Abstract

This discussion paper seeks to reshape the contemporary understanding of visual adaptation. Received wisdom says that input luminance is scaled down in the retina. There is, first, a near-logarithmic compression described by the Naka–Rushton equation and, second, a control of gain (better attenuation) by feedback from the output of each ganglion cell that is equivalent to modifying the half-saturation constant in the Naka–Rushton equation. The reinterpretation proposed here asserts the following instead: (a) the scaling down in the retina is accomplished by receptive fields of different areas, which function over different ranges of luminance, ranges inversely proportional to the area of the receptive field. (b) The visual pathway is differentially coupled to the physical stimulus, so that the maintained discharge increases only as the square root of the luminance. (c) The Naka–Rushton equation describes merely the saturation of neural response as input increases; when a neuron is overloaded, output tends to regularity and onward transmission is blocked by a subsequent stage of differential coupling. Three existing studies of the relation between input to and output from retinal ganglion cells are reinterpreted in the light of this alternative view of visual adaptation.

© 2013 Optical Society of America

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    [CrossRef]
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2013 (1)

2012 (1)

B. Scholl, K. W. Latimer, and N. J. Priebe, “A retinal source of spatial contrast gain control,” J. Neurosci. 32, 9824–9830 (2012).
[CrossRef]

2010 (3)

D. Laming, “Fechner’s law: where does the log transform come from?” Seeing Perceiving 23, 155–171 (2010).

J. Cafaro and F. Rieke, “Noise correlations improve response fidelity and stimulus encoding,” Nature 468, 964–967 (2010).
[CrossRef]

D. Laming, “Statistical information and uncertainty: a critique of applications in experimental psychology,” Entropy 12, 720–771 (2010).
[CrossRef]

2008 (1)

D. L. Beaudoin, M. B. Manookin, and J. B. Demb, “Distinct expression of contrast gain control in parallel synaptic pathways converging on a retinal ganglion cell,” J. Physiol. 586, 5487–5502 (2008).
[CrossRef]

2007 (1)

D. L. Beaudoin, B. G. Borghuis, and J. B. Demb, “Cellular basis for contrast gain control over the receptive field center of mammalian retinal ganglion cells,” J. Neurosci. 27, 2636–2645 (2007).
[CrossRef]

2006 (1)

V. Bonin, V. Mante, and M. Carandini, “The statistical computation underlying contrast gain control,” J. Neurosci. 26, 6346–6353 (2006).
[CrossRef]

2001 (1)

E. S. Yamada, L. C. L. Silveira, V. H. Perry, and E. C. S. Franco, “M and P retinal ganglion cells of the owl monkey: morphology, size and photoreceptor convergence,” Vis. Res. 41, 119–131 (2001), Fig. 6, p. 126.
[CrossRef]

1998 (1)

A. Reeves, S. Wu, and T. J. Schirillo, “The effect of photon noise on the detection of white flashes,” Vis. Res. 38, 691–703 (1998).
[CrossRef]

1997 (1)

M. E. Rudd and L. G. Brown, “A model of Weber and noise gain control in the retina of the toad Bufo marinus,” Vis. Res. 37, 2433–2453 (1997).
[CrossRef]

1993 (1)

D. M. Dacey, “The mosaic of midget ganglion cells in the human retina,” J. Neurosci. 13, 5334–5355 (1993).

1992 (1)

C. R. Cavonius, O. Estévez, and L. H. van der Tweel, “Counterphase dichoptic flicker is seen as its own second harmonic,” Ophthalmic Physiolog. Opt. 12, 153–156 (1992).
[CrossRef]

1986 (2)

R. F. Hess and K. Nordby, “Spatial and temporal limits of vision in the achromat,” J. Physiol. 371, 365–385 (1986).

R. F. Hess and K. Nordby, “Spatial and temporal properties of human rod vision in the achromat,” J. Physiol. 371, 387–406 (1986).

1984 (1)

R. Shapley and C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retin. Res. 3, 263–346 (1984).
[CrossRef]

1983 (1)

M. J. Valeton and D. van Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vis. Res. 231539–1547 (1983).
[CrossRef]

1982 (2)

S. M. Dawis and R. L. Purple, “Adaptation in cones: a general model,” Biophys. J. 39, 151–155 (1982).
[CrossRef]

R. A. Linsenmeier, L. J. Frishman, H. G. Jakiela, and C. Enroth-Cugell, “Receptive field properties of X and Y cells in the cat retina derived from contrast sensitivity measurements,” Vis. Res. 22, 1173–1183 (1982).
[CrossRef]

1981 (1)

T. D. Lamb, “The involvement of rod photoreceptors in dark adaptation,” Vis. Res. 21, 1773–1782 (1981).
[CrossRef]

1979 (3)

G. E. Legge, “Spatial frequency masking in human vision: Binocular interactions,” J. Opt. Soc. Am. 69, 838–847 (1979).
[CrossRef]

C. R. Cavonius, “Binocular interactions in flicker,” Quart. J. Exp. Psychol. 31, 273–280 (1979).
[CrossRef]

W. S. Geisler, “Evidence for the equivalent-background hypothesis in cones,” Vis. Res. 19, 799–805 (1979).
[CrossRef]

1978 (2)

W. S. Geisler, “The effects of photopigment depletion on brightness and threshold,” Vis. Res. 18, 269–278 (1978).
[CrossRef]

W. S. Geisler, “Adaptation, afterimages and cone saturation,” Vis. Res. 18, 279–289 (1978).
[CrossRef]

1977 (1)

D. H. Hubel and T. N. Wiesel, “Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. Lond. Ser. B 198, 1–59 (1977).
[CrossRef]

1976 (1)

H. B. Barlow and W. R. Levick, “Threshold setting by the surround of cat retinal ganglion cells,” J. Physiol. 259, 737–757 (1976).

