Abstract

Thresholds for seeing light from a stimulus are determined by a mechanism that pairs subliminal excitations from both halves of a twin unit. Such excitations stem from a package of k1 receptor responses. A half-unit contains one red or one green cone and P rods. The receptor’s “Weber machine” controls the receptor’s gain. Each half of a twin unit contains a “de Vries machine,” which controls the half’s k number. In the dark the receptor’s dark noise events reset its Weber machine and the receptor’s relation to its de Vries machine. A pairing product for light perception also represents a direction event. The local time signs of the two subliminal excitations are crucial for the polarity, size, and pace of the direction event. In relation to the time when and the area in which the stimulus is presented, these signs have average latency periods that depend on intensity and average locations that depend on movement. Polarity depends on which of the two subliminal excitations happens to arrive first at the twin’s pairing facility. The intra- and inter-twin pairings in a persepton for the perceptions of light, edge and movement and the probability summation of the pairing products of the mutually independent three sets of twins of the retrinet improve intensity discrimination. Cross-pairings of intra-receptor pairings in red and green cones of a trion for yellow improve visual discrimination further. Discrimination of stimuli that exploit the model’s entire summation mechanisms and pairing facilities represents “what the perfect human eye sees best.” For the model this threshold of modulation in quantum absorption is the ideal limit that is prescribed by statistical physics. The lateral and meta interaction in a twin unit enhance the contrast of an edge and of a temporal transient. The precision of the local time sign of a half’s stimulation determines the spatiotemporal hyperfunctions for location and speed. The model’s design for the perfect retinal mosaic consists of red twins situated along clockwise and counterclockwise spirals and green twins along circles that are concentric with the fovea. The model’s descriptions of discrimination, adaptation, and hyperfunctions agree with experimental data.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. M. A. Bouman, “Mechanisms in peripheral dark adaptation,” J. Opt. Soc. Am. 42, 941–950 (1952).
    [CrossRef] [PubMed]
  4. M. A. Bouman, J. ten Doesschate, “Nervous and photochemical components in visual adaptation,” Ophthalmologica 126, 222–230 (1953).
    [CrossRef] [PubMed]
  5. M. A. Bouman, G. van den Brink, “Absolute threshold for moving point sources,” J. Opt. Soc. Am. 43, 895–898 (1953).
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    [CrossRef] [PubMed]
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  27. C. Noorlander, J. J. Koenderink, “Spatial and temporal discrimination ellipsoids in colour space,” J. Opt. Soc. Am. 73, 1533–1544 (1983).
    [CrossRef] [PubMed]
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  29. S. A. Burns, A. E. Elsner, “Color matching at high luminance: photopigment optical density and pupil entry,” J. Opt. Soc. Am. 10, 221–230 (1993).
    [CrossRef]
  30. M. A. Bouman, “Absolute threshold conditions for visual perception,” J. Opt. Soc. Am. 45, 36–43 (1955).
    [CrossRef] [PubMed]
  31. G. J. C. van der Horst, M. A. Bouman, “On searching for “Mach band type” phenomena in colour vision,” Vision Res. 7, 1027–1029 (1967).
    [CrossRef] [PubMed]
  32. M. A. Bouman, “On foveal and peripheral interaction in binocular vision,” Opt. Acta 1, 177–183 (1955).
    [CrossRef]
  33. J. J. Koenderink, “The concept of local sign,” in Limits in Perception, A. J. van Doorn, W. A. van de Grind, J. J. Koenderink, eds. (VNU Science Press, Utrecht, The Netherlands, 1984).
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    [CrossRef] [PubMed]
  35. S. P. McKee, L. Welch, “Sequential recruitment in the discrimination of velocity,” J. Opt. Soc. Am. A 2, 243–251 (2000).
    [CrossRef]
  36. A. Roorda, D. R. Williams, G. Y. Yoon, Y. Yamanchi, “The eye optics, the trichromatic cone mosaic and human vision,” Perception 29, Suppl. 43 (2000).
  37. M. Schultze, “Zur Anatomie und Physiologie der Retina,” Arch. Mikr. Anat. 2, 175–286 (1966).
    [CrossRef]
  38. P. Sheridan, T. Hintz, D. Alexander, “Pseudo-invariant image transformations on hexagonal lattice,” Image Vision Comput. 18, 907–917 (2000).
    [CrossRef]

2002

2000

P. Verghese, S. P. McKee, N. M. Grzywacz, “Stimulus configuration determines the detectability of motion signals in noise,” J. Opt. Soc. Am. A 17, 1525–1534 (2000).
[CrossRef]

A. Roorda, D. R. Williams, G. Y. Yoon, Y. Yamanchi, “The eye optics, the trichromatic cone mosaic and human vision,” Perception 29, Suppl. 43 (2000).

