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Die Verarbeitung stationärer optischer Nachrichten im Komplexauge von Limulus

Ommatidien-Sehfeld und räumliche Verteilung der Inhibition

Summary

The functional properties of the processing of visual information by the complex eye of Limulus was studied. The spatial distribution of activity that results in the optic nerve when the Limulus eye is exposed to a stationary optical pattern depends upon the transfer characteristics of two subsystems: the dioptric apparatus and the nervous interactions comprising the lateral inhibition system. — The transfer characteristic of the dioptric apparatus is determined by the sensitivity distribution function of single ommatidia. This distribution was measured and found to be approximately of Gauss-function type. The sensitivity falls off to 1/e at a distance of one ommatidium; thus the visual fields of adjacent ommatidia strongly overlap. As a consequence of the overlap, amplitudes of the spatial Fourier components, of which the brightness distribution of the optical surround is made up, are more and more reduced with increasing frequency in the intensity distribution on the receptor mosaic. The amplitude of the spatial frequency 1/λ=0,25 (λ in units of interommatidial distance) is reduced to half of the maximum value, which is attained at zero frequency. It is shown that the amplitude frequency characteristic of the sensitivity distribution function has no zeros, which means that no loss of optical information results from overlap of visual fields. Thus the resolving power of the dioptric apparatus is limited only by the number of receptors per unit area. — The transfer characteristic of the lateral inhibition system in the Limulus eye depends on the distribution of the inhibitory coefficients around the individual receptors. This distribution function was determined from excitatory responses in the optic nerve elicited by a spatial light intensity step function on the receptor mosaic. It is found that this distribution is also Gaussian in form, but decays to 1/e at a distance of eight to nine ommatidia along the major axis of the eye. The average value of the inhibitory coefficients between adjacent ommatidia was found to be 0,025. The amplitude frequency response of the inhibitory system is constant for high spatial frequencies down to 1/λ=0,1 while amplitudes of lower frequency sinusoids are reduced down to nearly half of the maximum value at frequency zero. The amplitude frequency characteristic of the inhibitory system ensures a one to one correspondence between the intensity distribution on the receptor mosaic and the excitation distribution in the optic nerve. The overall transfer characteristic of the eye is derived from the transfer characteristics of the dioptric apparatus and the inhibitory system. This characteristic is of bandpass type with a maximum amplitude response at a frequency of 1/λ=0,07. The overall transfer characteristic was independently confirmed in a separate experiment. The nature of the overall transfer characteristic shows that the inhibitory system does not exactly correct for the overlap of the visual fields of single ommatidia, which in principal the system could do if the distributions of inhibitory coefficients and ommatidia sensitivity were equal. The overall transfer characteristic of the Limulus eye garantees a one to one correspondence between patterns in the optical surround and excitation distributions in the optic nerve. — The average values of the inhibitory coefficients derived from these experiments are at least a factor ten smaller than those determined directly by other investigators. Possible explanations of this discrepency are discussed. — In a separate chapter the overall transfer characteristic for eyes submerged in water is described. It was found that this characteristic does not differ from that determined in air for the eye region which was investigated in the experiments. This result is explained by two properties of the eye which are dependent on the refractive index of the surround medium and whose influences cancel each other: the visual fields of ommatidia are reduced under water, while the divergence angles between the optical axes of adjacent ommatidia also diminish.

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Literatur

  1. Demoll, R.: Die Augen von Limulus. Zool. Jb., Abt. Anat. u. Ontog. 38, 443 (1914).

  2. Exner, S.: Die Physiologie der fazettierten Augen, von Krebsen und Insekten. Leipzig u. Wien: Deuticke 1891.

  3. Fermi, G., u. W. Reichardt: Optomotorische Reaktionen der Fliege Musca domestica. Kybernetik 2, 15 (1963).

  4. Götz, K. G.: Optomotorische Untersuchung des visuellen Systems einiger Augenmutanten der Fruchtfliege Drosophila. Kybernetik 2, 77 (1964).

  5. Graham, G. H., and H. K. Hartline: The response of single visual sense cells to lights of different wave lengths. J. gen. Physiol. 18, 917 (1935).

  6. Hartline, H., and F. Ratliff: Inhibitory interaction of receptor units in the eye of Limulus. J. gen.Physiol. 40, 357 (1957); - Spatial summation of inhibitory influences in the eye of Limulus, and the mutual interaction of receptor units. J. gen. Physiol. 41, 1049 (1958).

  7. Hartline, H., H. Wagner and F. Ratliff: Inhibition in the eye of Limulus. J. gen. Physiol. 39, 651 (1956).

  8. Hartline, H. K.: Intensity and duration in the excitation of single photoreceptor units. J. cell comp. Physiol. 5, 229 (1934).

  9. Hubbard, R., and G. Wald: Visual pigment of the horseshoe crab, Limulus polyphemus. Nature (Lond.) 186, 212 (1960).

  10. MacNichol, E. F., and J. A. H. Jacobs: Electronic device for mesuring reciprocal time intervals. Rev. Sci. Instr. 26, 1176 (1955).

  11. MacNichol, E. F., and R. Benolken: Blocking effect of ethyl alcohol on inhibitory synapses in the eye of Limulus. Science 124, 681 (1956).

  12. Miller, W. H.: Morphology of the ommatidia of the compound eye of Limulus. J. biophy. biochem. Cytol. 3, 421–428 (1957).

  13. Ratlitf, F., and H. K. Hartline: The responses of Limulus optic nerve fibers to patterns of illumination on the receptor mosaic. J. gen. Physiol. 42, 1241 (1959).

  14. Ratliff, F., H. K. Hartline and W. H. Miller: Spatial and temporal aspects of retinal inhibitory interaction. J. Opt. Soc. Amer. 53, 110 (1963).

  15. Ratliff, F., W. H. Miller and H. K. Hartline: Neural interaction in the eye and the integration of receptor activity. Ann. N.Y. Acad. Sci. 74, 210 (1958).

  16. Reichardt, W.: Über das optische Auflösungsvermögen der Facettenaugen von Limulus. Kybernetik 1, 57 (1961).

  17. Reichardt, W., u. G. MacGinitie: Zur Theorie der lateralen Inhibition. Kybernetik 1, 155–165 (1962).

  18. Varju, D.: Vergleich zweier Modelle für laterale Inhibition. Kybernetik 1, 200 (1962).

  19. Watermann, T. H.: Directional sensitivity of single ommatidia in the compound eye of Limulus. Proc. nat. Acad. Sci. (Wash.) 40, 252 (1954).

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This research was supported in part by the United States Air Force under Grant No. AF-EOAR-62-41 and monitored by the European Office, Office of Aerospace Research.

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Kirschfeld, K., Reichardt, W. Die Verarbeitung stationärer optischer Nachrichten im Komplexauge von Limulus. Kybernetik 2, 43–61 (1964). https://doi.org/10.1007/BF00288558

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