1975 (1)

C. Enroth-Cugell and P. Lennie, “The control of retinal ganglion cell discharge by receptive field surrounds,” J. Physiol. 247, 551–578 (1975).

1974 (1)

J. Nachmias and R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vis. Res. 14, 1039–1042 (1974).
[CrossRef]

1973 (1)

C. Enroth-Cugell and R. M. Shapley, “Flux, not retinal illumination, is what cat retinal ganglion cells really care about,” J. Physiol. 233, 311–326 (1973).

1972 (1)

C. Enroth-Cugell and L. H. Pinto, “Properties of the surround response mechanism of cat retinal ganglion cells and centre-surround interaction,” J. Physiol. 220, 403–439 (1972).

1971 (1)

H. B. Barlow, W. R. Levick, and M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vis. Res. 11, 87–101 (1971).
[CrossRef]

1969 (3)

H. B. Barlow and W. R. Levick, “Changes in the maintained discharge with adaptation level in the cat retina,” J. Physiol. 202, 699–718 (1969).

B. Sakmann and O. D. Creutzfeldt, “Scotopic and mesopic light adaptation in the cat’s retina,” Pflugers Archiv 313, 168–185 (1969).

C. Blakemore and F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969).

1968 (1)

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).

1967 (1)

R. W. Rodieck, “Maintained activity of cat retinal ganglion cells,” J. Neurophysiol. 30, 1043–1070 (1967), Fig. 4, p. 1050.

1966 (3)

K.-I. Naka and W. A. H. Rushton, “S-potentials from luminosity units in the retina of fish (Cyprinidae),” J. Physiol. 185, 587–599 (1966).

C. Enroth-Cugell and J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. 157, 517–552 (1966).

G. W. Hughes and L. Maffei, “Retinal ganglion cell response to sinusoidal light stimulation,” J. Neurophysiol. 29, 333–352 (1966).

1965 (3)

R. W. Rodieck and J. Stone, “Analysis of receptive fields of cat retinal ganglion cells,” J. Neurophysiol. 28, 833–849 (1965).

F. W. Campbell and D. G. Green, “Monocular versus binocular visual acuity,” Nature 208, 191–192 (1965).
[CrossRef]

W. A. H. Rushton, “The Ferrier lecture, 1962. Visual adaptation,” Proc. R. Soc. Lond. B 162, 20–46 (1965).
[CrossRef]

1961 (2)

W. A. H. Rushton, “Rhodopsin measurement and dark-adaptation in a subject deficient in cone vision,” J. Physiol. 156, 193–205 (1961).

E. G. Heinemann, “The relation of apparent brightness to the threshold for differences in luminance,” J. Exp. Psychol. 61, 389–399 (1961).
[CrossRef]

1957 (2)

S. W. Kuffler, R. Fitzhugh, and H. B. Barlow, “Maintained activity in the cat’s retina in light and darkness,” J. Gen. Physiol. 40, 683–702 (1957).
[CrossRef]

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, “Change of organization in the receptive fields of the cat’s retina during dark adaptation,” J. Physiol. 137, 338–354 (1957).

1955 (1)

E. G. Heinemann, “Simultaneous brightness induction as a function of inducing- and test-field luminances,” J. Exp. Psychol. 50, 89–96 (1955).
[CrossRef]

1948 (1)

1947 (1)

B. H. Crawford, “Visual adaptation in relation to brief conditioning stimuli,” Proc. R. Soc. B 134, 283–302 (1947).
[CrossRef]

Barlow, H. B.

H. B. Barlow and W. R. Levick, “Threshold setting by the surround of cat retinal ganglion cells,” J. Physiol. 259, 737–757 (1976).

H. B. Barlow, W. R. Levick, and M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vis. Res. 11, 87–101 (1971).
[CrossRef]

H. B. Barlow and W. R. Levick, “Changes in the maintained discharge with adaptation level in the cat retina,” J. Physiol. 202, 699–718 (1969).

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, “Change of organization in the receptive fields of the cat’s retina during dark adaptation,” J. Physiol. 137, 338–354 (1957).

S. W. Kuffler, R. Fitzhugh, and H. B. Barlow, “Maintained activity in the cat’s retina in light and darkness,” J. Gen. Physiol. 40, 683–702 (1957).
[CrossRef]

Beaudoin, D. L.