P. Sheridan, T. Hintz, D. Alexander, “Pseudo-invariant image transformations on hexagonal lattice,” Image Vision Comput. 18, 907–917 (2000).
[CrossRef]

S. P. McKee, L. Welch, “Sequential recruitment in the discrimination of velocity,” J. Opt. Soc. Am. A 2, 243–251 (2000).
[CrossRef]

1996

F. Rieke, D. A. Baylor, “Molecular origin of continuous dark noise in rod photoreceptors,” Biophys. J. 71, 2553–2572 (1996).

1993

S. A. Burns, A. E. Elsner, “Color matching at high luminance: photopigment optical density and pupil entry,” J. Opt. Soc. Am. 10, 221–230 (1993).
[CrossRef]

1984

J. J. Koenderink, “Geometrical structures determined by the functional order in nervous nets,” Biol. Cybern. 50, 43–50 (1984).
[CrossRef] [PubMed]

1983

1978

1976

1974

V. Virsu, J. Romavo, “Visual resolution, contrast sensitivity and the cortical magnification factor,” Exp. Brain Res. 37, 475–494 (1974).

1972

M. A. Bouman, J. J. Koenderink, “Psychophysical basis of coincidence mechanisms in the human visual system,” Rev. Physiol. 65, 126–173 (1972).

1970

W. A. van de Grind, J. J. Koenderink, M. A. Bouman, “Models of the processing of quantum signals by the human peripheral retina,” Kybernetik 6, 213–227 (1970).
[CrossRef] [PubMed]

F. Fischer, H. K. May, “Invarianzen in der Katzenretina: Gesetzmaessige Beziehungen zwischen Empfindlichkeit, Groesse and Lage rezeptiver Felder von Ganglienzellen,” Exp. Brain Res. 11, 448–464 (1970).
[CrossRef]

1969

1968

W. A. van de Grind, M. A. Bouman, “A model of a retinal sampling-unit based on fluctuation theory,” Kybernetik 4, 136–141 (1968).
[CrossRef] [PubMed]

1967

G. J. C. van der Horst, M. A. Bouman, “On searching for “Mach band type” phenomena in colour vision,” Vision Res. 7, 1027–1029 (1967).
[CrossRef] [PubMed]

F. L. van Nes, J. J. Koenderink, H. Nas, M. A. Bouman, “Spatiotemporal modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 1082–1088 (1967).
[CrossRef] [PubMed]

1966

M. Schultze, “Zur Anatomie und Physiologie der Retina,” Arch. Mikr. Anat. 2, 175–286 (1966).
[CrossRef]

1964

M. A. Bouman, “Efficiency and economy in impulse transmission in the visual system,” Acta Psychologica (Amsterdam) 23, 239–241 (1964).

1957

1955

M. A. Bouman, “Absolute threshold conditions for visual perception,” J. Opt. Soc. Am. 45, 36–43 (1955).
[CrossRef] [PubMed]

M. A. Bouman, “On foveal and peripheral interaction in binocular vision,” Opt. Acta 1, 177–183 (1955).
[CrossRef]

1954

G. van den Brink, M. A. Bouman, “Variation of integrative capacity in time and space: an adaptational phenomenon,” J. Opt. Soc. Am. 44, 614–620 (1954).
[CrossRef]

1953

M. A. Bouman, J. ten Doesschate, “Nervous and photochemical components in visual adaptation,” Ophthalmologica 126, 222–230 (1953).
[CrossRef] [PubMed]

M. A. Bouman, G. van den Brink, “Absolute threshold for moving point sources,” J. Opt. Soc. Am. 43, 895–898 (1953).
[CrossRef] [PubMed]

1952

1950

1947

H. K. Hartline, L. J. Milne, J. H. Wagman, “Fluctuation of response of visual sense cell,” Fed. Proc. 6, 124 (1947).

Alexander, D.

