Abstract

In order to establish the luminous-efficiency function for mesopic vision of the standard observer, luminous efficiency functions were measured with the direct heterochromatic brightness-matching method at retinal illuminance in the range of −2–2 log photopic trolands in order to cover the scotopic, mesopic, and photopic conditions. A steady visual field of 10° arc was presented foveally. The functions underwent the usual complicated change from a rod type of luminous-efficiency function close to V′(λ) to a cone function that had a wide and almost double-peaked shape. A simple formula to represent the mesopic luminous-efficiency functions was derived in which log sensitivities of scotopic and photopic vision were linearly added after being multiplied by coefficients that were dependent on the luminance level. Saturation functions were also obtained at the various luminance levels for which luminous efficiency was investigated. In spite of a great variation of luminance level, the saturation function remained more or less the same, which indicates that the chromatic channels retain their contributions to the brightness sensation at low retinal illumination.

© 1981 Optical Society of America

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References

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  1. H. V. Walters and W. D. Wright, “The spectral sensitivity of the fovea and extra-fovea in the Purkinje range,” Proc. R. Soc. London, Ser. B 131, 340 (1943); W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).
    [Crossref]
  2. J. A. S. Kinney, “Sensitivity of the eye to spectral radiation at scotopic and mesopic intensity levels,” J. Opt. Soc. Am. 45, 507–514 (1955).
    [Crossref] [PubMed]
  3. J. A. S. Kinney, “Comparison of scotopic, mesopic and photopic spectral sensitivity curves,” J. Opt. Soc. Am. 48, 185–190 (1958).
    [Crossref] [PubMed]
  4. J. A. S. Kinney, “Effect of field sizes and position on mesopic spectral sensitivity,” J. Opt. Soc. Am. 54, 671–677 (1964).
    [Crossref] [PubMed]
  5. R. E. Bedford and G. W. Wyszecki, “Luminous functions for various field sizes and levels of retinal illuminance,” J. Opt. Soc. Am. 48, 406–411 (1958).
    [Crossref] [PubMed]
  6. C. S. Bridgman, “The luminosity curve as affected by the relation between rod and cone adaptation,” J. Opt. Soc. Am. 43, 733–737 (1953).
    [Crossref] [PubMed]
  7. D. A. Palmer, “The definition of a standard observer for mesopic photometry,” Vision Res. 7, 619–628 (1967).
    [Crossref] [PubMed]
  8. D. A. Palmer, “Standard observer for large-field photometry at any level,” J. Opt. Soc. Am. 58, 1296–1299 (1968).
    [Crossref] [PubMed]
  9. D. A. Palmer, “Rod-cone mechanism underlying the Purkinje shift,” Nature 262, 601–603 (1976).
    [Crossref] [PubMed]
  10. S. Kokoschka and H. W. Bodmann, “Ein konsistentes System für photometrischen Strahlungsbewertung im gesamten Adaptationsbereich,” CIE Pub. No. 36 (Commission Internationale de l’Eclairage, Paris, 1976), pp. 217–225.
  11. “Light as a true visual quantity: principles of measurement,” CIE Pub. No. 41 (Commission International de l’Eclairage, Paris, 1978), p. 37.
  12. J. P. Comerford and P. K. Kaiser, “Luminous-efficiency functions determined by heterochromatic brightness matching,” J. Opt. Soc. Am. 65, 466–468 (1975).
    [Crossref] [PubMed]
  13. M. Ikeda and H. Shimozono, “Luminous efficiency functions determined by successive brightness matching,” J. Opt. Soc. Am. 68, 1767–1771 (1978).
    [Crossref]
  14. 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]
  15. S. L. Guth, R. W. Massof, and T. Benzschawel, “Vector model for normal and dichromatic color vision,” J. Opt. Soc. Am. 70, 197–212 (1980).
    [Crossref] [PubMed]
  16. H. Yaguchi and M. Ikeda, “Luminous efficiency functions by the heterochromatic brightness matching for a wide range of retinal illuminance,” J. Light Vis. Environ. (to be published).
  17. P. K. Kaiser and J. P. Comerford, “Flicker photometry of equally bright lights,” Vision Res. 15, 1399–1402 (1975).
    [Crossref] [PubMed]
  18. P. K. Kaiser, “Request for brightness-matching data and mathematical colour-vision models,” Color Res. Appl. 3, 148 (1978).
    [Crossref]
  19. Technical Committee TC-1.4 of the Commission Internationale de l’Eclairage was established at the Kyoto Session (1979) by the Luminous Efficiency Functions Subcommittee to collect sufficient information regarding luminous-efficiency functions by using heterochromatic brightness matching.

