Abstract

The contrast sensitivity of the human eye for sinusoidal illuminance changes was measured as a function of spatial frequency, for monochromatic light with wavelengths of 450, 525, and 650 nm. At each wavelength, data were obtained for a number of illuminance levels. All observations were taken at equal accommodation, and corrected for chromatic aberration. If the wavelength-dependent effects of diffraction on the modulation transfer are taken into account, no difference is found between the photopic contrast-sensitivity functions for red, green, or blue. For mean retinal illuminances B0 smaller than 300 td, threshold modulation M at a given frequency is found to increase in proportion to B0-12 (de Vries–Rose law). For B0 greater than 300 td M remains a constant fraction of it (Weber–Fechner law). After separation of the optical modulation transfer of the eye media from the measured psychophysical data, the remaining function can be considered as composed of a neural and a light-diffusion transfer function. The latter can be compared with the analytic transfer function of photographic film.

© 1967 Optical Society of America

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References

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  1. P. M. Duffieux, L’intégrale de Fourier et ses Applications d l’Optique (chez l’auteur, Rennes, 1946).
  2. Otto H. Schade, J. Opt. Soc. Am. 46, 721 (1956).
    [Crossref] [PubMed]
  3. A. Arnulf and O. Dupuy, Compt. Rend. 250, 2757 (1960).
  4. Yves Le Grand, Optique physiologique (Éditions de la Revue d’Optique, Paris, 1956), Vol. 3.
  5. H. de Vries, Physica 10, 553 (1943).
    [Crossref]
  6. A. Rose, J. Opt. Soc. Am. 38, 196 (1948).
    [Crossref] [PubMed]
  7. F. W. Campbell, J. G. Robson, and G. Westheimer, J. Physiol. 145, 579 (1959).
  8. H. A. W. Schober and R. Hilz, J. Opt. Soc. Am. 55, 1086 (1965).
    [Crossref]
  9. J. G. Robson and F. W. Campbell, “The Physiological Basis for Form Discrimination” (symposium at Walter S. Hunter Laboratory of Psychology, Brown University, Providence, R. I., Jan. 1964).
  10. A. S. Patel, J. Opt. Soc. Am. 56, 689 (1966).
    [Crossref] [PubMed]
  11. O. Bryngdahl, Opt. Acta 12, 1 (1965).
    [Crossref]
  12. O. Bryngdahl, Opt. Acta 13, 55 (1966).
    [Crossref]
  13. G. Westheimer, J. Physiol. 152, 67 (1960).
  14. F. W. Campbell and D. G. Green, J. Physiol. 181, 576 (1965).
  15. The technique involves the visual equalizing of an incoherent grating with a coherent one of the same spatial frequency. The modulation of the first is attenuated by the eye optics, whereas the modulation of the other is not.
  16. Otto H. Schade, RCA Rev. 9, 653 (1948).
  17. S. L. Polyak, The Vertebrate Visual System (Chicago University Press, Chicago, 1957).

1966 (2)

1965 (3)

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

O. Bryngdahl, Opt. Acta 12, 1 (1965).
[Crossref]

H. A. W. Schober and R. Hilz, J. Opt. Soc. Am. 55, 1086 (1965).
[Crossref]

1960 (2)

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

G. Westheimer, J. Physiol. 152, 67 (1960).

1959 (1)

F. W. Campbell, J. G. Robson, and G. Westheimer, J. Physiol. 145, 579 (1959).

1956 (1)

1948 (2)

A. Rose, J. Opt. Soc. Am. 38, 196 (1948).
[Crossref] [PubMed]

Otto H. Schade, RCA Rev. 9, 653 (1948).

1943 (1)

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

Arnulf, A.

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

Bryngdahl, O.

O. Bryngdahl, Opt. Acta 13, 55 (1966).
[Crossref]

O. Bryngdahl, Opt. Acta 12, 1 (1965).
[Crossref]

Campbell, F. W.

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

F. W. Campbell, J. G. Robson, and G. Westheimer, J. Physiol. 145, 579 (1959).

J. G. Robson and F. W. Campbell, “The Physiological Basis for Form Discrimination” (symposium at Walter S. Hunter Laboratory of Psychology, Brown University, Providence, R. I., Jan. 1964).

de Vries, H.

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

Duffieux, P. M.

P. M. Duffieux, L’intégrale de Fourier et ses Applications d l’Optique (chez l’auteur, Rennes, 1946).

Dupuy, O.

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

Green, D. G.

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

Hilz, R.

Le Grand, Yves

Yves Le Grand, Optique physiologique (Éditions de la Revue d’Optique, Paris, 1956), Vol. 3.

Patel, A. S.

Polyak, S. L.

S. L. Polyak, The Vertebrate Visual System (Chicago University Press, Chicago, 1957).

Robson, J. G.

F. W. Campbell, J. G. Robson, and G. Westheimer, J. Physiol. 145, 579 (1959).

J. G. Robson and F. W. Campbell, “The Physiological Basis for Form Discrimination” (symposium at Walter S. Hunter Laboratory of Psychology, Brown University, Providence, R. I., Jan. 1964).

Rose, A.

Schade, Otto H.

Schober, H. A. W.

Westheimer, G.