P. Sheridan, T. Hintz, D. Alexander, “Pseudo-invariant image transformations on hexagonal lattice,” Image Vision Comput. 18, 907–917 (2000).
[CrossRef]

Ampt, C. G. F.

M. A. Bouman, C. G. F. Ampt, “Fluctuation theory in vision and its mechanistic model,” in Performance of the Eye at Low Luminances, Vol. 125 of Excerpta Medica, International Congressional Series (Excerpta Medica, Amsterdam, 1965), pp. 57–69.

Barlow, H. B.

H. B. Barlow, W. R. Levick, “Coding of light intensity by the cat retina,” in Proceedings of the International School of Physics “Enrico Fermi” (Academic, New York, 1969), pp. 384–396.

Baylor, D. A.

F. Rieke, D. A. Baylor, “Molecular origin of continuous dark noise in rod photoreceptors,” Biophys. J. 71, 2553–2572 (1996).

Bouman, M. A.

M. A. Bouman, “Spatiotemporal configuration dependent pairing of nerve events in dark-adapted human vision,” J. Opt. Soc. Am. A 19, 241–253 (2002).
[CrossRef]

J. J. Koenderink, M. A. Bouman, A. E. Buenos de Mesquita, S. Slappendel, “Perimetry of contrast detection thresholds of moving spatial sine wave patterns,” I–IV, J. Opt. Soc. Am. 68, 845–865 (1978).
[CrossRef] [PubMed]

M. A. Bouman, J. J. Koenderink, “Psychophysical basis of coincidence mechanisms in the human visual system,” Rev. Physiol. 65, 126–173 (1972).

W. A. van de Grind, J. J. Koenderink, M. A. Bouman, “Models of the processing of quantum signals by the human peripheral retina,” Kybernetik 6, 213–227 (1970).
[CrossRef] [PubMed]

M. A. Bouman, “My image of the retina,” Q. Rev. Biophys. 2, 25–64 (1969).
[CrossRef] [PubMed]

G. J. C. van der Horst, M. A. Bouman, “Spatiotemporal chromaticity discrimination,” J. Opt. Soc. Am. 59, 1482–1488 (1969).
[CrossRef] [PubMed]

W. A. van de Grind, M. A. Bouman, “A model of a retinal sampling-unit based on fluctuation theory,” Kybernetik 4, 136–141 (1968).
[CrossRef] [PubMed]

G. J. C. van der Horst, M. A. Bouman, “On searching for “Mach band type” phenomena in colour vision,” Vision Res. 7, 1027–1029 (1967).
[CrossRef] [PubMed]

F. L. van Nes, J. J. Koenderink, H. Nas, M. A. Bouman, “Spatiotemporal modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 1082–1088 (1967).
[CrossRef] [PubMed]

M. A. Bouman, “Efficiency and economy in impulse transmission in the visual system,” Acta Psychologica (Amsterdam) 23, 239–241 (1964).

G. van den Brink, M. A. Bouman, “Visual contrast thresholds for moving point sources,” J. Opt. Soc. Am. 47, 612–618 (1957).
[CrossRef] [PubMed]

M. A. Bouman, “Absolute threshold conditions for visual perception,” J. Opt. Soc. Am. 45, 36–43 (1955).
[CrossRef] [PubMed]

M. A. Bouman, “On foveal and peripheral interaction in binocular vision,” Opt. Acta 1, 177–183 (1955).
[CrossRef]

G. van den Brink, M. A. Bouman, “Variation of integrative capacity in time and space: an adaptational phenomenon,” J. Opt. Soc. Am. 44, 614–620 (1954).
[CrossRef]

M. A. Bouman, J. ten Doesschate, “Nervous and photochemical components in visual adaptation,” Ophthalmologica 126, 222–230 (1953).
[CrossRef] [PubMed]

M. A. Bouman, G. van den Brink, “Absolute threshold for moving point sources,” J. Opt. Soc. Am. 43, 895–898 (1953).
[CrossRef] [PubMed]

M. A. Bouman, “Mechanisms in peripheral dark adaptation,” J. Opt. Soc. Am. 42, 941–950 (1952).
[CrossRef] [PubMed]

M. A. Bouman, “Peripheral contrast threshold for various and different wavelengths for adapting field and test stimulus,” J. Opt. Soc. Am. 42, 820–831 (1952).
[CrossRef] [PubMed]

M. A. Bouman, “Peripheral contrast thresholds of the human eye,” J. Opt. Soc. Am. 40, 825–832 (1950).
[CrossRef]

M. A. Bouman, “Quanta noise and vision,” in Theoretical Physics and Biology (North-Holland, Amsterdam, 1969), pp. 246–250.

