Abstract

A model for vision is proposed. Its basic units are RC stages whose time constants—in three instances—are parametrically controlled. The requirements of compressing the dynamic range of the input and of fitting luminance pulse-detection data suffice to determine the arrangement and parameters of the components. This model accurately predicts the psychophysical results of flicker detection (DeLange characteristics at above 10 Hz), the Ferry–Porter and Weber laws in the ranges where they apply, the effects of light adaptation, and it accounts for individual differences. By considering the variable RC stage as an approximate analog of a synaptic excitatory process which is controlled by inhibition, significant correspondences are observed between the internal connectivity of the model and the neural connectivity of the retina.

© 1968 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. Fatt and B. Katz, J. Physiol. (London) 121, 374 (1953).
  2. J. S. Coombs, J. C. Eccles, and P. Fatt, J. Physiol. (London) 130, 396 (1955).
  3. M. G. F. Fuortes and A. L. Hodgkin, J. Physiol. (London) 172, 239 (1964).
  4. J. Levinson, J. Opt. Soc. Am. 56, 95/529E (1966).
  5. For a review of LP filters in relation to vision see G. Sperling, Doc. Ophthalmol. 18, 3 (1964).
    [Crossref]
  6. The constants in Eqs. (2a–b–c) are chosen to agree with those in Ref. 3.
  7. G. S. Brindley, Physiology of the Retina and the Visual Pathway (Edward Arnold Ltd., London, 1960), p. 187f.
  8. Calculated by assuming retinal absorption of 1.4 × 1015 quanta/cm2 (Refs. 10, 11) and an average foveal cone density of 1.4 × 107 cones/cm2 (Ref. 12).
  9. G. S. Brindley, Proc. Phys. Soc. (London) 68B, 862 (1955).
  10. W. A. H. Rushton, Ann. N. Y. Acad. Sci. 74, 291 (1958).
    [Crossref]
  11. S. Polyak, The Vertebrate Visual System (Univ. Chicago Press, Chicago, 1955), p. 268.
  12. G. G. Furman, Kybernetik 2, 257 (1965).
    [Crossref] [PubMed]
  13. R. B. Marimont, J. Physiol. (London) 179, 489 (1965).
  14. W. Rall, Exptl. Neurol. 2, 503 (1960).
    [Crossref]
  15. W. Rall, in R. F. Reiss, Neural Theory and Modeling (Stanford Univ. Press, California, 1964), p. 73. The variable-τ RC stage is equivalent to a neuron which receives its excitatory and inhibitory inputs directly onto the soma, which has an equilibrium potential for inhibition (K+ and/or Cl− ions) equal to the resting potential, and in which excitation is restricted to small values.
  16. C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).
  17. R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).
    [Crossref] [PubMed]
  18. , Library of Congress, Washington, D. C. 20540.
  19. H. DeLange, J. Opt. Soc. Am. 48, 777 (1958).
    [Crossref]
  20. D. H. Kelly, J. Opt. Soc. Am. 51, 422 (1961).
    [Crossref] [PubMed]
  21. J. Levinson, J. Opt. Soc. Am. 56, 1442A (1966).
  22. H. E. Henkes and L. H. van der Tweel, Eds., Flicker (Dr. W. Junk, Publishers, The Hague, 1964).
  23. J. L. Brown, in G. H. Graham and et al., Vision and Visual Perception (John Wiley & Sons, Inc., New York, 1965), p. 251.
  24. D. H. Kelly, Doc. Ophthalmol. 18, 17 (1964).
    [Crossref]
  25. Unpublished data of J. Levinson in which flicker and pulse thresholds are compared directly in the same observer under the same conditions, indicate that the model’s ∊-discrepancy (between flicker and pulse thresholds) is a factor of 2. Much of the discrepancy vanishes if predictions are made from peak-to-peak instead of from average-to-peak (personal communication).
