Abstract

A theory and model of the visual system are presented to explain the detection of static sinusoidal gratings near the threshold. The model incorporates a set of independent decision centers and associated photoreceptive fields (PRFs). The decision criterion value at each decision center is proportional to the standard deviation of the excitation current transmitted from a PRF to its associated decision center caused by quantum fluctuations in the absorption of light. It is well known that the spatial-frequency-response (SFR) function and the spatial-impulse-response (SIR) function of a photodetector are a Fourier transform pair. A systematic examination of the SIR and SFR functions of PRF configurations consisting of rectangular regions of alternately excitatory and inhibitory response reveals that modulation sensitivity of the visual system is explained at scotopic and photopic illuminance by a set of PRFs composed of a single excitatory region and a central excitatory region bordered by inhibitory regions, respectively. The complete model is shown to yield a high degree of conformity between theoretical and experimental threshold modulation curves.

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  1. P. M. Duffieux and G. Lansraux, Rev. d' Opt. 24, 65 (1945); 24, 151 (1945); 24, 215 (1945).
  2. For a general review of spatial-frequency-response characteristics, see L. Levi, Progress in Optics VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970), p. 343.
  3. Recognition depends on detection of structural detail. For a useful rule of thumb expressed in terms of resolution frequency by J. Johnson see Perception of Displayed Information, edited by L. M. Biberman (Plenum, New York, 1973), p. 4.
  4. A. Van Meeteren, Visual Aspects of Image Intensification (Bronder-offset, Rotterdam, 1973), p. 77.
  5. F. W. Campbell and R. W. Gubisch, J. Physiol. (Lond.) 186, 558 (1966).
  6. D. H. Kelly, J. Opt. Soc. Am. 64, 983 (1974).
  7. F. L. Van Nes and MI. Boaman, J. Opt. Soc. Am. 57, 401 (1967).
  8. O. H. Schade, Sr., J. Opt. Soc. Am. 46, 721 (1956).
  9. J. J. De Palma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).
  10. D. H. Kelly, J. Opt. Soc. Am. 56, 1628 (1966).
  11. J. G. Robson, J. Opt. Soc. Am. 56, 1141 (1966).
  12. The author is indebted to one of the reviewers for calling attention to the sensitivity of the slope to temporal rate, shown by D. H. Kelly, Vision Res. 12, 89 (1972).
  13. F. W. Campbell and J. G. Robson, J. Physiol. (Lond.) 197, 551 (1968).
  14. To explain Mach band phenomena, G. V. Békésy [J. Opt. Soc. Am. 50, 1060 (1960)] proposed a spatial function, qualitatively similar to the SIR function deduced from threshold modulation data by Ref. 8, to describe the interaction of suprathreshold responses from proximate regions of the visual field at some highet level of the visual pathway.
  15. C. Blakemore and F. W. Campbell, J. Physiol, (Lond.) 203, 237 (1969).
  16. M. B. Sachs, J. Naclhmias, and J. G. .Robson, J. Opt. Soc. Am. 61, 1176 (1971).
  17. D. H. Hubel and T. N. Wiesel, J. Physiol. (Lond.) 154, 572 (1960).
  18. A. D. Schnitzler, J. Opt. Soc. Am. 63, 1357 (1973).
  19. For early references to the concept of a signal- to-noise limitation in visual detection, see Ref. 18.
  20. A. Papoulis, System and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  21. Y. W. Lee, Statistical Theory of Communications (Wiley, New York, 1960).
  22. R. A. Moses, Adler's Physiology of the Eye (Mosby, St. Louis, 1970).
  23. D. H. Kelly and R. E. Savoie, Percept. Psychophys. 14, 313 (1973).
  24. H. R. Blackwell, J. Opt. Soc. Am. 53, 129 (1963).

Békésy, G. V.

To explain Mach band phenomena, G. V. Békésy [J. Opt. Soc. Am. 50, 1060 (1960)] proposed a spatial function, qualitatively similar to the SIR function deduced from threshold modulation data by Ref. 8, to describe the interaction of suprathreshold responses from proximate regions of the visual field at some highet level of the visual pathway.

Blackwell, H. R.

H. R. Blackwell, J. Opt. Soc. Am. 53, 129 (1963).

Blakemore, C.

C. Blakemore and F. W. Campbell, J. Physiol, (Lond.) 203, 237 (1969).

Boaman, M.

F. L. Van Nes and MI. Boaman, J. Opt. Soc. Am. 57, 401 (1967).

Campbell, F. W.

F. W. Campbell and R. W. Gubisch, J. Physiol. (Lond.) 186, 558 (1966).

F. W. Campbell and J. G. Robson, J. Physiol. (Lond.) 197, 551 (1968).

C. Blakemore and F. W. Campbell, J. Physiol, (Lond.) 203, 237 (1969).

De Palma, J. J.

J. J. De Palma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).

Duffieux, P. M.

P. M. Duffieux and G. Lansraux, Rev. d' Opt. 24, 65 (1945); 24, 151 (1945); 24, 215 (1945).

Gubisch, R. W.

F. W. Campbell and R. W. Gubisch, J. Physiol. (Lond.) 186, 558 (1966).

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, J. Physiol. (Lond.) 154, 572 (1960).

Johnson, J.

