic efficacy factor, equals km′ 1700.06 lm/W.

W. S. Stiles, “Adaptation, chromatic adaptation, colour transformation,” Annales d.t. Real. Soc. Espanola d. Fis. Y. Quinn. 57, 149–175 (1961).

M. Aguilar, W. S. Stiles, “Saturation of the rod mechanism of the retina at high levels of illumination,” Opt. Acta 1, 59–65 (1954).
[Crossref]

G. Wyszecki, W. S. Stiles, Color Science—Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

Stockman, A.

A. Stockman, D. M. MacLeod, N. E. Johnson, “Spectral sensitivities of the human cones,” J. Opt. Soc. Am. A 10, 2491–2521 (1993).
[Crossref]

L. T. Sharpe, C. Fach, A. Stockman, “The field adaptation of the human rod visual system,” J. Physiol. (London) 445, 319–343 (1992).

L. T. Sharpe, C. Fach, K. Nordby, A. Stockman, “The incremental threshold of the rod visual system and Weber’s law,” Science 244, 354–356 (1989).
[Crossref] [PubMed]

Trezona, P. W.

P. W. Trezona, “The tetrachromatic colour match as a colorimetric technique,” Vis. Res. 13, 9–25 (1973).
[Crossref]

Wässle, H.

H. Wässle, U. Grünert, M. H. Chun, B. B. Boycott, “The rod pathway of the macaque monkey retina: identification of AII-amacrine cells with antibodies against calretinin,” J. Comp. Neurol. 361, 537–551 (1995).
[Crossref] [PubMed]

Williams, D. R.

J. Krauskopf, D. R. Williams, D. W. Heeley, “Cardinal directions of color space” Vision Res. 22, 1123–1131 (1982).
[Crossref] [PubMed]

Wyszecki, G.

Because the CIE does not define a photopic spectral efficacy factor for the 10° data, we will follow the simplification of W. S. Stiles, G. Wyszecki, “Rod intrusion in large-field color matching,” Acta Chromatica, 2, 155–163 (1973), and use the 2° efficacy factor for the 10° values;hence Km equals 683.002 lm/W. The scotopic efficacy factor, equals km′ 1700.06 lm/W.

G. Wyszecki, W. S. Stiles, Color Science—Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

Zaidi, Q.

A. Shapiro, Q. Zaidi, “The effects of prolonged temporal modulation on the differential response of color mechanisms,” Vision Res. 32, 2065–2075 (1992).
[Crossref] [PubMed]

Q. Zaidi, A. Shapiro, D. Hood, “The effect of adaptation on the differential sensitivity of the S-cone color system,” Vision Res. 32, 1297–1318 (1992).
[Crossref] [PubMed]

Acta Chromatica (1)

Because the CIE does not define a photopic spectral efficacy factor for the 10° data, we will follow the simplification of W. S. Stiles, G. Wyszecki, “Rod intrusion in large-field color matching,” Acta Chromatica, 2, 155–163 (1973), and use the 2° efficacy factor for the 10° values;hence Km equals 683.002 lm/W. The scotopic efficacy factor, equals km′ 1700.06 lm/W.

Annales d.t. Real. Soc. Espanola d. Fis. Y. Quinn. (1)

W. S. Stiles, “Adaptation, chromatic adaptation, colour transformation,” Annales d.t. Real. Soc. Espanola d. Fis. Y. Quinn. 57, 149–175 (1961).

Arch. Mikr. Anat. Entwicklungsmech. (1)

M. Schultze, “Zur Anatomie und Physiologie der Retina,” Arch. Mikr. Anat. Entwicklungsmech. 2, 175–286 (1866).
[Crossref]

Color Res. Appl. (3)

R. M. Boynton, N. Kambe, “Chromatic difference steps of moderate size measured along theoretically critical axes,” Color Res. Appl. 5, 13–23 (1980).
[Crossref]

V. C. Smith, J. Pokorny, “The design and use of a cone chromaticity space,” Color Res. Appl. 21, 375–383 (1996).
[Crossref]

A. G. Shapiro, J. Pokorny, V. C. Smith, “An investigation of scotopic threshold-versus-illuminance curves for the analysis of color-matching data,” Color Res. Appl. 21, 80–86 (1996).
[Crossref]

J. Comp. Neurol. (1)

H. Wässle, U. Grünert, M. H. Chun, B. B. Boycott, “The rod pathway of the macaque monkey retina: identification of AII-amacrine cells with antibodies against calretinin,” J. Comp. Neurol. 361, 537–551 (1995).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Physiol. (London) (2)

L. T. Sharpe, C. Fach, A. Stockman, “The field adaptation of the human rod visual system,” J. Physiol. (London) 445, 319–343 (1992).