G. Westheimer, J. Physiol. 152, 67 (1960).

F. W. Campbell, J. G. Robson, and G. Westheimer, J. Physiol. 145, 579 (1959).

Compt. Rend. (1)

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

J. Opt. Soc. Am. (4)

J. Physiol. (3)

G. Westheimer, J. Physiol. 152, 67 (1960).

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

F. W. Campbell, J. G. Robson, and G. Westheimer, J. Physiol. 145, 579 (1959).

Opt. Acta (2)

O. Bryngdahl, Opt. Acta 12, 1 (1965).
[Crossref]

O. Bryngdahl, Opt. Acta 13, 55 (1966).
[Crossref]

Physica (1)

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

RCA Rev. (1)

Otto H. Schade, RCA Rev. 9, 653 (1948).

Other (5)

S. L. Polyak, The Vertebrate Visual System (Chicago University Press, Chicago, 1957).

The technique involves the visual equalizing of an incoherent grating with a coherent one of the same spatial frequency. The modulation of the first is attenuated by the eye optics, whereas the modulation of the other is not.

J. G. Robson and F. W. Campbell, “The Physiological Basis for Form Discrimination” (symposium at Walter S. Hunter Laboratory of Psychology, Brown University, Providence, R. I., Jan. 1964).

P. M. Duffieux, L’intégrale de Fourier et ses Applications d l’Optique (chez l’auteur, Rennes, 1946).

Yves Le Grand, Optique physiologique (Éditions de la Revue d’Optique, Paris, 1956), Vol. 3.

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Figures (10)

Fig. 1
Fig. 1

Experimental setup. T indicates a variable transmittance sinusoidal test object, seen in Maxwellian view through an artificial pupil. The modulation of the sine waves was varied by a veiling illuminance on the semitransparent mirror H.

Fig. 2
Fig. 2

Threshold modulation curves for green light, λ=525 nm, at seven retinal illuminance levels and pupil diameter of 2 mm. The short horizontal lines indicate supra- and subthreshold modulations for each spatial frequency. For 900 td they are replaced by dots. The threshold modulation curves for 5900 td and 900 td are identical.

Fig. 3
Fig. 3

Threshold modulation curves for λ=525 nm at three illuminance levels with mean values of supra- and sub-threshold modulation for λ=650 nm and λ=450 nm. Open triangles indicate values for 650 nm at 90 td, closed triangles for 650 nm at 0.9 td. Closed circles represent the data for 450 nm at 0.9 td, open circles for 450 nm at 0.009 td. Pupil diameter ω=2 mm.

Fig. 4
Fig. 4

Threshold modulation curves for λ=525 nm at four illuminance levels with mean values of supra- and sub-threshold modulations for λ=650 nm and λ=450 nm. Open triangles indicate values for 650 nm at 900 td and 0.09 td, closed triangles for 650 nm at 9 td. Closed circles represent the data for 450 nm at 9 td, open circles for 450 nm at 0.09 and 0.0009 td. Pupil diameter ω=2 mm.

Fig. 5
Fig. 5

The dependence of threshold modulation M on retinal illuminance B0 for eight spatial frequencies and green light, λ=525 nm. Pupil diameter ω=2 mm. Each pair of dots indicates the average values of the measured supra- and sub-threshold modulations, respectively. The lines have slopes of −1/2 and 0.

Fig. 6
Fig. 6

The dependence of threshold modulation M on retinal illuminance B0 for seven spatial frequencies and blue light, λ=450 nm. Pupil diameter ω=2 mm. Each pair of dots indicates the average values of the measured supra- and sub-threshold modulations, respectively. For 0.5 cpd the dots are replaced by open triangles. The lines for frequencies of 8 cpd and higher have slopes of −1/2.

Fig. 7
Fig. 7

The dependence of threshold modulation M on retinal illuminance B0 for six spatial frequencies and red light, λ=650 nm. Pupil diameter ω=2 mm. Each pair of dots indicates the average values of the measured supra- and sub-threshold modulations, respectively. For 8 cpd the dots are replaced by open squares, for 4 cpd by open triangles. The lines for frequencies of 8 cpd and higher have slopes of−1/2 and 0.

Fig. 8
Fig. 8

Maximum spatial frequency which can be resolved at a certain modulation percentage as a function of retinal illuminance for green light, λ=525 nm and a pupil diameter ω=2 mm. Division of the ordinate numbers by 60 yields resolution values which are comparable with classical visual acuity units.

Fig. 9
Fig. 9

Modulation transfer function of eye media (Curve A) and deduced retina–perception-center contrast-sensitivity functions for λ=525 nm and pupil diameter ω=2 mm. The parameters denote the retinal illuminance in photopic trolands. Closed circles represent the mean of the modulation transfer values for ω=1.57 and ω=2.5 mm from Arnulf and Dupuy.3 The thresholds indicated with open circles and open and closed triangles (pertaining to 90 and 270 td, respectively) were deduced from the mean of the psychophysically determined average supra- and sub-threshold modulations with the corresponding transfer values of curve A.

Fig. 10
Fig. 10

Modulation transfer function of eye media (upper curve), due to diffraction and the deduced contrast-sensitivity function, caused by light scatter within the retina and the neural transfer function, for λ=525 nm, B0=14.4 td, and a pupil diameter ω=0.8 mm. Each pair of points represents the deduced average supra- and sub-threshold modulations at the frequency in question. Spatial frequencies are plotted in cycles/mm on the retina.

Tables (1)

Tables Icon

Table I Supra- and sub-threshold modulations in % for three accommodation conditions. λ=525 nm, B0=90 td, ω=2 mm.