D. L. Beaudoin, M. B. Manookin, and J. B. Demb, “Distinct expression of contrast gain control in parallel synaptic pathways converging on a retinal ganglion cell,” J. Physiol. 586, 5487–5502 (2008).
[CrossRef]

D. L. Beaudoin, B. G. Borghuis, and J. B. Demb, “Cellular basis for contrast gain control over the receptive field center of mammalian retinal ganglion cells,” J. Neurosci. 27, 2636–2645 (2007).
[CrossRef]

Blakemore, C.

C. Blakemore and F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969).

Bonin, V.

V. Bonin, V. Mante, and M. Carandini, “The statistical computation underlying contrast gain control,” J. Neurosci. 26, 6346–6353 (2006).
[CrossRef]

Borghuis, B. G.

D. L. Beaudoin, B. G. Borghuis, and J. B. Demb, “Cellular basis for contrast gain control over the receptive field center of mammalian retinal ganglion cells,” J. Neurosci. 27, 2636–2645 (2007).
[CrossRef]

Brown, L. G.

M. E. Rudd and L. G. Brown, “A model of Weber and noise gain control in the retina of the toad Bufo marinus,” Vis. Res. 37, 2433–2453 (1997).
[CrossRef]

Cafaro, J.

J. Cafaro and F. Rieke, “Noise correlations improve response fidelity and stimulus encoding,” Nature 468, 964–967 (2010).
[CrossRef]

Campbell, F. W.

C. Blakemore and F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969).

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).

F. W. Campbell and D. G. Green, “Monocular versus binocular visual acuity,” Nature 208, 191–192 (1965).
[CrossRef]

Carandini, M.

V. Bonin, V. Mante, and M. Carandini, “The statistical computation underlying contrast gain control,” J. Neurosci. 26, 6346–6353 (2006).
[CrossRef]

Cavonius, C. R.

C. R. Cavonius, O. Estévez, and L. H. van der Tweel, “Counterphase dichoptic flicker is seen as its own second harmonic,” Ophthalmic Physiolog. Opt. 12, 153–156 (1992).
[CrossRef]

C. R. Cavonius, “Binocular interactions in flicker,” Quart. J. Exp. Psychol. 31, 273–280 (1979).
[CrossRef]

Cornsweet, T. N.

T. N. Cornsweet, Visual Perception (Academic, 1970).

Crawford, B. H.

B. H. Crawford, “Visual adaptation in relation to brief conditioning stimuli,” Proc. R. Soc. B 134, 283–302 (1947).
[CrossRef]

Creutzfeldt, O. D.

B. Sakmann and O. D. Creutzfeldt, “Scotopic and mesopic light adaptation in the cat’s retina,” Pflugers Archiv 313, 168–185 (1969).

Dacey, D. M.

D. M. Dacey, “The mosaic of midget ganglion cells in the human retina,” J. Neurosci. 13, 5334–5355 (1993).

Davenport, W. B.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, 1958), Chaps. 8 and 9.

Dawis, S. M.

S. M. Dawis and R. L. Purple, “Adaptation in cones: a general model,” Biophys. J. 39, 151–155 (1982).
[CrossRef]

Demb, J. B.

D. L. Beaudoin, M. B. Manookin, and J. B. Demb, “Distinct expression of contrast gain control in parallel synaptic pathways converging on a retinal ganglion cell,” J. Physiol. 586, 5487–5502 (2008).
[CrossRef]

D. L. Beaudoin, B. G. Borghuis, and J. B. Demb, “Cellular basis for contrast gain control over the receptive field center of mammalian retinal ganglion cells,” J. Neurosci. 27, 2636–2645 (2007).
[CrossRef]

Enroth-Cugell, C.

R. Shapley and C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retin. Res. 3, 263–346 (1984).
[CrossRef]

R. A. Linsenmeier, L. J. Frishman, H. G. Jakiela, and C. Enroth-Cugell, “Receptive field properties of X and Y cells in the cat retina derived from contrast sensitivity measurements,” Vis. Res. 22, 1173–1183 (1982).
[CrossRef]

C. Enroth-Cugell and P. Lennie, “The control of retinal ganglion cell discharge by receptive field surrounds,” J. Physiol. 247, 551–578 (1975).

C. Enroth-Cugell and R. M. Shapley, “Flux, not retinal illumination, is what cat retinal ganglion cells really care about,” J. Physiol. 233, 311–326 (1973).

C. Enroth-Cugell and L. H. Pinto, “Properties of the surround response mechanism of cat retinal ganglion cells and centre-surround interaction,” J. Physiol. 220, 403–439 (1972).

C. Enroth-Cugell and J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. 157, 517–552 (1966).

Estévez, O.

C. R. Cavonius, O. Estévez, and L. H. van der Tweel, “Counterphase dichoptic flicker is seen as its own second harmonic,” Ophthalmic Physiolog. Opt. 12, 153–156 (1992).
[CrossRef]

Fitzhugh, R.

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, “Change of organization in the receptive fields of the cat’s retina during dark adaptation,” J. Physiol. 137, 338–354 (1957).

S. W. Kuffler, R. Fitzhugh, and H. B. Barlow, “Maintained activity in the cat’s retina in light and darkness,” J. Gen. Physiol. 40, 683–702 (1957).
[CrossRef]

Franco, E. C. S.