  26. J. C. Eccles, The Physiology of Synapses (Springer-Verlag, Berlin, Göttingen, Heidelberg, 1964).
    [Crossref]
  27. For a review see B. Katz, Nerve, Muscle, and Synapse (McGraw–Hill Book Co., New York, 1966).
  28. K. T. Brown and K. Watanabe, Science 148, 1113 (1965).
    [Crossref] [PubMed]
  29. J. E. Dowling, Science 147, 57 (1965).
    [Crossref] [PubMed]
  30. L. Missoten, The Ultrastructure of the Retina (Arscia, Brussels, 1965).
  31. J. E. Dowling and B. B. Boycott, Proc. Royal Soc. (London) 166B, 80 (1966/67).
  32. M. Kidd, J. Anat. (London) 96, 179 (1962).
  33. W. K. Stell, Anat. Record 153, 389 (1965).
    [Crossref]
  34. J. E. Dowling, J. E. Brown, and Diane Major, Science 153, 1639 (1966).
    [Crossref] [PubMed]
  35. A. I. Cohen, J. Anat. (London) 99, 595 (1965).
  36. J. E. Dowling and B. B. Boycott, Cold Spring Harbor Symp. Quant. Biol. 30, 393 (1966).
    [Crossref]
  37. If the internal resistance of the bipolar axon is small, then the sequence of recurrent loops it generates as it connects to various ganglion-cell dendrites can be represented by a single 1-stage FB filter. The anatomy then provides two successive 1-stage FB filters, each with delayed feedback, a system which is similar to the 2-stage FB filter of the model.
  38. For a similar separation of the loci of excitation and of inhibition in a peripheral visual neuron, see R. L. Purple and F. A. Dodge, Cold Spring Harbor Symp. Quant. Biol. 30, 529 (1966).
    [Crossref]
  39. D. R. Curtis and J. C. Eccles, J. Physiol. (London) 145, 529 (1959).
  40. L. H. van der Tweel, Doc. Ophthalmol. 18, 287 (1964).
    [Crossref]
  41. A. S. Schwartz and D. B. Lindsley, Bol. Inst. Estud. Med. Biol. (Mex) 22, 249 (1964).
  42. H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol (London) 137, 327 (1957).
  43. R. Ratoosh and C. H. Graham, J. Exptl. Psychol. 42, 367 (1951).
    [Crossref]
  44. W. M. Kincaid, H. R. Blackwell, and A. B. Kristofferson, J. Opt. Soc. Am. 50, 143 (1960).
    [Crossref] [PubMed]
  45. G. Westheimer, J. Physiol. (London) 190, 139 (1967).
  46. A. Rose, J. Opt. Soc. Am. 38, 196 (1948).
    [Crossref] [PubMed]
  47. H. DeVries, Physica 10, 553 (1943).
    [Crossref]
  48. H. B. Barlow, J. Physiol. (London) 136, 469 (1957).
  49. H. R. Blackwell, J. Opt. Soc. Am. 53, 129 (1963).
    [Crossref] [PubMed]
  50. J. A. Swets, Signal Detection and Recognition by Human Observers (J. Wiley& Sons. Inc., New York, 1964).
  51. For various different assumptions that have been made about noise distribution to enable theoretical estimates of the effects of visual noise on flicker thresholds see R. C. Jones, Washington Acad. Sci. 47, 100 (1957); L. H. van der Tweel, Ann. N. Y. Acad. Sci. 89, 829 (1961); and D. H. Kelly, J. Opt. Soc. Am. 51, 747 (1961).
    [Crossref] [PubMed]
  52. G. H. Mowbray and J. W. Gebhard, in W. H. Sinaiko, Ed., Selected Papers on Human Factors in the Design and Use of Control Systems (Dover Publications, Inc., New York, 1961).
  53. T. N. Cornsweet and H. M. Pinsker, J. Physiol. (London) 176, 294 (1965).
  54. See, for example, J. Levinson and L. D. Harmon, Kybernetik 1, 107 (1961).
    [Crossref] [PubMed]
  55. W. R. Biersdorf, J. Opt. Soc. Am. 45, 920 (1955).
    [Crossref] [PubMed]
  56. D. Kahneman and J. Norman, J. Exptl. Psychol. 68, 215 (1964).
    [Crossref]
  57. D. Kahneman, J. Exptl. Psychol. 71, 543 (1966).
    [Crossref]