M. A. Bouman, C. G. F. Ampt, “Fluctuation theory in vision and its mechanistic model,” in Performance of the Eye at Low Luminances, Vol. 125 of Excerpta Medica, International Congressional Series (Excerpta Medica, Amsterdam, 1965), pp. 57–69.

Buenos de Mesquita, A. E.

Burns, S. A.

S. A. Burns, A. E. Elsner, “Color matching at high luminance: photopigment optical density and pupil entry,” J. Opt. Soc. Am. 10, 221–230 (1993).
[CrossRef]

Elsner, A. E.

S. A. Burns, A. E. Elsner, “Color matching at high luminance: photopigment optical density and pupil entry,” J. Opt. Soc. Am. 10, 221–230 (1993).
[CrossRef]

Fischer, F.

F. Fischer, H. K. May, “Invarianzen in der Katzenretina: Gesetzmaessige Beziehungen zwischen Empfindlichkeit, Groesse and Lage rezeptiver Felder von Ganglienzellen,” Exp. Brain Res. 11, 448–464 (1970).
[CrossRef]

Grzywacz, N. M.

Hartline, H. K.

H. K. Hartline, L. J. Milne, J. H. Wagman, “Fluctuation of response of visual sense cell,” Fed. Proc. 6, 124 (1947).

Hintz, T.

P. Sheridan, T. Hintz, D. Alexander, “Pseudo-invariant image transformations on hexagonal lattice,” Image Vision Comput. 18, 907–917 (2000).
[CrossRef]

Koenderink, J. J.

J. J. Koenderink, “Geometrical structures determined by the functional order in nervous nets,” Biol. Cybern. 50, 43–50 (1984).
[CrossRef] [PubMed]

C. Noorlander, J. J. Koenderink, “Spatial and temporal discrimination ellipsoids in colour space,” J. Opt. Soc. Am. 73, 1533–1544 (1983).
[CrossRef] [PubMed]

J. J. Koenderink, M. A. Bouman, A. E. Buenos de Mesquita, S. Slappendel, “Perimetry of contrast detection thresholds of moving spatial sine wave patterns,” I–IV, J. Opt. Soc. Am. 68, 845–865 (1978).
[CrossRef] [PubMed]

M. A. Bouman, J. J. Koenderink, “Psychophysical basis of coincidence mechanisms in the human visual system,” Rev. Physiol. 65, 126–173 (1972).

W. A. van de Grind, J. J. Koenderink, M. A. Bouman, “Models of the processing of quantum signals by the human peripheral retina,” Kybernetik 6, 213–227 (1970).
[CrossRef] [PubMed]

F. L. van Nes, J. J. Koenderink, H. Nas, M. A. Bouman, “Spatiotemporal modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 1082–1088 (1967).
[CrossRef] [PubMed]

J. J. Koenderink, “The concept of local sign,” in Limits in Perception, A. J. van Doorn, W. A. van de Grind, J. J. Koenderink, eds. (VNU Science Press, Utrecht, The Netherlands, 1984).

Levick, W. R.

H. B. Barlow, W. R. Levick, “Coding of light intensity by the cat retina,” in Proceedings of the International School of Physics “Enrico Fermi” (Academic, New York, 1969), pp. 384–396.

May, H. K.

F. Fischer, H. K. May, “Invarianzen in der Katzenretina: Gesetzmaessige Beziehungen zwischen Empfindlichkeit, Groesse and Lage rezeptiver Felder von Ganglienzellen,” Exp. Brain Res. 11, 448–464 (1970).
[CrossRef]

McKee, S. P.

Milne, L. J.