E. S. Yamada, L. C. L. Silveira, V. H. Perry, and E. C. S. Franco, “M and P retinal ganglion cells of the owl monkey: morphology, size and photoreceptor convergence,” Vis. Res. 41, 119–131 (2001), Fig. 6, p. 126.
[CrossRef]

Frishman, L. J.

R. A. Linsenmeier, L. J. Frishman, H. G. Jakiela, and C. Enroth-Cugell, “Receptive field properties of X and Y cells in the cat retina derived from contrast sensitivity measurements,” Vis. Res. 22, 1173–1183 (1982).
[CrossRef]

Geisler, W. S.

W. S. Geisler, “Evidence for the equivalent-background hypothesis in cones,” Vis. Res. 19, 799–805 (1979).
[CrossRef]

W. S. Geisler, “The effects of photopigment depletion on brightness and threshold,” Vis. Res. 18, 269–278 (1978).
[CrossRef]

W. S. Geisler, “Adaptation, afterimages and cone saturation,” Vis. Res. 18, 279–289 (1978).
[CrossRef]

Green, D. G.

F. W. Campbell and D. G. Green, “Monocular versus binocular visual acuity,” Nature 208, 191–192 (1965).
[CrossRef]

Heinemann, E. G.

E. G. Heinemann, “The relation of apparent brightness to the threshold for differences in luminance,” J. Exp. Psychol. 61, 389–399 (1961).
[CrossRef]

E. G. Heinemann, “Simultaneous brightness induction as a function of inducing- and test-field luminances,” J. Exp. Psychol. 50, 89–96 (1955).
[CrossRef]

Hess, R. F.

R. F. Hess and K. Nordby, “Spatial and temporal limits of vision in the achromat,” J. Physiol. 371, 365–385 (1986).

R. F. Hess and K. Nordby, “Spatial and temporal properties of human rod vision in the achromat,” J. Physiol. 371, 387–406 (1986).

Hood, D. C.

D. C. Hood, “Psychophysical and physiological tests of physiological explanations of light adaptation,” in Visual Psychophysics: Its Physiological Basis, J. Armington, J. Krauskopf, and B. Wooten, eds. (Academic, 1978), pp. 141–155.

Hubel, D. H.

D. H. Hubel and T. N. Wiesel, “Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. Lond. Ser. B 198, 1–59 (1977).
[CrossRef]

Hughes, G. W.

G. W. Hughes and L. Maffei, “Retinal ganglion cell response to sinusoidal light stimulation,” J. Neurophysiol. 29, 333–352 (1966).

Jakiela, H. G.

R. A. Linsenmeier, L. J. Frishman, H. G. Jakiela, and C. Enroth-Cugell, “Receptive field properties of X and Y cells in the cat retina derived from contrast sensitivity measurements,” Vis. Res. 22, 1173–1183 (1982).
[CrossRef]

Kuffler, S. W.

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, “Change of organization in the receptive fields of the cat’s retina during dark adaptation,” J. Physiol. 137, 338–354 (1957).

S. W. Kuffler, R. Fitzhugh, and H. B. Barlow, “Maintained activity in the cat’s retina in light and darkness,” J. Gen. Physiol. 40, 683–702 (1957).
[CrossRef]

Lamb, T. D.

T. D. Lamb, “The involvement of rod photoreceptors in dark adaptation,” Vis. Res. 21, 1773–1782 (1981).
[CrossRef]

Laming, D.

D. Laming, “Probability summation—a critique,” J. Opt. Soc. Am. A 30, 300–315 (2013).
[CrossRef]

D. Laming, “Statistical information and uncertainty: a critique of applications in experimental psychology,” Entropy 12, 720–771 (2010).
[CrossRef]

D. Laming, “Fechner’s law: where does the log transform come from?” Seeing Perceiving 23, 155–171 (2010).

D. Laming, Sensory Analysis (Academic, 1986).

D. Laming, “Contrast sensitivity,” in Vision and Visual Dysfunction, J. J. Kulikowski, V. Walsh, and I. J. Murray, eds., Vol. 5 of Limits of Visual Perception (Macmillan, 1991), pp. 38–39.

D. Laming, “Spatial frequency channels,” in Vision and Visual Dysfunction, J. J. Kulikowski, V. Walsh, and I. J. Murray, eds., Vol. 5 of Limits of Visual Perception (Macmillan, 1991), pp. 97–105.

D. Laming, The Measurement of Sensation (Oxford, 1997), Chap. 6, pp. 83–86 and Chap. 7, 104–105.

D. Laming, Human Judgment: The Eye of the Beholder (Thomson Learning, 2004).

Latimer, K. W.

B. Scholl, K. W. Latimer, and N. J. Priebe, “A retinal source of spatial contrast gain control,” J. Neurosci. 32, 9824–9830 (2012).
[CrossRef]

Legge, G. E.

Lennie, P.

C. Enroth-Cugell and P. Lennie, “The control of retinal ganglion cell discharge by receptive field surrounds,” J. Physiol. 247, 551–578 (1975).

Levick, W. R.

H. B. Barlow and W. R. Levick, “Threshold setting by the surround of cat retinal ganglion cells,” J. Physiol. 259, 737–757 (1976).

