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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 56, Iss. 1 — Jan. 1, 1966
  • pp: 95–97

One-Stage Model for Visual Temporal Integration

JOHN LEVINSON  »View Author Affiliations

JOSA, Vol. 56, Issue 1, pp. 95-97 (1966)

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Many characteristics of visual temporal integration, found in both psychophysics and physiology, have been thought of as arising from a number of cascaded integrations, or exponential delays. As an alternative, a single process is proposed which has a temporal response identical with that of the many-stage model. This process is readily visualized as taking place within a single receptor cell. It consists of a number of subprocesses, the number being proportional to the number of photons absorbed. Each subprocess consists of three steps: (1) initiation by photon absorption, (2) counting of a series of random events, and (3) emission of a signal when the count reaches a specific number. Response is taken to be the summation of all the signals produced by the subprocesses. Temporal delay and spread of the response is entirely attributed to the time required to accumulate the independent random events of step (2). Possible physiological correlates of the three steps are touched on, but only speculatively.

JOHN LEVINSON, "One-Stage Model for Visual Temporal Integration," J. Opt. Soc. Am. 56, 95-97 (1966)

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  1. H. de Lange, J. Opt. Soc. Am. 44, 380 (1954); 48, 777, 784 (1958); and 51, 415 (1961).
  2. J. Levinson, Science 130, 919 (1959).
  3. J. Levinson and L. D. Harmon Kybernetik 1, 107 (1961).
  4. D. H. Kelly J. Opt. Soc. Am. 1, 747 (1961).
  5. R. D. DeVoe, Doc. Ophthalmol. 18, 128 (1964).
  6. F. W. Campbell and J. G. Robson, Doc. Ophthalmol. 18, 83 (1964).
  7. M. G. F. Fuortes and A. L. Hodgkin, J. Physiol. (London) 172, 239 (1964).
  8. More than 40 years ago, H. E. Ives, J. Opt. Soc. Am. 6, 343 (1922) proposed "A Theory of Intermittent Vision" based on diffusion of photoproduct down the length of a single receptor. Unfortunately, this model predicts results which are not as closely in accord with de Lange's data1 as those predicted by the cascaded integrator. Ives was clearly aware that his model was approximated by cascaded integrators (as evidenced by his illustration, ibid., p. 358) but he strongly preferred a single process to a multiplicity of them. The model proposed in the present paper is thus in the spirit of Ives's approach: cause for some satisfaction to one who has resumed some of Ives's work in the same Laboratories.
  9. S. Hecht and C. D. Verrijp, J. Gen. Physiol. 17, 269 (1933).
  10. I am heartily grateful for fruitful discussions with my colleagues G. G. Harris, L. D. Harmon, L. S. Frishkopf, W. A. van Bergeijk, and S. Sternberg. T. C. Anderson and G. G. Harris also pointed out independently that Eq. (2) may be so interpreted as to apply to the proposed single process directly, thus rendering the identity of response inevitable without further derivation. This provides an appealing alternative exposition.
  11. A. G. Chynoweth and W. G. Scheider, J. Chem. Phys. 22, 1021 (1954).

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