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Opt. Acta (1)

M. Aguilar, W. S. Stiles, “Saturation of the rod mechanism of the retina at high levels of illumination,” Opt. Acta 1, 59–65 (1954).
[Crossref]

Physiol. Rev. (1)

S. Hecht, “Rods, cones, and the chemical basis of vision,” Physiol. Rev. 17, 239–290 (1937).

Proc. R. Soc. London Ser. B (1)

W. A. H. Rushton, “Visual adaptation. The Ferrier lecture,” Proc. R. Soc. London Ser. B 162, 20–46 (1965).
[Crossref]

Science (1)

L. T. Sharpe, C. Fach, K. Nordby, A. Stockman, “The incremental threshold of the rod visual system and Weber’s law,” Science 244, 354–356 (1989).
[Crossref] [PubMed]

Sitzungber. Kaiseerl. Wien. Akad. Wiss. Math.-naturwiss. Kl. (1)

E. Schrödinger, “Ueber das Verhaltnis der Vierfarben zur Dreifarbentheorie,” Sitzungber. Kaiseerl. Wien. Akad. Wiss. Math.-naturwiss. Kl. 134, Abt. Ila, 471–190 (1925);Commentary by Qasim Zaid and translation by the National Translation Center, “On the relationship of four-color theory to three-color theory,” Color Res. Appl. 19, 37–47 (1994).

Trends Neurosci. (1)

N. W. Daw, E. J. Jensen, W. J. Bunken, “Rod pathways in the mammalian reinae,” Trends Neurosci. 13(3), 110–115 (1990).
[Crossref] [PubMed]

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

R. W. Rodieck, “Which two lights that match for cones show the greatest ratio for rods?,” Vis. Res. 16, 303–307 (1976).
[Crossref] [PubMed]

P. W. Trezona, “The tetrachromatic colour match as a colorimetric technique,” Vis. Res. 13, 9–25 (1973).
[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

A. Shapiro, Q. Zaidi, “The effects of prolonged temporal modulation on the differential response of color mechanisms,” Vision Res. 32, 2065–2075 (1992).
[Crossref] [PubMed]

Other (11)

In our illustrationA=Cp,Km×[4.23×1034.58×1025.41×1022.68×1039.40×1024.60×1025.39×1022.31×1031.153.42×1026.58×1024.02×1028.00×10−27.66×109.23×1029.46],a value determined from Eq. (8b).

J. Pokorny, V. C. Smith, “Colorimetry and color discrimination,” in Handbook of Perception and Human Performance, Vol I: Sensory Processes and Perception, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986) pp. 8-1–8-51.

Y. LeGrand, Light, Colour and Vision, 2nd ed. (Chapman & Hall, London, 1968), p. 106.

I. E. Loewenfeld, The Pupil: Anatomy, Physiology, and Clinical Applications (Iowa State U. Press, Ames, Iowa, 1993), Vols. I and II.

J. Pokorny, V. Smith, “How much light reaches the retina?” Doc. Ophthalmol. Proc. Ser. (to be published).

K. Knoblach, “Duel bases in dichromatic color space,” in Colour Vision Deficiencies XII, B. Drum, ed., (Kluwer, Dordrecht, The Netherlands, 1995), pp. 165–176.
[Crossref]

In all our examples pupil area is assumed to be equal to π mm2.

G. Wyszecki, W. S. Stiles, Color Science—Concepts and Methods, Quantitative Data and Formulae, 2nd ed. (Wiley, New York, 1982).

R. F. Hess, “Rod mediated vision: role of post-receptoral filters,” in Night Vision, R. F. Hess, L. T. Sharpe, K. Nordby, eds. (Cambridge U. Press, Cambridge, 1990), pp. 3–48.