H. B. Barlow, W. R. Levick, and M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vis. Res. 11, 87–101 (1971).
[CrossRef]

H. B. Barlow and W. R. Levick, “Changes in the maintained discharge with adaptation level in the cat retina,” J. Physiol. 202, 699–718 (1969).

Linsenmeier, R. A.

R. A. Linsenmeier, L. J. Frishman, H. G. Jakiela, and C. Enroth-Cugell, “Receptive field properties of X and Y cells in the cat retina derived from contrast sensitivity measurements,” Vis. Res. 22, 1173–1183 (1982).
[CrossRef]

Maffei, L.

G. W. Hughes and L. Maffei, “Retinal ganglion cell response to sinusoidal light stimulation,” J. Neurophysiol. 29, 333–352 (1966).

Manookin, M. B.

D. L. Beaudoin, M. B. Manookin, and J. B. Demb, “Distinct expression of contrast gain control in parallel synaptic pathways converging on a retinal ganglion cell,” J. Physiol. 586, 5487–5502 (2008).
[CrossRef]

Mante, V.

V. Bonin, V. Mante, and M. Carandini, “The statistical computation underlying contrast gain control,” J. Neurosci. 26, 6346–6353 (2006).
[CrossRef]

Nachmias, J.

J. Nachmias and R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vis. Res. 14, 1039–1042 (1974).
[CrossRef]

Naka, K.-I.

K.-I. Naka and W. A. H. Rushton, “S-potentials from luminosity units in the retina of fish (Cyprinidae),” J. Physiol. 185, 587–599 (1966).

Nordby, K.

R. F. Hess and K. Nordby, “Spatial and temporal limits of vision in the achromat,” J. Physiol. 371, 365–385 (1986).

R. F. Hess and K. Nordby, “Spatial and temporal properties of human rod vision in the achromat,” J. Physiol. 371, 387–406 (1986).

Perry, V. H.

E. S. Yamada, L. C. L. Silveira, V. H. Perry, and E. C. S. Franco, “M and P retinal ganglion cells of the owl monkey: morphology, size and photoreceptor convergence,” Vis. Res. 41, 119–131 (2001), Fig. 6, p. 126.
[CrossRef]

Pinto, L. H.

C. Enroth-Cugell and L. H. Pinto, “Properties of the surround response mechanism of cat retinal ganglion cells and centre-surround interaction,” J. Physiol. 220, 403–439 (1972).

Priebe, N. J.

B. Scholl, K. W. Latimer, and N. J. Priebe, “A retinal source of spatial contrast gain control,” J. Neurosci. 32, 9824–9830 (2012).
[CrossRef]

Purple, R. L.

S. M. Dawis and R. L. Purple, “Adaptation in cones: a general model,” Biophys. J. 39, 151–155 (1982).
[CrossRef]

Reeves, A.

A. Reeves, S. Wu, and T. J. Schirillo, “The effect of photon noise on the detection of white flashes,” Vis. Res. 38, 691–703 (1998).
[CrossRef]

Rieke, F.

J. Cafaro and F. Rieke, “Noise correlations improve response fidelity and stimulus encoding,” Nature 468, 964–967 (2010).
[CrossRef]

Riggs, L. A.

L. A. Riggs, “Light as a stimulus for vision,” in Vision and Visual Perception, C. H. Graham, ed. (Wiley, 1965), pp. 1–38.

Robson, J. G.

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).

C. Enroth-Cugell and J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. 157, 517–552 (1966).

Rodieck, R. W.

R. W. Rodieck, “Maintained activity of cat retinal ganglion cells,” J. Neurophysiol. 30, 1043–1070 (1967), Fig. 4, p. 1050.

R. W. Rodieck and J. Stone, “Analysis of receptive fields of cat retinal ganglion cells,” J. Neurophysiol. 28, 833–849 (1965).

Root, W. L.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, 1958), Chaps. 8 and 9.

Rose, A.

Rudd, M. E.

M. E. Rudd and L. G. Brown, “A model of Weber and noise gain control in the retina of the toad Bufo marinus,” Vis. Res. 37, 2433–2453 (1997).
[CrossRef]

Rushton, W. A. H.

K.-I. Naka and W. A. H. Rushton, “S-potentials from luminosity units in the retina of fish (Cyprinidae),” J. Physiol. 185, 587–599 (1966).

W. A. H. Rushton, “The Ferrier lecture, 1962. Visual adaptation,” Proc. R. Soc. Lond. B 162, 20–46 (1965).
[CrossRef]

W. A. H. Rushton, “Rhodopsin measurement and dark-adaptation in a subject deficient in cone vision,” J. Physiol. 156, 193–205 (1961).

Ryle, G.

G. Ryle, The Concept of Mind (Hutchinson, 1949).

Sakmann, B.

B. Sakmann and O. D. Creutzfeldt, “Scotopic and mesopic light adaptation in the cat’s retina,” Pflugers Archiv 313, 168–185 (1969).

Sansbury, R. V.

J. Nachmias and R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vis. Res. 14, 1039–1042 (1974).
[CrossRef]

Schirillo, T. J.

A. Reeves, S. Wu, and T. J. Schirillo, “The effect of photon noise on the detection of white flashes,” Vis. Res. 38, 691–703 (1998).
[CrossRef]

Scholl, B.