1967 (1)

G. Westheimer, J. Physiol. (London) 190, 139 (1967).

1966 (6)

J. E. Dowling and B. B. Boycott, Cold Spring Harbor Symp. Quant. Biol. 30, 393 (1966).
[Crossref]

For a similar separation of the loci of excitation and of inhibition in a peripheral visual neuron, see R. L. Purple and F. A. Dodge, Cold Spring Harbor Symp. Quant. Biol. 30, 529 (1966).
[Crossref]

J. E. Dowling, J. E. Brown, and Diane Major, Science 153, 1639 (1966).
[Crossref] [PubMed]

J. Levinson, J. Opt. Soc. Am. 56, 95/529E (1966).

J. Levinson, J. Opt. Soc. Am. 56, 1442A (1966).

D. Kahneman, J. Exptl. Psychol. 71, 543 (1966).
[Crossref]

1965 (7)

T. N. Cornsweet and H. M. Pinsker, J. Physiol. (London) 176, 294 (1965).

K. T. Brown and K. Watanabe, Science 148, 1113 (1965).
[Crossref] [PubMed]

J. E. Dowling, Science 147, 57 (1965).
[Crossref] [PubMed]

G. G. Furman, Kybernetik 2, 257 (1965).
[Crossref] [PubMed]

R. B. Marimont, J. Physiol. (London) 179, 489 (1965).

A. I. Cohen, J. Anat. (London) 99, 595 (1965).

W. K. Stell, Anat. Record 153, 389 (1965).
[Crossref]

1964 (6)

L. H. van der Tweel, Doc. Ophthalmol. 18, 287 (1964).
[Crossref]

A. S. Schwartz and D. B. Lindsley, Bol. Inst. Estud. Med. Biol. (Mex) 22, 249 (1964).

For a review of LP filters in relation to vision see G. Sperling, Doc. Ophthalmol. 18, 3 (1964).
[Crossref]

D. H. Kelly, Doc. Ophthalmol. 18, 17 (1964).
[Crossref]

M. G. F. Fuortes and A. L. Hodgkin, J. Physiol. (London) 172, 239 (1964).

D. Kahneman and J. Norman, J. Exptl. Psychol. 68, 215 (1964).
[Crossref]

1963 (1)

1962 (1)

M. Kidd, J. Anat. (London) 96, 179 (1962).

1961 (2)

D. H. Kelly, J. Opt. Soc. Am. 51, 422 (1961).
[Crossref] [PubMed]

See, for example, J. Levinson and L. D. Harmon, Kybernetik 1, 107 (1961).
[Crossref] [PubMed]

1960 (2)

1959 (1)

D. R. Curtis and J. C. Eccles, J. Physiol. (London) 145, 529 (1959).

1958 (2)

W. A. H. Rushton, Ann. N. Y. Acad. Sci. 74, 291 (1958).
[Crossref]

H. DeLange, J. Opt. Soc. Am. 48, 777 (1958).
[Crossref]

1957 (3)

H. B. Barlow, J. Physiol. (London) 136, 469 (1957).

For various different assumptions that have been made about noise distribution to enable theoretical estimates of the effects of visual noise on flicker thresholds see R. C. Jones, Washington Acad. Sci. 47, 100 (1957); L. H. van der Tweel, Ann. N. Y. Acad. Sci. 89, 829 (1961); and D. H. Kelly, J. Opt. Soc. Am. 51, 747 (1961).
[Crossref] [PubMed]

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol (London) 137, 327 (1957).

1956 (1)

R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).
[Crossref] [PubMed]

1955 (3)

G. S. Brindley, Proc. Phys. Soc. (London) 68B, 862 (1955).

J. S. Coombs, J. C. Eccles, and P. Fatt, J. Physiol. (London) 130, 396 (1955).

W. R. Biersdorf, J. Opt. Soc. Am. 45, 920 (1955).
[Crossref] [PubMed]

1953 (1)

P. Fatt and B. Katz, J. Physiol. (London) 121, 374 (1953).

1951 (1)

R. Ratoosh and C. H. Graham, J. Exptl. Psychol. 42, 367 (1951).
[Crossref]

1948 (1)

1943 (1)

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

1938 (1)

C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).

Barlow, H. B.

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol (London) 137, 327 (1957).

H. B. Barlow, J. Physiol. (London) 136, 469 (1957).

Biersdorf, W. R.

Blackwell, H. R.

Boycott, B. B.

J. E. Dowling and B. B. Boycott, Proc. Royal Soc. (London) 166B, 80 (1966/67).

J. E. Dowling and B. B. Boycott, Cold Spring Harbor Symp. Quant. Biol. 30, 393 (1966).
[Crossref]

Brindley, G. S.

G. S. Brindley, Proc. Phys. Soc. (London) 68B, 862 (1955).

G. S. Brindley, Physiology of the Retina and the Visual Pathway (Edward Arnold Ltd., London, 1960), p. 187f.

Brown, J. E.

J. E. Dowling, J. E. Brown, and Diane Major, Science 153, 1639 (1966).
[Crossref] [PubMed]

Brown, J. L.

J. L. Brown, in G. H. Graham and et al., Vision and Visual Perception (John Wiley & Sons, Inc., New York, 1965), p. 251.

Brown, K. T.

K. T. Brown and K. Watanabe, Science 148, 1113 (1965).
[Crossref] [PubMed]

Cohen, A. I.

A. I. Cohen, J. Anat. (London) 99, 595 (1965).

Coombs, J. S.

J. S. Coombs, J. C. Eccles, and P. Fatt, J. Physiol. (London) 130, 396 (1955).

Cornsweet, T. N.

T. N. Cornsweet and H. M. Pinsker, J. Physiol. (London) 176, 294 (1965).

Curtis, D. R.