H. Anton, Elementary Linear Algebra (Wiley, New York, 1977), pp. 117–118.

D. H. Brainard, “Colorimetry,” in Handbook of Optics, 2nd ed., M. Bass et al., eds. (McGraw-Hill, New York, 1995), pp. 26.1–26.54.

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Figures (8)

Fig. 1
Fig. 1

Relative spectral energy distributions of three CRT phosphors. The distributions are labeled P1 (solid curve), P2 (long-dashed curve), and P3 (short-dashed curve) when scaled to their maximum attainable energy levels.

Fig. 2
Fig. 2

Relative S-, L-, and M-cone fundamentals (solid curves) used for the analysis. These fundamentals are linear transformations of CIE 1964 color-matching functions. The heights were adjusted so that (1) l ¯ 10 and m ¯ 10 sum to y ¯ 10 and (2) s ¯ 10 and y ¯ 10 have equal area. The rod photoreceptor sensitivity distribution r ¯ (dashed curve) used in analysis II has the spectral distribution of V λ with the height adjusted so that r ¯ and y ¯ 10 have equal area.

Fig. 3
Fig. 3

Isoscotopic lines plotted in chromaticity diagrams. A, CIE 10° chromaticities that result from the intersection of five planes of equal scotopic luminance (40, 55, 70, 85, and 100 scotopic cd/m2) and a plane with a photopic luminance of 30 photopic cd/m2, all generated from the primaries P1, P2, and P3. The dashed polygon boundary indicates the range of chromaticities attainable at 30 photopic cd/m2. In each panel the dots show the chromaticities of the phosphors, and the open circle shows the chromaticity of a light metameric to an equal-energy white (0.3333, 0.3333). All five isoscotopic lines approach convergence at 0.3909, 0. B, Intersection of three equal scotopic planes (110, 140, and 170 scotopic cd/m2) and a plane of 60 photopic cd/m2. These lines also approach convergence at 0.3909,0. The dashed polygon boundary indicates the range of chromaticities attainable at 60 photopic cd/m2. C, lines that result from the same intersections as in panel A but expressed in a cone chromaticity diagram. The isoscotopic lines are parallel to each other.

Fig. 4
Fig. 4

Output of Eqs. (6a) and (6b) fitted to the Aguilar–Stiles21 TVI data. Equations (6a) and (6b) are used as an estimate of rod threshold at a particular scotopic luminance level.

Fig. 5
Fig. 5

CIE 10° chromaticities of equal-photopic-luminance lights that differ in scotopic luminance from midwhite [(0.3333, 0.3333), striped circle] by an amount greater than the rod threshold. In each panel the dots indicate the chromaticities of the phosphors, the dashed boundary indicates the range of attainable lights at a photopic luminance level, and the shaded areas indicate the region above rod threshold. A, Lights with a luminance of 30 photopic cd/m2. All lights with chromaticities along the heavy dashed line have a scotopic luminance of 64.6 cd/m2. Lights along the solid lines have a scotopic luminance of 64.6 + 15.0 cd/m2 or 64.6 − 15.0 cd/m2. B, Lights with a luminance of 50 photopic cd/m2. All lights with chromaticities along the heavy dashed line have a scotopic luminance of 107.6 cd/m2. Lights with chromaticities on the solid lines have a scotopic luminance of 107.6 + 53.4 cd/m2 or 107.6 − 53.4 cd/m2.

Fig. 6
Fig. 6

Same calculations as shown in Fig. 5 but expressed in a cone-based chromaticity diagram. A, Lights with a luminance of 30 photopic cd/m2, B, Lights with a luminance of 50 photopic cd/m2.

Fig. 7
Fig. 7

Effects of chromaticity on discriminable rod signals at 30 photopic cd/m2. Symbols are the same as in Fig. 5. A, All lights with chromaticities on the heavy dashed line have a scotopic luminance of 34.1 cd/m2. Lights with chromaticities on the solid line have a scotopic luminance of 34.1 + 6.8 cd/m2. B, Lights with chromaticities on the heavy dashed line have a scotopic luminance of 124.1 cd/m2. Lights with chromaticities on the solid line have a scotopic luminance of 124.1−74.2 cd/m2.