H. K. Hartline, L. J. Milne, J. H. Wagman, “Fluctuation of response of visual sense cell,” Fed. Proc. 6, 124 (1947).

Nas, H.

Noorlander, C.

Ratliff, F.

F. Ratliff, “Some inter-relations among physics, physiology and psychology in the study of vision,” in Psychology: a Study of a Science (McGraw Hill, New York, 1962), Vol. 4, pp. 417–482.

Reichardt, W.

W. Reichardt, “Autocorrelation, a principle for the evaluation of sensory information by the central nervous system,” in Sensory Communication, W. A. Rosenblith, ed., (MIT Press, Cambridge, Mass., 1961), pp. 303–319.

Rieke, F.

F. Rieke, D. A. Baylor, “Molecular origin of continuous dark noise in rod photoreceptors,” Biophys. J. 71, 2553–2572 (1996).

Romavo, J.

V. Virsu, J. Romavo, “Visual resolution, contrast sensitivity and the cortical magnification factor,” Exp. Brain Res. 37, 475–494 (1974).

Roorda, A.

A. Roorda, D. R. Williams, G. Y. Yoon, Y. Yamanchi, “The eye optics, the trichromatic cone mosaic and human vision,” Perception 29, Suppl. 43 (2000).

Schultze, M.

M. Schultze, “Zur Anatomie und Physiologie der Retina,” Arch. Mikr. Anat. 2, 175–286 (1966).
[CrossRef]

Sheridan, P.

P. Sheridan, T. Hintz, D. Alexander, “Pseudo-invariant image transformations on hexagonal lattice,” Image Vision Comput. 18, 907–917 (2000).
[CrossRef]

Shimamura, K.

Slappendel, S.

ten Doesschate, J.

M. A. Bouman, J. ten Doesschate, “Nervous and photochemical components in visual adaptation,” Ophthalmologica 126, 222–230 (1953).
[CrossRef] [PubMed]

van de Grind, W. A.

W. A. van de Grind, J. J. Koenderink, M. A. Bouman, “Models of the processing of quantum signals by the human peripheral retina,” Kybernetik 6, 213–227 (1970).
[CrossRef] [PubMed]

W. A. van de Grind, M. A. Bouman, “A model of a retinal sampling-unit based on fluctuation theory,” Kybernetik 4, 136–141 (1968).
[CrossRef] [PubMed]

van den Brink, G.

van der Horst, G. J. C.

G. J. C. van der Horst, M. A. Bouman, “Spatiotemporal chromaticity discrimination,” J. Opt. Soc. Am. 59, 1482–1488 (1969).
[CrossRef] [PubMed]

G. J. C. van der Horst, M. A. Bouman, “On searching for “Mach band type” phenomena in colour vision,” Vision Res. 7, 1027–1029 (1967).
[CrossRef] [PubMed]

van Nes, F. L.

Verghese, P.

Virsu, V.

V. Virsu, J. Romavo, “Visual resolution, contrast sensitivity and the cortical magnification factor,” Exp. Brain Res. 37, 475–494 (1974).

Wagman, J. H.

H. K. Hartline, L. J. Milne, J. H. Wagman, “Fluctuation of response of visual sense cell,” Fed. Proc. 6, 124 (1947).

Welch, L.

Westheimer, G.

Williams, D. R.

A. Roorda, D. R. Williams, G. Y. Yoon, Y. Yamanchi, “The eye optics, the trichromatic cone mosaic and human vision,” Perception 29, Suppl. 43 (2000).

Yamanchi, Y.

A. Roorda, D. R. Williams, G. Y. Yoon, Y. Yamanchi, “The eye optics, the trichromatic cone mosaic and human vision,” Perception 29, Suppl. 43 (2000).

Yoon, G. Y.

A. Roorda, D. R. Williams, G. Y. Yoon, Y. Yamanchi, “The eye optics, the trichromatic cone mosaic and human vision,” Perception 29, Suppl. 43 (2000).

Acta Psychologica (Amsterdam)

M. A. Bouman, “Efficiency and economy in impulse transmission in the visual system,” Acta Psychologica (Amsterdam) 23, 239–241 (1964).

Arch. Mikr. Anat.

M. Schultze, “Zur Anatomie und Physiologie der Retina,” Arch. Mikr. Anat. 2, 175–286 (1966).
[CrossRef]

Biol. Cybern.