B. Scholl, K. W. Latimer, and N. J. Priebe, “A retinal source of spatial contrast gain control,” J. Neurosci. 32, 9824–9830 (2012).
[CrossRef]

Shapley, R.

R. Shapley and C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retin. Res. 3, 263–346 (1984).
[CrossRef]

Shapley, R. M.

C. Enroth-Cugell and R. M. Shapley, “Flux, not retinal illumination, is what cat retinal ganglion cells really care about,” J. Physiol. 233, 311–326 (1973).

Silveira, L. C. L.

E. S. Yamada, L. C. L. Silveira, V. H. Perry, and E. C. S. Franco, “M and P retinal ganglion cells of the owl monkey: morphology, size and photoreceptor convergence,” Vis. Res. 41, 119–131 (2001), Fig. 6, p. 126.
[CrossRef]

Stone, J.

R. W. Rodieck and J. Stone, “Analysis of receptive fields of cat retinal ganglion cells,” J. Neurophysiol. 28, 833–849 (1965).

Valeton, M. J.

M. J. Valeton and D. van Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vis. Res. 231539–1547 (1983).
[CrossRef]

van der Tweel, L. H.

C. R. Cavonius, O. Estévez, and L. H. van der Tweel, “Counterphase dichoptic flicker is seen as its own second harmonic,” Ophthalmic Physiolog. Opt. 12, 153–156 (1992).
[CrossRef]

van Nes, F. L.

F. L. van Nes, “Experimental studies in spatiotemporal contrast transfer by the human eye,” Doctoral thesis (Utrecht University, 1968).

van Norren, D.

M. J. Valeton and D. van Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vis. Res. 231539–1547 (1983).
[CrossRef]

Wiesel, T. N.

D. H. Hubel and T. N. Wiesel, “Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. Lond. Ser. B 198, 1–59 (1977).
[CrossRef]

Wu, S.

A. Reeves, S. Wu, and T. J. Schirillo, “The effect of photon noise on the detection of white flashes,” Vis. Res. 38, 691–703 (1998).
[CrossRef]

Yamada, E. S.

E. S. Yamada, L. C. L. Silveira, V. H. Perry, and E. C. S. Franco, “M and P retinal ganglion cells of the owl monkey: morphology, size and photoreceptor convergence,” Vis. Res. 41, 119–131 (2001), Fig. 6, p. 126.
[CrossRef]

Yoon, M.

H. B. Barlow, W. R. Levick, and M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vis. Res. 11, 87–101 (1971).
[CrossRef]

Biophys. J. (1)

S. M. Dawis and R. L. Purple, “Adaptation in cones: a general model,” Biophys. J. 39, 151–155 (1982).
[CrossRef]

Entropy (1)

D. Laming, “Statistical information and uncertainty: a critique of applications in experimental psychology,” Entropy 12, 720–771 (2010).
[CrossRef]

J. Exp. Psychol. (2)

E. G. Heinemann, “Simultaneous brightness induction as a function of inducing- and test-field luminances,” J. Exp. Psychol. 50, 89–96 (1955).
[CrossRef]

E. G. Heinemann, “The relation of apparent brightness to the threshold for differences in luminance,” J. Exp. Psychol. 61, 389–399 (1961).
[CrossRef]

J. Gen. Physiol. (1)

S. W. Kuffler, R. Fitzhugh, and H. B. Barlow, “Maintained activity in the cat’s retina in light and darkness,” J. Gen. Physiol. 40, 683–702 (1957).
[CrossRef]

J. Neurophysiol. (3)

R. W. Rodieck, “Maintained activity of cat retinal ganglion cells,” J. Neurophysiol. 30, 1043–1070 (1967), Fig. 4, p. 1050.

R. W. Rodieck and J. Stone, “Analysis of receptive fields of cat retinal ganglion cells,” J. Neurophysiol. 28, 833–849 (1965).

G. W. Hughes and L. Maffei, “Retinal ganglion cell response to sinusoidal light stimulation,” J. Neurophysiol. 29, 333–352 (1966).

J. Neurosci. (4)

V. Bonin, V. Mante, and M. Carandini, “The statistical computation underlying contrast gain control,” J. Neurosci. 26, 6346–6353 (2006).
[CrossRef]

B. Scholl, K. W. Latimer, and N. J. Priebe, “A retinal source of spatial contrast gain control,” J. Neurosci. 32, 9824–9830 (2012).
[CrossRef]

D. L. Beaudoin, B. G. Borghuis, and J. B. Demb, “Cellular basis for contrast gain control over the receptive field center of mammalian retinal ganglion cells,” J. Neurosci. 27, 2636–2645 (2007).
[CrossRef]

D. M. Dacey, “The mosaic of midget ganglion cells in the human retina,” J. Neurosci. 13, 5334–5355 (1993).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Physiol. (14)

C. Enroth-Cugell and J. G. Robson, “The contrast sensitivity of retinal ganglion cells of the cat,” J. Physiol. 157, 517–552 (1966).

C. Enroth-Cugell and R. M. Shapley, “Flux, not retinal illumination, is what cat retinal ganglion cells really care about,” J. Physiol. 233, 311–326 (1973).