Recognition depends on detection of structural detail. For a useful rule of thumb expressed in terms of resolution frequency by J. Johnson see Perception of Displayed Information, edited by L. M. Biberman (Plenum, New York, 1973), p. 4.

Kelly, D. H.

D. H. Kelly, J. Opt. Soc. Am. 64, 983 (1974).

D. H. Kelly and R. E. Savoie, Percept. Psychophys. 14, 313 (1973).

D. H. Kelly, J. Opt. Soc. Am. 56, 1628 (1966).

Lansraux, G.

P. M. Duffieux and G. Lansraux, Rev. d' Opt. 24, 65 (1945); 24, 151 (1945); 24, 215 (1945).

Lee, Y. W.

Y. W. Lee, Statistical Theory of Communications (Wiley, New York, 1960).

Levi, L.

For a general review of spatial-frequency-response characteristics, see L. Levi, Progress in Optics VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970), p. 343.

Lowry, E. M.

J. J. De Palma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).

Moses, R. A.

R. A. Moses, Adler's Physiology of the Eye (Mosby, St. Louis, 1970).

Naclhmias, J.

M. B. Sachs, J. Naclhmias, and J. G. .Robson, J. Opt. Soc. Am. 61, 1176 (1971).

Papoulis, A.

A. Papoulis, System and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

Robson, J. G.

F. W. Campbell and J. G. Robson, J. Physiol. (Lond.) 197, 551 (1968).

M. B. Sachs, J. Naclhmias, and J. G. .Robson, J. Opt. Soc. Am. 61, 1176 (1971).

J. G. Robson, J. Opt. Soc. Am. 56, 1141 (1966).

Sachs, M. B.

M. B. Sachs, J. Naclhmias, and J. G. .Robson, J. Opt. Soc. Am. 61, 1176 (1971).

Savoie, R. E.

D. H. Kelly and R. E. Savoie, Percept. Psychophys. 14, 313 (1973).

Schade, Sr., O. H.

O. H. Schade, Sr., J. Opt. Soc. Am. 46, 721 (1956).

Schnitzler, A. D.

A. D. Schnitzler, J. Opt. Soc. Am. 63, 1357 (1973).

Van Meeteren, A.

A. Van Meeteren, Visual Aspects of Image Intensification (Bronder-offset, Rotterdam, 1973), p. 77.

Van Nes, F. L.

F. L. Van Nes and MI. Boaman, J. Opt. Soc. Am. 57, 401 (1967).

Wiesel, T. N.

D. H. Hubel and T. N. Wiesel, J. Physiol. (Lond.) 154, 572 (1960).

Other

P. M. Duffieux and G. Lansraux, Rev. d' Opt. 24, 65 (1945); 24, 151 (1945); 24, 215 (1945).

For a general review of spatial-frequency-response characteristics, see L. Levi, Progress in Optics VIII, edited by E. Wolf (North-Holland, Amsterdam, 1970), p. 343.

Recognition depends on detection of structural detail. For a useful rule of thumb expressed in terms of resolution frequency by J. Johnson see Perception of Displayed Information, edited by L. M. Biberman (Plenum, New York, 1973), p. 4.

A. Van Meeteren, Visual Aspects of Image Intensification (Bronder-offset, Rotterdam, 1973), p. 77.

F. W. Campbell and R. W. Gubisch, J. Physiol. (Lond.) 186, 558 (1966).

D. H. Kelly, J. Opt. Soc. Am. 64, 983 (1974).

F. L. Van Nes and MI. Boaman, J. Opt. Soc. Am. 57, 401 (1967).

O. H. Schade, Sr., J. Opt. Soc. Am. 46, 721 (1956).

J. J. De Palma and E. M. Lowry, J. Opt. Soc. Am. 52, 328 (1962).

D. H. Kelly, J. Opt. Soc. Am. 56, 1628 (1966).

J. G. Robson, J. Opt. Soc. Am. 56, 1141 (1966).

The author is indebted to one of the reviewers for calling attention to the sensitivity of the slope to temporal rate, shown by D. H. Kelly, Vision Res. 12, 89 (1972).

F. W. Campbell and J. G. Robson, J. Physiol. (Lond.) 197, 551 (1968).

To explain Mach band phenomena, G. V. Békésy [J. Opt. Soc. Am. 50, 1060 (1960)] proposed a spatial function, qualitatively similar to the SIR function deduced from threshold modulation data by Ref. 8, to describe the interaction of suprathreshold responses from proximate regions of the visual field at some highet level of the visual pathway.

C. Blakemore and F. W. Campbell, J. Physiol, (Lond.) 203, 237 (1969).

M. B. Sachs, J. Naclhmias, and J. G. .Robson, J. Opt. Soc. Am. 61, 1176 (1971).

D. H. Hubel and T. N. Wiesel, J. Physiol. (Lond.) 154, 572 (1960).

A. D. Schnitzler, J. Opt. Soc. Am. 63, 1357 (1973).

For early references to the concept of a signal- to-noise limitation in visual detection, see Ref. 18.

A. Papoulis, System and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

Y. W. Lee, Statistical Theory of Communications (Wiley, New York, 1960).

R. A. Moses, Adler's Physiology of the Eye (Mosby, St. Louis, 1970).

D. H. Kelly and R. E. Savoie, Percept. Psychophys. 14, 313 (1973).

H. R. Blackwell, J. Opt. Soc. Am. 53, 129 (1963).

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