Summary
The retinal rods are usually assumed to function, at least under certain stimulus conditions, as single-photon-detectors. Thus the problem arises how a stream of events (the elementary photon responses) with Poisson statistics, but in general with a modulated mean, can be processed. Since the human visual system has a dynamic range of some 10 decades and optic nerve fibers cannot carry higher event rates than, say, 400–1,000 events/sec, “event rate reduction” seems to be necessary. Event rate reduction of modulated Poisson processes is possible with K-scalers (devices that only pass the K-th event following the previous output event). In view of the enormous dynamic range mentioned above, adaptation of the scaling factor is necessary. An adapting scaler that implements the Weber-law proves to furnish an interesting receptor model. Such a Weber-machine can function as a single-event detector at low input intensities and as an event rate differentiator at high intensities.
Absolute threshold measurements have led to the idea that at least 2–12 photons have to be absorbed in a retinal sampling-unit within some coincidence interval T in order to perceive a flash. Such a coincidence detection can be combined with the idea of adapting scalers in a “deVries-Rose machine” or “square-root-coincidence scaler” (van de Grind and Bouman, 1968). Placing the deVries-Rose machines as centres of convergence at the bipolar level and the Weber machines at the receptor level, we get a model that makes understandable both absolute threshold phenomena and increment threshold data for the scotopic as well as the photopic range of luminances.
The incorporation of adaptation phenomena by the creation of “adaptation pools” is possible if the horizontal cells are postulated to regulate the scaling factors of the receptors (Weber machines) and the amacrine cells those of the bipolars (deVries-Rose machines).
The stepresponses of the two types of machines as displayed in P.S.T.-histograms can be directly compared with those of many visual (and auditory) cells as reported in the literature. This greatly reinforces our trust in the present approach.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Bouman, M. A.: History and present status of quantum theory in vision. In: Sensory communications, ed. W. A. Rosenblith. M.I.T. Press 1961.
—: My image of the retina. Quart. Rev. Biophys. 2, Nr 1, 25–64 (1969).
Bouman, M. A. Ampt, C. G. F.: Fluctuation theory in vision and its mechanistic model. In: Performance of the eye at low luminances, eds. M. A. Bouman, J. J. Vos. Exerpta Medica Int. Congr. Ser. No 125, 57–69 (1966).
— Velden, H. A. van der: The two quanta-explanation of the dependence of the threshold values and visual acuity on the visual angle and the time of observation. J. opt. Soc. Amer. 37, 908 (1947).
— Vos, J. J., Walraven, P. L.: Fluctuation theory of luminance and chromaticity discrimination. J. opt. Soc. Amer. 53, 121–128 (1963).
Brink, G. van den, Bouman, M. A.: Visual contrast thresholds for moving point sources. J. opt. Soc. Amer. 47, 612–618 (1957).
Clark Jones, R.: Quantum efficiency of human vision. J. opt. Soc. Amer. 49, 645–653 (1959).
Dowling, J. E.: The site of visual adaptation. Science 155, 273–279 (1967).
— Werbung, F. S.: Organization of the retina of the mudpuppy Necturus maculosis. I. Synaptic structure. J. Neurophysiol. 32, 315–338 (1969).
Gaines, B. R.: Stochastic computing. AFIPS, S.J.C.C. 30, 149–156 (1967).
Graham, C. H., ed.: Vision and visual perception. London: Wiley & Sons (1965).
Grind, W. A. van de, Bouman, M. A.: A model of a retinal sampling-unit based on fluctuation theory. Kybernetik 4, 136–141 (1968).
— Schalm, T. van, Bouman, M. A.: A coincidence model of the processing of quantum signals by the human retina. Kybernetik 4, 141–146 (1968).
Kiang, N. Y.-S.: Discharge patterns of single fibers in cat's auditory nerve. Research Monograph 35. M.I.T. Press 1965.
Koenderink, J. J., Grind, W. A. van de, Bouman, M. A.: Models of retinal signal processing at high luminances. Kybernetik 6, 227 (1970).
Lipetz, L. L.: Glial control of neuronal activity. IEEE Trans. on Mil. Electron. 7, 144–155 (1963).
Ratliff, F.: Mach bands: Quantitative studies on neural networks in the retina, ed. R. Bush. Holden-Day Inc. 1965.
Ribeiro, S. T.: Random pulse machines. IEEE Trans. on E.C. 16, 261–267 (1967).
Rose, A.: Relative sensitivities of television pickup tubes, photographic film, and the human eye. Proc. I. R. E. 30, 293–300 (1942).
—: The sensitivity performance of the human eye on an absolute scale. J. opt. Soc. Amer. 38, 196–208 (1948).
—: Quantum effects in vision. Advanc. biol. med. Phys. 5, 211–242 (1957).
Rushton, W. A. H.: Flash photolysis in human cones. Photochem. and Photobiol. 3, 561–577 (1964).
—: Visual adaption. The Ferrier Lecture 1962. Proc. roy. Soc. B 162, 20–46 (1965).
Schade, O. H.: Optical and photoelectric analog of the eye. J. opt. Soc. Amer. 46, 721–739 (1956).
Siebert, W. M., Gambardella, G.: Phenomenological model for a form of adaptation in primary auditory nerve fibers. M.I.T.-Q.P.R. Nr 88, 330–334 (1968).
Stone, J., Fabian, M.: Summing properties of the cat's retinal ganglion cell. Vision Res. 8, 1023–1040 (1968).
Trabka, E. A.: On Stiles' line element in brightness-color space and the color power of the blue. Vision Res. 8, 613–616 (1968).
—: Parameter values for nonideal detectors in a color vision model. Vision Res. 8, 613–616 (1968).
—: Effect of scaling optic-nerve impulses on increment thresholds. J. opt. Soc. Amer. 59, 345–349 (1969).
Vries, H. I. de: The quantum nature of light and its bearing upon the threshold of vision, the differential sensitivity, and the visual acuity of the eye. Physica 10, 553–564 (1943).
Werblin, F. S., Dowling, J. E.: Organization of the retina of the mudpuppy Necturus maculosis. II. Intracellular Recordings. J. Neurophysiol. 32, 339–355 (1969).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van de Grind, W.A., Koenderink, J.J. & Bouman, M.A. Models of the processing of quantum signals by the human peripheral retina. Kybernetik 6, 213–227 (1970). https://doi.org/10.1007/BF00276722
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00276722