J. J. Koenderink, “Geometrical structures determined by the functional order in nervous nets,” Biol. Cybern. 50, 43–50 (1984).
[CrossRef] [PubMed]

Biophys. J.

F. Rieke, D. A. Baylor, “Molecular origin of continuous dark noise in rod photoreceptors,” Biophys. J. 71, 2553–2572 (1996).

Exp. Brain Res.

F. Fischer, H. K. May, “Invarianzen in der Katzenretina: Gesetzmaessige Beziehungen zwischen Empfindlichkeit, Groesse and Lage rezeptiver Felder von Ganglienzellen,” Exp. Brain Res. 11, 448–464 (1970).
[CrossRef]

V. Virsu, J. Romavo, “Visual resolution, contrast sensitivity and the cortical magnification factor,” Exp. Brain Res. 37, 475–494 (1974).

Fed. Proc.

H. K. Hartline, L. J. Milne, J. H. Wagman, “Fluctuation of response of visual sense cell,” Fed. Proc. 6, 124 (1947).

Image Vision Comput.

P. Sheridan, T. Hintz, D. Alexander, “Pseudo-invariant image transformations on hexagonal lattice,” Image Vision Comput. 18, 907–917 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. J. Koenderink, M. A. Bouman, A. E. Buenos de Mesquita, S. Slappendel, “Perimetry of contrast detection thresholds of moving spatial sine wave patterns,” I–IV, J. Opt. Soc. Am. 68, 845–865 (1978).
[CrossRef] [PubMed]

F. L. van Nes, J. J. Koenderink, H. Nas, M. A. Bouman, “Spatiotemporal modulation transfer in the human eye,” J. Opt. Soc. Am. 57, 1082–1088 (1967).
[CrossRef] [PubMed]

G. van den Brink, M. A. Bouman, “Variation of integrative capacity in time and space: an adaptational phenomenon,” J. Opt. Soc. Am. 44, 614–620 (1954).
[CrossRef]

M. A. Bouman, “Peripheral contrast thresholds of the human eye,” J. Opt. Soc. Am. 40, 825–832 (1950).
[CrossRef]

M. A. Bouman, “Peripheral contrast threshold for various and different wavelengths for adapting field and test stimulus,” J. Opt. Soc. Am. 42, 820–831 (1952).
[CrossRef] [PubMed]

M. A. Bouman, “Mechanisms in peripheral dark adaptation,” J. Opt. Soc. Am. 42, 941–950 (1952).
[CrossRef] [PubMed]

M. A. Bouman, G. van den Brink, “Absolute threshold for moving point sources,” J. Opt. Soc. Am. 43, 895–898 (1953).
[CrossRef] [PubMed]

M. A. Bouman, “Absolute threshold conditions for visual perception,” J. Opt. Soc. Am. 45, 36–43 (1955).
[CrossRef] [PubMed]

G. van den Brink, M. A. Bouman, “Visual contrast thresholds for moving point sources,” J. Opt. Soc. Am. 47, 612–618 (1957).
[CrossRef] [PubMed]

G. J. C. van der Horst, M. A. Bouman, “Spatiotemporal chromaticity discrimination,” J. Opt. Soc. Am. 59, 1482–1488 (1969).
[CrossRef] [PubMed]

G. Westheimer, K. Shimamura, S. P. McKee, “Interference with line-orientation sensitivity,” J. Opt. Soc. Am. 66, 332–338 (1976).
[CrossRef] [PubMed]

C. Noorlander, J. J. Koenderink, “Spatial and temporal discrimination ellipsoids in colour space,” J. Opt. Soc. Am. 73, 1533–1544 (1983).
[CrossRef] [PubMed]

S. A. Burns, A. E. Elsner, “Color matching at high luminance: photopigment optical density and pupil entry,” J. Opt. Soc. Am. 10, 221–230 (1993).
[CrossRef]

J. Opt. Soc. Am. A

Kybernetik

W. A. van de Grind, J. J. Koenderink, M. A. Bouman, “Models of the processing of quantum signals by the human peripheral retina,” Kybernetik 6, 213–227 (1970).
[CrossRef] [PubMed]