D. L. Beaudoin, M. B. Manookin, and J. B. Demb, “Distinct expression of contrast gain control in parallel synaptic pathways converging on a retinal ganglion cell,” J. Physiol. 586, 5487–5502 (2008).
[CrossRef]

C. Blakemore and F. W. Campbell, “On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. 203, 237–260 (1969).

F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).

K.-I. Naka and W. A. H. Rushton, “S-potentials from luminosity units in the retina of fish (Cyprinidae),” J. Physiol. 185, 587–599 (1966).

H. B. Barlow and W. R. Levick, “Threshold setting by the surround of cat retinal ganglion cells,” J. Physiol. 259, 737–757 (1976).

H. B. Barlow, R. Fitzhugh, and S. W. Kuffler, “Change of organization in the receptive fields of the cat’s retina during dark adaptation,” J. Physiol. 137, 338–354 (1957).

H. B. Barlow and W. R. Levick, “Changes in the maintained discharge with adaptation level in the cat retina,” J. Physiol. 202, 699–718 (1969).

W. A. H. Rushton, “Rhodopsin measurement and dark-adaptation in a subject deficient in cone vision,” J. Physiol. 156, 193–205 (1961).

R. F. Hess and K. Nordby, “Spatial and temporal limits of vision in the achromat,” J. Physiol. 371, 365–385 (1986).

R. F. Hess and K. Nordby, “Spatial and temporal properties of human rod vision in the achromat,” J. Physiol. 371, 387–406 (1986).

C. Enroth-Cugell and P. Lennie, “The control of retinal ganglion cell discharge by receptive field surrounds,” J. Physiol. 247, 551–578 (1975).

C. Enroth-Cugell and L. H. Pinto, “Properties of the surround response mechanism of cat retinal ganglion cells and centre-surround interaction,” J. Physiol. 220, 403–439 (1972).

Nature (2)

J. Cafaro and F. Rieke, “Noise correlations improve response fidelity and stimulus encoding,” Nature 468, 964–967 (2010).
[CrossRef]

F. W. Campbell and D. G. Green, “Monocular versus binocular visual acuity,” Nature 208, 191–192 (1965).
[CrossRef]

Ophthalmic Physiolog. Opt. (1)

C. R. Cavonius, O. Estévez, and L. H. van der Tweel, “Counterphase dichoptic flicker is seen as its own second harmonic,” Ophthalmic Physiolog. Opt. 12, 153–156 (1992).
[CrossRef]

Pflugers Archiv (1)

B. Sakmann and O. D. Creutzfeldt, “Scotopic and mesopic light adaptation in the cat’s retina,” Pflugers Archiv 313, 168–185 (1969).

Proc. R. Soc. B (1)

B. H. Crawford, “Visual adaptation in relation to brief conditioning stimuli,” Proc. R. Soc. B 134, 283–302 (1947).
[CrossRef]

Proc. R. Soc. Lond. B (1)

W. A. H. Rushton, “The Ferrier lecture, 1962. Visual adaptation,” Proc. R. Soc. Lond. B 162, 20–46 (1965).
[CrossRef]

Proc. R. Soc. Lond. Ser. B (1)

D. H. Hubel and T. N. Wiesel, “Functional architecture of macaque monkey visual cortex,” Proc. R. Soc. Lond. Ser. B 198, 1–59 (1977).
[CrossRef]

Prog. Retin. Res. (1)

R. Shapley and C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retin. Res. 3, 263–346 (1984).
[CrossRef]

Quart. J. Exp. Psychol. (1)

C. R. Cavonius, “Binocular interactions in flicker,” Quart. J. Exp. Psychol. 31, 273–280 (1979).
[CrossRef]

Seeing Perceiving (1)

D. Laming, “Fechner’s law: where does the log transform come from?” Seeing Perceiving 23, 155–171 (2010).

Vis. Res. (11)

J. Nachmias and R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vis. Res. 14, 1039–1042 (1974).
[CrossRef]

W. S. Geisler, “The effects of photopigment depletion on brightness and threshold,” Vis. Res. 18, 269–278 (1978).
[CrossRef]

W. S. Geisler, “Adaptation, afterimages and cone saturation,” Vis. Res. 18, 279–289 (1978).
[CrossRef]

W. S. Geisler, “Evidence for the equivalent-background hypothesis in cones,” Vis. Res. 19, 799–805 (1979).
[CrossRef]

M. E. Rudd and L. G. Brown, “A model of Weber and noise gain control in the retina of the toad Bufo marinus,” Vis. Res. 37, 2433–2453 (1997).
[CrossRef]

R. A. Linsenmeier, L. J. Frishman, H. G. Jakiela, and C. Enroth-Cugell, “Receptive field properties of X and Y cells in the cat retina derived from contrast sensitivity measurements,” Vis. Res. 22, 1173–1183 (1982).
[CrossRef]

E. S. Yamada, L. C. L. Silveira, V. H. Perry, and E. C. S. Franco, “M and P retinal ganglion cells of the owl monkey: morphology, size and photoreceptor convergence,” Vis. Res. 41, 119–131 (2001), Fig. 6, p. 126.
[CrossRef]