1980 (1)

1978 (2)

M. Ikeda and H. Shimozono, “Luminous efficiency functions determined by successive brightness matching,” J. Opt. Soc. Am. 68, 1767–1771 (1978).
[Crossref]

P. K. Kaiser, “Request for brightness-matching data and mathematical colour-vision models,” Color Res. Appl. 3, 148 (1978).
[Crossref]

1976 (1)

D. A. Palmer, “Rod-cone mechanism underlying the Purkinje shift,” Nature 262, 601–603 (1976).
[Crossref] [PubMed]

1975 (2)

1973 (1)

1968 (1)

1967 (1)

D. A. Palmer, “The definition of a standard observer for mesopic photometry,” Vision Res. 7, 619–628 (1967).
[Crossref] [PubMed]

1964 (1)

1958 (2)

1955 (1)

1953 (1)

1943 (1)

H. V. Walters and W. D. Wright, “The spectral sensitivity of the fovea and extra-fovea in the Purkinje range,” Proc. R. Soc. London, Ser. B 131, 340 (1943); W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).
[Crossref]

Bedford, R. E.

Benzschawel, T.

Bodmann, H. W.

S. Kokoschka and H. W. Bodmann, “Ein konsistentes System für photometrischen Strahlungsbewertung im gesamten Adaptationsbereich,” CIE Pub. No. 36 (Commission Internationale de l’Eclairage, Paris, 1976), pp. 217–225.

Bridgman, C. S.

Comerford, J. P.

Guth, S. L.

Ikeda, M.

M. Ikeda and H. Shimozono, “Luminous efficiency functions determined by successive brightness matching,” J. Opt. Soc. Am. 68, 1767–1771 (1978).
[Crossref]

H. Yaguchi and M. Ikeda, “Luminous efficiency functions by the heterochromatic brightness matching for a wide range of retinal illuminance,” J. Light Vis. Environ. (to be published).

Kaiser, P. K.

P. K. Kaiser, “Request for brightness-matching data and mathematical colour-vision models,” Color Res. Appl. 3, 148 (1978).
[Crossref]

P. K. Kaiser and J. P. Comerford, “Flicker photometry of equally bright lights,” Vision Res. 15, 1399–1402 (1975).
[Crossref] [PubMed]

J. P. Comerford and P. K. Kaiser, “Luminous-efficiency functions determined by heterochromatic brightness matching,” J. Opt. Soc. Am. 65, 466–468 (1975).
[Crossref] [PubMed]

Kinney, J. A. S.

Kokoschka, S.

S. Kokoschka and H. W. Bodmann, “Ein konsistentes System für photometrischen Strahlungsbewertung im gesamten Adaptationsbereich,” CIE Pub. No. 36 (Commission Internationale de l’Eclairage, Paris, 1976), pp. 217–225.

Lodge, H. R.

Massof, R. W.

Palmer, D. A.

D. A. Palmer, “Rod-cone mechanism underlying the Purkinje shift,” Nature 262, 601–603 (1976).
[Crossref] [PubMed]

D. A. Palmer, “Standard observer for large-field photometry at any level,” J. Opt. Soc. Am. 58, 1296–1299 (1968).
[Crossref] [PubMed]

D. A. Palmer, “The definition of a standard observer for mesopic photometry,” Vision Res. 7, 619–628 (1967).
[Crossref] [PubMed]

Shimozono, H.

Walters, H. V.

H. V. Walters and W. D. Wright, “The spectral sensitivity of the fovea and extra-fovea in the Purkinje range,” Proc. R. Soc. London, Ser. B 131, 340 (1943); W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).
[Crossref]

Wright, W. D.

H. V. Walters and W. D. Wright, “The spectral sensitivity of the fovea and extra-fovea in the Purkinje range,” Proc. R. Soc. London, Ser. B 131, 340 (1943); W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).
[Crossref]

Wyszecki, G. W.

Yaguchi, H.

H. Yaguchi and M. Ikeda, “Luminous efficiency functions by the heterochromatic brightness matching for a wide range of retinal illuminance,” J. Light Vis. Environ. (to be published).

Color Res. Appl. (1)

P. K. Kaiser, “Request for brightness-matching data and mathematical colour-vision models,” Color Res. Appl. 3, 148 (1978).
[Crossref]

J. Opt. Soc. Am. (10)

J. P. Comerford and P. K. Kaiser, “Luminous-efficiency functions determined by heterochromatic brightness matching,” J. Opt. Soc. Am. 65, 466–468 (1975).
[Crossref] [PubMed]

M. Ikeda and H. Shimozono, “Luminous efficiency functions determined by successive brightness matching,” J. Opt. Soc. Am. 68, 1767–1771 (1978).
[Crossref]

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]

S. L. Guth, R. W. Massof, and T. Benzschawel, “Vector model for normal and dichromatic color vision,” J. Opt. Soc. Am. 70, 197–212 (1980).
[Crossref] [PubMed]

J. A. S. Kinney, “Sensitivity of the eye to spectral radiation at scotopic and mesopic intensity levels,” J. Opt. Soc. Am. 45, 507–514 (1955).
[Crossref] [PubMed]