D. R. Curtis and J. C. Eccles, J. Physiol. (London) 145, 529 (1959).

DeLange, H.

DeVries, H.

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

Dodge, F. A.

For a similar separation of the loci of excitation and of inhibition in a peripheral visual neuron, see R. L. Purple and F. A. Dodge, Cold Spring Harbor Symp. Quant. Biol. 30, 529 (1966).
[Crossref]

Dowling, J. E.

J. E. Dowling and B. B. Boycott, Proc. Royal Soc. (London) 166B, 80 (1966/67).

J. E. Dowling, J. E. Brown, and Diane Major, Science 153, 1639 (1966).
[Crossref] [PubMed]

J. E. Dowling and B. B. Boycott, Cold Spring Harbor Symp. Quant. Biol. 30, 393 (1966).
[Crossref]

J. E. Dowling, Science 147, 57 (1965).
[Crossref] [PubMed]

Eccles, J. C.

D. R. Curtis and J. C. Eccles, J. Physiol. (London) 145, 529 (1959).

J. S. Coombs, J. C. Eccles, and P. Fatt, J. Physiol. (London) 130, 396 (1955).

J. C. Eccles, The Physiology of Synapses (Springer-Verlag, Berlin, Göttingen, Heidelberg, 1964).
[Crossref]

Fatt, P.

J. S. Coombs, J. C. Eccles, and P. Fatt, J. Physiol. (London) 130, 396 (1955).

P. Fatt and B. Katz, J. Physiol. (London) 121, 374 (1953).

Fitzhugh, R.

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol (London) 137, 327 (1957).

Fuortes, M. G. F.

M. G. F. Fuortes and A. L. Hodgkin, J. Physiol. (London) 172, 239 (1964).

Furman, G. G.

G. G. Furman, Kybernetik 2, 257 (1965).
[Crossref] [PubMed]

Gebhard, J. W.

G. H. Mowbray and J. W. Gebhard, in W. H. Sinaiko, Ed., Selected Papers on Human Factors in the Design and Use of Control Systems (Dover Publications, Inc., New York, 1961).

Graham, C. H.

R. Ratoosh and C. H. Graham, J. Exptl. Psychol. 42, 367 (1951).
[Crossref]

C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).

Graham, G. H.

J. L. Brown, in G. H. Graham and et al., Vision and Visual Perception (John Wiley & Sons, Inc., New York, 1965), p. 251.

Harmon, L. D.

See, for example, J. Levinson and L. D. Harmon, Kybernetik 1, 107 (1961).
[Crossref] [PubMed]

Herrick, R. M.

R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).
[Crossref] [PubMed]

Hodgkin, A. L.

M. G. F. Fuortes and A. L. Hodgkin, J. Physiol. (London) 172, 239 (1964).

Jones, R. C.

For various different assumptions that have been made about noise distribution to enable theoretical estimates of the effects of visual noise on flicker thresholds see R. C. Jones, Washington Acad. Sci. 47, 100 (1957); L. H. van der Tweel, Ann. N. Y. Acad. Sci. 89, 829 (1961); and D. H. Kelly, J. Opt. Soc. Am. 51, 747 (1961).
[Crossref] [PubMed]

Kahneman, D.

D. Kahneman, J. Exptl. Psychol. 71, 543 (1966).
[Crossref]

D. Kahneman and J. Norman, J. Exptl. Psychol. 68, 215 (1964).
[Crossref]

Katz, B.

P. Fatt and B. Katz, J. Physiol. (London) 121, 374 (1953).

For a review see B. Katz, Nerve, Muscle, and Synapse (McGraw–Hill Book Co., New York, 1966).

Kelly, D. H.

Kemp, E. H.

C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).

Kidd, M.

M. Kidd, J. Anat. (London) 96, 179 (1962).

Kincaid, W. M.

Kristofferson, A. B.

Kuffler, S. W.

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol (London) 137, 327 (1957).

Levinson, J.

J. Levinson, J. Opt. Soc. Am. 56, 1442A (1966).

J. Levinson, J. Opt. Soc. Am. 56, 95/529E (1966).

See, for example, J. Levinson and L. D. Harmon, Kybernetik 1, 107 (1961).
[Crossref] [PubMed]

Unpublished data of J. Levinson in which flicker and pulse thresholds are compared directly in the same observer under the same conditions, indicate that the model’s ∊-discrepancy (between flicker and pulse thresholds) is a factor of 2. Much of the discrepancy vanishes if predictions are made from peak-to-peak instead of from average-to-peak (personal communication).

Lindsley, D. B.