W. A. van de Grind, M. A. Bouman, “A model of a retinal sampling-unit based on fluctuation theory,” Kybernetik 4, 136–141 (1968).
[CrossRef] [PubMed]

Ophthalmologica

M. A. Bouman, J. ten Doesschate, “Nervous and photochemical components in visual adaptation,” Ophthalmologica 126, 222–230 (1953).
[CrossRef] [PubMed]

Opt. Acta

M. A. Bouman, “On foveal and peripheral interaction in binocular vision,” Opt. Acta 1, 177–183 (1955).
[CrossRef]

Perception

A. Roorda, D. R. Williams, G. Y. Yoon, Y. Yamanchi, “The eye optics, the trichromatic cone mosaic and human vision,” Perception 29, Suppl. 43 (2000).

Q. Rev. Biophys.

M. A. Bouman, “My image of the retina,” Q. Rev. Biophys. 2, 25–64 (1969).
[CrossRef] [PubMed]

Rev. Physiol.

M. A. Bouman, J. J. Koenderink, “Psychophysical basis of coincidence mechanisms in the human visual system,” Rev. Physiol. 65, 126–173 (1972).

Vision Res.

G. J. C. van der Horst, M. A. Bouman, “On searching for “Mach band type” phenomena in colour vision,” Vision Res. 7, 1027–1029 (1967).
[CrossRef] [PubMed]

Other

W. Reichardt, “Autocorrelation, a principle for the evaluation of sensory information by the central nervous system,” in Sensory Communication, W. A. Rosenblith, ed., (MIT Press, Cambridge, Mass., 1961), pp. 303–319.

F. Ratliff, “Some inter-relations among physics, physiology and psychology in the study of vision,” in Psychology: a Study of a Science (McGraw Hill, New York, 1962), Vol. 4, pp. 417–482.

H. B. Barlow, W. R. Levick, “Coding of light intensity by the cat retina,” in Proceedings of the International School of Physics “Enrico Fermi” (Academic, New York, 1969), pp. 384–396.

M. A. Bouman, C. G. F. Ampt, “Fluctuation theory in vision and its mechanistic model,” in Performance of the Eye at Low Luminances, Vol. 125 of Excerpta Medica, International Congressional Series (Excerpta Medica, Amsterdam, 1965), pp. 57–69.

M. A. Bouman, “Quanta noise and vision,” in Theoretical Physics and Biology (North-Holland, Amsterdam, 1969), pp. 246–250.

J. J. Koenderink, “The concept of local sign,” in Limits in Perception, A. J. van Doorn, W. A. van de Grind, J. J. Koenderink, eds. (VNU Science Press, Utrecht, The Netherlands, 1984).

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Figures (7)

Fig. 1
Fig. 1

(a) Index of relative summation f(t, 0) of subliminal excitations in the two flashes, each lasting 0.01 seconds and subtending geometrically 2 min of arc, from a green pair as a function of the interval t between them. Results are given B=0 in the dark and for B=5×10-1 W/sr m2 on a green background in the fovea. The results for other retinal locations and for test stimuli with different backgrounds and other color combinations are the same as (a). (b) Same as in (a) but as a function f(0, d) of the distance d between the two flashes on the retina. The results for other combinations of colors of test stimulus and background and for other intensities of background in the fovea are similar to the results in (b). (c) Same as in (b), f(0, d) at 7 deg eccentricity nasal from the fovea, for green flashes in the dark and on a green background 5×10-1 W/sr m2. (Data are from the Ph.D. thesis of G. van den Brink, Utrecht University, Utrecht, The Netherlands, 1957); see also Ref. 5.

Fig. 2
Fig. 2

Total average number of receptor responses of the 50% probability N0 (50), as a function of AT or of LT and in each frame from bottom to top curve, that (1) at least one extra k package of receptor responses will occur in a twin unit’s half in formula (1), and (2) light from the test stimulus will be perceived as in formula (2), and (3) movement or edge will be perceived from the thin line moving at speed v=λ/τ as in formula (5) for S=1, and (4) as in (3) but for S=2 in formula (5). N0 (50) is given as a function of AT or LT when k=1, 4, and 16.