Fig. 8
Fig. 8

A, Relative spectral energy distributions of the four LED’s. In this diagram each distribution is normalized to 1.0 at its peak energy level. The distributions are labeled P1 (solid curves), P2 (dashed curve), P3 (dotted curve) and P4 (dotted-dashed curve) when they are scaled to their maximum attainable radiances. Shown also are the chromaticities of the phosphors in a CIE diagram (B) and in a cone-based diagram (C).

Equations (31)

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Q i = p 1 , i P 1 + p 2 , i P 2 + p 3 , i P 3 ,
Y 10 = p 1 , i P 1 , pht + p 2 , i P 2 , pht + p 3 , i P 3 , pht .
Y = p 1 , i P 1 , sct + p 2 , i P 2 , sct + p 3 , i P 3 , sct .
[ Y 10 Y ] = [ p 1 , i p 2 , i p 3 , i ] [ P 1 , pht P 1 , sct P 2 , pht P 2 , sct P 3 , pht P 3 , sct ]
p 1 , τ = τ | P 2 , pht P 2 , sct P 3 , pht P 3 , sct | + p 1 , 0 ,
p 2 , τ = τ | P 1 , pht P 1 , sct P 3 , pht P 3 , sct | + p 2 , 0 ,
p 3 , τ = τ | P 1 , pht P 1 , sct P 2 , pht P 2 , sct | + p 3 , 0 ,
[ l ¯ 10 ( λ ) m ¯ 10 ( λ ) s ¯ 10 ( λ ) ] = [ + 0.15516 + 0.54308 0.03287 0.15516 + 0.45692 + 0.03287 0.00000 0.00000 + 1.00000 ] × [ x ¯ 10 ( λ ) y ¯ 10 ( λ ) z ¯ 10 ( λ ) ] ,
Δ I = k ( I n + I 0 n ) 1 / m when I < 10 2.2 scotopic trolands ( Td ) ,
Δ I = c 1 + k 1 ( I 10 2.2 ) k 2 when 10 2.2 I < 10 3.0 scotopic Td ,
S = C p , K m λ Q ( λ ) s ¯ 10 ( λ ) ,
M = C p , K m λ Q ( λ ) m ¯ 10 ( λ ) ,
L = C p , K m λ Q ( λ ) l ¯ 10 ( λ ) ,
R = C p , K m λ Q ( λ ) r ¯ 10 ( λ ) ,
β = α A ,
A = C p , K m [ λ P 1 , λ s ¯ ( λ ) λ P 1 , λ m ¯ ( λ ) λ P 1 , λ l ¯ ( λ ) λ P 1 , λ r ¯ ( λ ) λ P 2 , λ s ¯ ( λ ) λ P 2 , λ m ¯ ( λ ) λ P 2 , λ l ¯ ( λ ) λ P 2 , λ r ¯ ( λ ) λ P 3 , λ s ¯ ( λ ) λ P 3 , λ m ¯ ( λ ) λ P 3 , λ l ¯ ( λ ) λ P 3 , λ r ¯ ( λ ) λ P 4 , λ s ¯ ( λ ) λ P 4 , λ m ¯ ( λ ) λ P 4 , λ l ¯ ( λ ) λ P 4 , λ r ¯ ( λ ) ] ,
α = β A 1 .
β τ = β 0 + τ β Δ for < τ < + .
α τ = ( β 0 + τ β Δ ) A 1 .
α τ = α 0 + τ α Δ ,
α τ = β 0 A 1 , α Δ = β Δ A 1 .
β τ = [ 1000 333.0 667 1240 ] + τ [ 0 0 0 1 ] .
α τ = α 0 + τ α Δ ,
α 0 = [ 1.74 × 10 1 2.78 × 10 1 3.18 × 10 1 2.29 × 10 1 ] , α Δ = [ 1.75 × 10 4 7.89 × 10 4 8.89 × 10 4 2.75 × 10 4 ] .
rod contrast = 100 max ( rod TD ) min ( rod TD ) max ( rod TD ) + min ( rod TD ) .
l ¯ 10 , m ¯ 10 , s ¯ 10
V λ
y ¯ 10
P 1 , P 2 , P 3 , P 4
p 1 , p 2 , p 3 , p 4
A=Cp,Km×[4.23×1034.58×1025.41×1022.68×1039.40×1024.60×1025.39×1022.31×1031.153.42×1026.58×1024.02×1028.00×1027.66×109.23×1029.46],

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