A. S. Schwartz and D. B. Lindsley, Bol. Inst. Estud. Med. Biol. (Mex) 22, 249 (1964).

Major, Diane

J. E. Dowling, J. E. Brown, and Diane Major, Science 153, 1639 (1966).
[Crossref] [PubMed]

Marimont, R. B.

R. B. Marimont, J. Physiol. (London) 179, 489 (1965).

Missoten, L.

L. Missoten, The Ultrastructure of the Retina (Arscia, Brussels, 1965).

Mowbray, G. H.

G. H. Mowbray and J. W. Gebhard, in W. H. Sinaiko, Ed., Selected Papers on Human Factors in the Design and Use of Control Systems (Dover Publications, Inc., New York, 1961).

Norman, J.

D. Kahneman and J. Norman, J. Exptl. Psychol. 68, 215 (1964).
[Crossref]

Pinsker, H. M.

T. N. Cornsweet and H. M. Pinsker, J. Physiol. (London) 176, 294 (1965).

Polyak, S.

S. Polyak, The Vertebrate Visual System (Univ. Chicago Press, Chicago, 1955), p. 268.

Purple, R. L.

For a similar separation of the loci of excitation and of inhibition in a peripheral visual neuron, see R. L. Purple and F. A. Dodge, Cold Spring Harbor Symp. Quant. Biol. 30, 529 (1966).
[Crossref]

Rall, W.

W. Rall, Exptl. Neurol. 2, 503 (1960).
[Crossref]

W. Rall, in R. F. Reiss, Neural Theory and Modeling (Stanford Univ. Press, California, 1964), p. 73. The variable-τ RC stage is equivalent to a neuron which receives its excitatory and inhibitory inputs directly onto the soma, which has an equilibrium potential for inhibition (K+ and/or Cl− ions) equal to the resting potential, and in which excitation is restricted to small values.

Ratoosh, R.

R. Ratoosh and C. H. Graham, J. Exptl. Psychol. 42, 367 (1951).
[Crossref]

Reiss, R. F.

W. Rall, in R. F. Reiss, Neural Theory and Modeling (Stanford Univ. Press, California, 1964), p. 73. The variable-τ RC stage is equivalent to a neuron which receives its excitatory and inhibitory inputs directly onto the soma, which has an equilibrium potential for inhibition (K+ and/or Cl− ions) equal to the resting potential, and in which excitation is restricted to small values.

Rose, A.

Rushton, W. A. H.

W. A. H. Rushton, Ann. N. Y. Acad. Sci. 74, 291 (1958).
[Crossref]

Schwartz, A. S.

A. S. Schwartz and D. B. Lindsley, Bol. Inst. Estud. Med. Biol. (Mex) 22, 249 (1964).

Sperling, G.

For a review of LP filters in relation to vision see G. Sperling, Doc. Ophthalmol. 18, 3 (1964).
[Crossref]

Stell, W. K.

W. K. Stell, Anat. Record 153, 389 (1965).
[Crossref]

Swets, J. A.

J. A. Swets, Signal Detection and Recognition by Human Observers (J. Wiley& Sons. Inc., New York, 1964).

van der Tweel, L. H.

L. H. van der Tweel, Doc. Ophthalmol. 18, 287 (1964).
[Crossref]

Watanabe, K.

K. T. Brown and K. Watanabe, Science 148, 1113 (1965).
[Crossref] [PubMed]

Westheimer, G.

G. Westheimer, J. Physiol. (London) 190, 139 (1967).

Anat. Record (1)

W. K. Stell, Anat. Record 153, 389 (1965).
[Crossref]

Ann. N. Y. Acad. Sci. (1)

W. A. H. Rushton, Ann. N. Y. Acad. Sci. 74, 291 (1958).
[Crossref]

Bol. Inst. Estud. Med. Biol. (Mex) (1)

A. S. Schwartz and D. B. Lindsley, Bol. Inst. Estud. Med. Biol. (Mex) 22, 249 (1964).

Cold Spring Harbor Symp. Quant. Biol. (2)

J. E. Dowling and B. B. Boycott, Cold Spring Harbor Symp. Quant. Biol. 30, 393 (1966).
[Crossref]

For a similar separation of the loci of excitation and of inhibition in a peripheral visual neuron, see R. L. Purple and F. A. Dodge, Cold Spring Harbor Symp. Quant. Biol. 30, 529 (1966).
[Crossref]

Doc. Ophthalmol. (3)

L. H. van der Tweel, Doc. Ophthalmol. 18, 287 (1964).
[Crossref]

For a review of LP filters in relation to vision see G. Sperling, Doc. Ophthalmol. 18, 3 (1964).
[Crossref]