Fig. 3
Fig. 3

(a) Threshold energy of a green point source moving at 7 deg concentrically around the fovea, as a function of the length of the track L that is equal to the duration T times the speed v: L=vT, against a green background of intensity 5×10-1 W/sr m2 and in the dark. (b) Threshold energy of a green point-shaped flash of 0.01 seconds at 7 deg eccentricity nasal from the fovea (curve I) and of a green point source that moves for 1 second over a length of track of 640 min of arc (curve II), both expressed as a function of the intensity of the green background. From G. van den Brink, Ph.D. Thesis, Utrecht University, Utrecht, The Netherlands, (1957); see also Refs. 5 and 6.

Fig. 4
Fig. 4

Numbers kR, kG of receptor responses that the de Vries–Weber tandems need for an extra excitation in a twin unit’s half; as a function of the intensity log(R+G+r)=-1 ,+6; R, G, and r are the number of quanta per period τ in a red cone, a green cone and P rods, for three spectral energy distributions: (a) R=4G=8r, (b) R=G=r, (c) 4R=G=16r, for P=0 and P=64 in formulas (3) and (4).

Fig. 5
Fig. 5

Lowest modulation thresholds of moving sine-wave patterns, irrespective of temporal or spatial frequency, as a function of the width of the field, the light of dominant wavelength 582 nm being modulated either in intensity M% (closed circles) or in the wavelength’s red–green direction M nm (open circles), intensity level 350 trolands. From C. Noorlander, Ph.D. thesis, Utrecht University, Utrecht, The Netherlands, 1981; see also Refs. 3 and 27.

Fig. 6
Fig. 6

Threshold energy in relative units as a function of time during dark adaptation after exposure of the retina to bright daylight; green and circular test flashes with diameter in minutes of arc as parameter. The amplitude of variation is larger for larger diameters, which demonstrates the decrease in k of the de Vries gain control. After Ref. 4, also formula (4).

Fig. 7
Fig. 7

Perfect retinal mosaic: two blades of red twin units on a clockwise and a counterclockwise spiral, one blade of green twin units on circles concentric around the fovea; for the mediation of yellow by cross-pairings between red and green cones, the blades are connected at locations where their twin units intertwine. For its direction events each twin has two fibers in the optic nerve, one for each of its two polarities. For its color signals each trion has four fibers in the optic nerve; one for each of the colors red, yellow, and green and one for the rod’s white.

Equations (26)

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w(N0)=1-[P(N0)]4AT,
P(N0)=exp(-N0/4AT)0(k-1)(1/p!)(N0/4AT)p;
k1,integer.
W(N0)=1-1-{1-[P(N00)]2}2AT.
R0=R[1-exp(-4/R)];
G0=G[1-exp(-4/G)]; r0=r[exp(-4P/r)]
kR=1/2+1/4+R0+r0;
kG=1/2+1/4+G0+r0;
kR, kG1,integerandkB=1
W(N0)=1-(1-[1-(P(N0))2]2+[1-(P(N0))2]2 {1-[1-(P(N0))2]S}6)LT,
S=2,TandL3.
K=12[(K1+1)(K2+1)]1/2=n1/k1=n2/k2;
K1=1/2+1/4+n1;K2=1/2+1/4+n2.
K=[K1K2]1/2,
1-w(N0)=1-x1+x22!- 1+x1+x22!++x(k-1)(k-1)!4AT;
x=N0/4AT
=1-xkk!+kxk+1(k+1)!-k(k+1)x(k+2)2!(k+2)!+4AT,
1-W(N0){1-[1-exp(-xk)/k!]2}AT[1-x2k/(k!)2]AT,
N0(50)(AT)(2k-1)/2k.
W(N0)=1-}1-[1-(P(N0))2]2}LT;
P(N0)=exp(-N0/4LT)0k-11/p!N04LTp;
L1,T1.
W(R0, G0, r0)=1-{1-[1-(P(R0, r0))2]2}2AT{1-[1-(P(G0, r0))2]2}AT
P(R0, r0)=expR08AT+r012AT0kR-1(1/p!)×R08AT+r012ATp
R=1232+14+R11-exp-4R1+r11-exp-4Pr11/2×32+14+R21-exp-4R2+r21-exp-4Pr21/2.
k1R=1/R{R1[1-exp-(4/R1)]+r1[1-exp-(4P/r1)]}.

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