J. A. S. Kinney, “Comparison of scotopic, mesopic and photopic spectral sensitivity curves,” J. Opt. Soc. Am. 48, 185–190 (1958).
[Crossref] [PubMed]

J. A. S. Kinney, “Effect of field sizes and position on mesopic spectral sensitivity,” J. Opt. Soc. Am. 54, 671–677 (1964).
[Crossref] [PubMed]

R. E. Bedford and G. W. Wyszecki, “Luminous functions for various field sizes and levels of retinal illuminance,” J. Opt. Soc. Am. 48, 406–411 (1958).
[Crossref] [PubMed]

C. S. Bridgman, “The luminosity curve as affected by the relation between rod and cone adaptation,” J. Opt. Soc. Am. 43, 733–737 (1953).
[Crossref] [PubMed]

D. A. Palmer, “Standard observer for large-field photometry at any level,” J. Opt. Soc. Am. 58, 1296–1299 (1968).
[Crossref] [PubMed]

Nature (1)

D. A. Palmer, “Rod-cone mechanism underlying the Purkinje shift,” Nature 262, 601–603 (1976).
[Crossref] [PubMed]

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

H. V. Walters and W. D. Wright, “The spectral sensitivity of the fovea and extra-fovea in the Purkinje range,” Proc. R. Soc. London, Ser. B 131, 340 (1943); W. D. Wright, Researches on Normal and Defective Colour Vision (Henry Kimpton, London, 1946).
[Crossref]

Vision Res. (2)

P. K. Kaiser and J. P. Comerford, “Flicker photometry of equally bright lights,” Vision Res. 15, 1399–1402 (1975).
[Crossref] [PubMed]

D. A. Palmer, “The definition of a standard observer for mesopic photometry,” Vision Res. 7, 619–628 (1967).
[Crossref] [PubMed]

Other (4)

S. Kokoschka and H. W. Bodmann, “Ein konsistentes System für photometrischen Strahlungsbewertung im gesamten Adaptationsbereich,” CIE Pub. No. 36 (Commission Internationale de l’Eclairage, Paris, 1976), pp. 217–225.

“Light as a true visual quantity: principles of measurement,” CIE Pub. No. 41 (Commission International de l’Eclairage, Paris, 1978), p. 37.

Technical Committee TC-1.4 of the Commission Internationale de l’Eclairage was established at the Kyoto Session (1979) by the Luminous Efficiency Functions Subcommittee to collect sufficient information regarding luminous-efficiency functions by using heterochromatic brightness matching.

H. Yaguchi and M. Ikeda, “Luminous efficiency functions by the heterochromatic brightness matching for a wide range of retinal illuminance,” J. Light Vis. Environ. (to be published).

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Figures (6)

Fig. 1
Fig. 1

Luminous efficiency functions at nine retinal-illuminance levels. Top to bottom: −2-log, −1.5-log, −1-log …., 1.5-log, and 2-log photopic trolands. Left, subject HS; right, TG.

Fig. 2
Fig. 2

Comparison of the present luminous-efficiency functions at two extreme luminance levels with related standard data. Left: the function at −2-log level versus the CIE V′(λ); right: the function at 2-log level versus the cone data reported in the CIE Technical Report.11 HS, open circles; TG, crosses; standard data, filled circles.

Fig. 3
Fig. 3

Adapting coefficients a (open circles) and b (filled circles) as a function of the retinal-illuminance level from subjects HS (top) and TG (bottom).

Fig. 4
Fig. 4

Comparison of the experimental luminous-efficiency functions S(λ) (open circles with solid lines) with the theoretical luminous-efficiency function ST(λ) (filled circles with dashed lines), defined by Eq. (2) in the text, at three retinal-illuminance levels, −1-log, 0-log, and 1-log level from the top. Left, subject HS; right, TG.

Fig. 5
Fig. 5

Saturation threshold versus retinal illuminance for two wavelengths, 500 and 600 nm. The latter is elevated by 1.2 log units. Vertical bars indicate the standard deviations. HS, open circles; TG, filled circles.

Fig. 6
Fig. 6

Saturation functions at various luminance levels. Levels: −2-log, open circles; −1-log, filled circles; 0-log, triangles; 1-log, half-filled circles; 2-log, squares. Subject, HS.

Equations (4)

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log S T ( λ ) = a log S R ( λ ) + b log S C ( λ ) + c ,
log S T ( λ ) = a [ log S R ( λ ) - M R ] + b [ log S C ( λ ) - M C ] + M ,
log S T ( λ ) = a [ log S R ( λ ) + ( M - M R ) ] + b [ log S C ( λ ) + ( M - M C ) ] + ɛ M ,
log S T ( λ ) = a [ log m R S R ( λ ) ] + b [ log m C S C ( λ ) ] .