D. H. Kelly, Doc. Ophthalmol. 18, 17 (1964).
[Crossref]

Exptl. Neurol. (1)

W. Rall, Exptl. Neurol. 2, 503 (1960).
[Crossref]

J. Anat. (London) (2)

M. Kidd, J. Anat. (London) 96, 179 (1962).

A. I. Cohen, J. Anat. (London) 99, 595 (1965).

J. Comp. Physiol. Psychol. (1)

R. M. Herrick, J. Comp. Physiol. Psychol. 49, 437 (1956).
[Crossref] [PubMed]

J. Exptl. Psychol. (3)

R. Ratoosh and C. H. Graham, J. Exptl. Psychol. 42, 367 (1951).
[Crossref]

D. Kahneman and J. Norman, J. Exptl. Psychol. 68, 215 (1964).
[Crossref]

D. Kahneman, J. Exptl. Psychol. 71, 543 (1966).
[Crossref]

J. Gen. Physiol. (1)

C. H. Graham and E. H. Kemp, J. Gen. Physiol. 21, 635 (1938).

J. Opt. Soc. Am. (8)

J. Physiol (London) (1)

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, J. Physiol (London) 137, 327 (1957).

J. Physiol. (London) (8)

G. Westheimer, J. Physiol. (London) 190, 139 (1967).

D. R. Curtis and J. C. Eccles, J. Physiol. (London) 145, 529 (1959).

H. B. Barlow, J. Physiol. (London) 136, 469 (1957).

T. N. Cornsweet and H. M. Pinsker, J. Physiol. (London) 176, 294 (1965).

P. Fatt and B. Katz, J. Physiol. (London) 121, 374 (1953).

J. S. Coombs, J. C. Eccles, and P. Fatt, J. Physiol. (London) 130, 396 (1955).

M. G. F. Fuortes and A. L. Hodgkin, J. Physiol. (London) 172, 239 (1964).

R. B. Marimont, J. Physiol. (London) 179, 489 (1965).

Kybernetik (2)

G. G. Furman, Kybernetik 2, 257 (1965).
[Crossref] [PubMed]

See, for example, J. Levinson and L. D. Harmon, Kybernetik 1, 107 (1961).
[Crossref] [PubMed]

Physica (1)

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

Proc. Phys. Soc. (London) (1)

G. S. Brindley, Proc. Phys. Soc. (London) 68B, 862 (1955).

Proc. Royal Soc. (London) (1)

J. E. Dowling and B. B. Boycott, Proc. Royal Soc. (London) 166B, 80 (1966/67).

Science (3)

K. T. Brown and K. Watanabe, Science 148, 1113 (1965).
[Crossref] [PubMed]

J. E. Dowling, Science 147, 57 (1965).
[Crossref] [PubMed]

J. E. Dowling, J. E. Brown, and Diane Major, Science 153, 1639 (1966).
[Crossref] [PubMed]

Washington Acad. Sci. (1)

For various different assumptions that have been made about noise distribution to enable theoretical estimates of the effects of visual noise on flicker thresholds see R. C. Jones, Washington Acad. Sci. 47, 100 (1957); L. H. van der Tweel, Ann. N. Y. Acad. Sci. 89, 829 (1961); and D. H. Kelly, J. Opt. Soc. Am. 51, 747 (1961).
[Crossref] [PubMed]

Other (15)

G. H. Mowbray and J. W. Gebhard, in W. H. Sinaiko, Ed., Selected Papers on Human Factors in the Design and Use of Control Systems (Dover Publications, Inc., New York, 1961).

J. A. Swets, Signal Detection and Recognition by Human Observers (J. Wiley& Sons. Inc., New York, 1964).

If the internal resistance of the bipolar axon is small, then the sequence of recurrent loops it generates as it connects to various ganglion-cell dendrites can be represented by a single 1-stage FB filter. The anatomy then provides two successive 1-stage FB filters, each with delayed feedback, a system which is similar to the 2-stage FB filter of the model.

L. Missoten, The Ultrastructure of the Retina (Arscia, Brussels, 1965).

H. E. Henkes and L. H. van der Tweel, Eds., Flicker (Dr. W. Junk, Publishers, The Hague, 1964).

J. L. Brown, in G. H. Graham and et al., Vision and Visual Perception (John Wiley & Sons, Inc., New York, 1965), p. 251.

Unpublished data of J. Levinson in which flicker and pulse thresholds are compared directly in the same observer under the same conditions, indicate that the model’s ∊-discrepancy (between flicker and pulse thresholds) is a factor of 2. Much of the discrepancy vanishes if predictions are made from peak-to-peak instead of from average-to-peak (personal communication).

J. C. Eccles, The Physiology of Synapses (Springer-Verlag, Berlin, Göttingen, Heidelberg, 1964).
[Crossref]

For a review see B. Katz, Nerve, Muscle, and Synapse (McGraw–Hill Book Co., New York, 1966).

The constants in Eqs. (2a–b–c) are chosen to agree with those in Ref. 3.

G. S. Brindley, Physiology of the Retina and the Visual Pathway (Edward Arnold Ltd., London, 1960), p. 187f.

Calculated by assuming retinal absorption of 1.4 × 1015 quanta/cm2 (Refs. 10, 11) and an average foveal cone density of 1.4 × 107 cones/cm2 (Ref. 12).

S. Polyak, The Vertebrate Visual System (Univ. Chicago Press, Chicago, 1955), p. 268.

, Library of Congress, Washington, D. C. 20540.

W. Rall, in R. F. Reiss, Neural Theory and Modeling (Stanford Univ. Press, California, 1964), p. 73. The variable-τ RC stage is equivalent to a neuron which receives its excitatory and inhibitory inputs directly onto the soma, which has an equilibrium potential for inhibition (K+ and/or Cl− ions) equal to the resting potential, and in which excitation is restricted to small values.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

(a). LP stage. Electrical analog of a low-pass-filter stage. The time constant τp = RpCp. The triangle here and in each of the figures indicates an isolating transconductance μ which produces an output current equal to μ times the input voltage Vj−1. The inscribed symbol is the value of μ. (b). FB filter. Electrical analog of an n stage parameter-controlled feedback filter (only the first and last stages are indicated). The last stage controls R of each stage as indicated. The time constant of each stage is τ = RC; when the output is zero (e.g., in the dark), the time constant of each stage is τ = τF = R0C. The value of μ is 1/R0. (c). FF filter. Electrical analog of a parameter-controlled feedforward filter with a single LP delay stage (τD = RDCD) in the controlling pathway. Other symbols are defined as in (b). See text for details.

Fig. 2
Fig. 2

Block diagram of the model to illustrate signal flow. The parameters to be estimated are indicated under each block: k is a constant to convert luminance units to voltage units; n-FB is a parameter controlled feedback filter of n stages, each with dark time constant τF; FF is a parameter controlled delayed feedforward filter also with dark time constant τF (the delay stage has time constant τD); p-LP is an LP filter consisting of p RC stages each with time constant τp; D represents a detector with threshold ±.

Fig. 3
Fig. 3

Log of minimum energy for detection (−logS) as a function of the duration T of a rectangular pulse, illustrating the definition of τ* and S*. Data are from Herrick.18 Background luminance is 470 td; ○●—increment test pulses; +—decrement pulses. Dashed asymptotes were drawn by inspection to data for decrement pulses; their intersections with the axes define τ1* and S1*. Lines through increment pulses of 7.2 and 314 msec (○) define τ2* and S2* as described in text. Other increment data (●) are not used in this calculation.

Fig. 4
Fig. 4

Comparison of observed values of sensitivity S* and critical duration τ* with predictions by the model. Data from Herrick’s18 observer JC (left) and from Graham and Kemp16 (right). Symbols indicate data on which τ* and S* are based. For JC: ○—increment pulses of 7.2 and 314 msec, ♢—increment pulses of 32.1 and 314 msec, +—decrement pulses, asymptotes drawn through all durations. For Graham and Kemp: ●—increment pulses of 5 and 500 msec, ♢—increment pulses of 2 and 500 msec. The lines of slope one in top row of graphs represent asymptotic Weber laws with the indicated Weber constant. Solid curves are generated by the model with shape parameters given in Table I. The coordinates are scaled so that curves pass through (0,0) when l = lref. See Table I for scale factors lref, τref, and Sref.

Fig. 5
Fig. 5

Comparison of observed with predicted sinusoidal-flicker thresholds. The theoretical DeLange characteristics are predicted by model with parameters given in Table I. Data are from DeLange’s19 observers L (left) and V (right). Luminance in trolands is indicated by the plotted symbols: “1” = 1, “2” = 10, “3” = 100, “4” = 1000, “5” = 10 000 (observer V only). Some data at intermediate luminance values have been omitted for clarity. The lightly drawn theoretical curves indicate predictions for two higher (one higher, observer V) and for two lower luminance values than were studied. The curve for highest luminance is virtually identical to the envelope of the series of curves.

Fig. 6
Fig. 6

Critical flicker frequency (CFF for 100% sinusoidal modulation) as a function of luminance. The data are from DeLange19 and include intermediate values omitted from Fig. 5. The theoretical predictions are the same as in Fig. 5. The slope of the approximately straight line segment of the curves is indicated in Hz/log10l (Ferry–Porter constant).

Fig. 7
Fig. 7

Response of model to small impulses [Δl · δ(t)] superimposed on backgrounds ranging in luminance from 0.7 × 10−3 td to 0.7 × 106 td. Successive background luminances differ by 10 X. The responses have been scaled to have the same maximum height; responses at the three least luminous backgrounds are superimposed.

Tables (1)

Tables Icon

Table I Estimated shape parameters and scale factors of the model: τF as determined from scale factor for time axis also is indicated. Values for τ are in msec, for l in trolands, and for 1/S in msec × trolands. (For Graham and Kemp,16 l is in mL and 1/S is in msec × mL.)

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

τ p d d t v j ( t ) + v j ( t ) = v j - 1 ( t )             j = 1 , , p .
τ = τ F / [ 1 + v n ( t ) ] ,
d d λ v j ( λ ) + v j ( λ ) [ 1 + v n ( λ ) ] = v j - 1 ( λ )             j = 1 , , n ,
v j ( t ) = ( μ R 0 ) n - j V j ( t ) / w .
d d λ v 1 ( λ ) + [ 1 + v 0 ( λ ) ] v 1 ( λ ) = v 0 ( λ )
τ D τ F d d λ v 0 ( λ ) + v 0 ( λ ) = v 0 ( λ ) ,
τ = τ F / [ 1 + v 0 ( λ ) ] ,
F ( λ ) = exp ( 0 λ [ 1 + v n ( λ ) ] d λ )
D F ( λ ) = F ( λ ) [ 1 + v n ( λ ) ]
D [ F ( λ ) v j ( λ ) ] = F ( λ ) v j - 1 ( λ )             j = 1 , n .
D n [ F ( λ ) v n ( λ ) ] = F ( λ ) v 0 ( λ ) .
D n + 1 F ( λ ) - D n F ( λ ) - v 0 ( λ ) F ( λ ) = 0.
D [ F ( λ ) v n + 1 ( λ ) ] = F ( λ ) v n ( λ )
v n + 1 ( λ ) = 1 F ( λ ) [ 0 λ [ D F ( λ ) - F ( λ ) ] d λ - F ( 0 ) v n + 1 ( 0 ) ] .
( D n + 1 - D n - A ) F ( λ ) = 0 , λ < λ 0 = B F ( λ 0 ) δ ( λ - λ 0 ) , λ λ 0 .
F ( λ ) = i = 0 n a i exp ( s i λ ) ,             λ λ 0 = i = 0 n a i exp ( s i λ ) + B A ( i = 0 n a i exp ( s i λ 0 ) ) × i = 0 n a i ( s i - 1 ) exp [ s i ( λ - λ 0 ) ] ,             λ λ 0 .
S n + 1 - S n - A = 0 ,
a i = s i / [ ( n + 1 ) s i - n ] .
v 0 ( λ ) = A ( 1 + m cos ω λ ) .
{ D n + 1 - D n - A [ 1 + m a 0 exp ( s 0 λ ) F ( λ ) cos ω λ ] } F ( λ ) = 0.
F ( λ ) = a 0 exp ( s 0 λ ) { 1 + A m cos ( ω λ - Φ ) × [ R 2 + A 2 - 2 A R cos ϕ ] - 1 2 } ,
R 2 = ( s 0 2 + ω 2 ) n [ ( s 0 - 1 ) 2 + ω 2 ] ϕ = n tan - 1 ( ω / s 0 ) + tan - 1 [ ω / ( s 0 - 1 ) ] Φ = tan - 1 [ ( R sin ϕ ) / ( R cos ϕ - A ) ] .
δ = A ω m [ R 2 + A 2 - 2 A R cos ϕ ] - 1 2 .
F ( λ ) a 0 exp ( s 0 λ ) [ 1 + ( δ / ω ) cos ( ω λ - Φ ) ] , λ .
v n ( λ ) ( s 0 - 1 ) - δ sin ( ω λ - Φ ) 1 + ( δ / ω ) cos ( ω λ - Φ ) .
v n ( λ ) = s 0 - 1 - δ sin ( ω λ - Φ ) ,
v 0 ( ) = v 0 ( ) v 1 ( ) = v 0 / [ 1 + v 0 ( ) ] .
v 1 ( λ ) = v 1 ( ) + β g ( λ ) +
v 0 ( λ ) = v 0 ( ) + β h ( λ ) + .
D g ( λ ) + [ 1 + v 0 ( ) ] g ( λ ) = f ( λ ) - v 1 ( ) h ( λ )
( τ D / τ F ) D h ( λ ) + h ( λ ) = f ( λ ) ,