H. B. Barlow, W. R. Levick, and M. Yoon, “Responses to single quanta of light in retinal ganglion cells of the cat,” Vis. Res. 11, 87–101 (1971).
[CrossRef]

A. Reeves, S. Wu, and T. J. Schirillo, “The effect of photon noise on the detection of white flashes,” Vis. Res. 38, 691–703 (1998).
[CrossRef]

T. D. Lamb, “The involvement of rod photoreceptors in dark adaptation,” Vis. Res. 21, 1773–1782 (1981).
[CrossRef]

M. J. Valeton and D. van Norren, “Light adaptation of primate cones: an analysis based on extracellular data,” Vis. Res. 231539–1547 (1983).
[CrossRef]

Other (14)

G. Ryle, The Concept of Mind (Hutchinson, 1949).

T. N. Cornsweet, Visual Perception (Academic, 1970).

D. Laming, Human Judgment: The Eye of the Beholder (Thomson Learning, 2004).

D. Laming, The Measurement of Sensation (Oxford, 1997), Chap. 6, pp. 83–86 and Chap. 7, 104–105.

But note that ν is assumed to be fixed. If the number ν is variable, the argument collapses.

Shorter Oxford English Dictionary, 3rd ed. (Oxford, 1944), p. 1007.

Even more compelling is that we can perceive counterphase flicker—courtesy of the nonlinearity specific to each eye [34,35].

F. L. van Nes, “Experimental studies in spatiotemporal contrast transfer by the human eye,” Doctoral thesis (Utrecht University, 1968).

L. A. Riggs, “Light as a stimulus for vision,” in Vision and Visual Perception, C. H. Graham, ed. (Wiley, 1965), pp. 1–38.

D. C. Hood, “Psychophysical and physiological tests of physiological explanations of light adaptation,” in Visual Psychophysics: Its Physiological Basis, J. Armington, J. Krauskopf, and B. Wooten, eds. (Academic, 1978), pp. 141–155.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw-Hill, 1958), Chaps. 8 and 9.

D. Laming, Sensory Analysis (Academic, 1986).

D. Laming, “Contrast sensitivity,” in Vision and Visual Dysfunction, J. J. Kulikowski, V. Walsh, and I. J. Murray, eds., Vol. 5 of Limits of Visual Perception (Macmillan, 1991), pp. 38–39.

D. Laming, “Spatial frequency channels,” in Vision and Visual Dysfunction, J. J. Kulikowski, V. Walsh, and I. J. Murray, eds., Vol. 5 of Limits of Visual Perception (Macmillan, 1991), pp. 97–105.

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Figures (10)

Fig. 1.
Fig. 1.

Sample oscilloscope traces to illustrate the sensory analysis of an increment in luminance. (a) Luminance profile incorporating an increment of duration T. (b) Positive and negative Poisson inputs to a receptive field unit, with the negative input delayed by an interval τ(<T). (c) Linear combination of the two traces in (b). (d) Half-wave rectified output, where the high-frequency components of the Poisson noise have been attenuated in recognition of the low-pass character of receptive field units. (Adapted from [12, p. 112]. © Copyright Elsevier, 1986. Reproduced by permission.)

Fig. 2.
Fig. 2.

Contrast thresholds from [29]. The rectilinear characteristic fitted to each set of thresholds represents a square-root law at low illuminances and Weber’s law at high illuminances. (From [30]. © Copyright Donald Laming, 2010.)

Fig. 3.
Fig. 3.

Transition illuminances estimated from the data of [29]. (From [12, p. 204]. © Copyright Elsevier 1986. Reproduced by permission.)

Fig. 4.
Fig. 4.

Differential coupling at very low luminance, analogous to Figs. 1(b)1(d). Individual Poisson events are sparse and rarely coincide. Events in the positive input seldom correspond to events in the negative, so that half-wave rectification (d) simply recovers the positive input. The negative input [(b) and (c)] has no effect. (From [12, p. 164]. © Copyright Elsevier 1986. Reproduced by permission.)

Fig. 5.
Fig. 5.

Auditory “thresholds” for test spots of varying diameters centered on the receptive field of a ganglion cell in the retina of a cat. Two sets of data are shown for adapting luminances of 5×104 and 5×102cd/m2. Data from [37].

Fig. 6.
Fig. 6.

Thresholds for the detection of sinusoidal (circles) and square-wave (open squares) gratings, switched on and off at 0.5 Hz. The small filled squares repeat the square-wave thresholds depressed by log(4/π) to facilitate comparison with the sine-wave thresholds. The continuous straight line has gradient 1 and emphasizes that below 2c/deg, sensitivity to sine waves decreases in proportion to the wavenumber. The horizontal dashed line likewise emphasizes that square-wave sensitivity is subject to a lower limit at low wavenumbers. Finally, the dotted line has gradient 0.75 and represents the maximum facilitation of square-wave sensitivity from odd-order harmonics. Data from [42]. Reproduced, by permission from Macmillan Publishers Ltd, from “Spatial frequency channels,” by D. Laming in Vision and Visual Dysfunction, Vol. 5: Limits of Visual Perception, J. J. Kulikowski, V. Walsh, and I. J. Murray, eds. (Macmillan, 1991), p. 103. Copyright Donald Laming.

Fig. 7.
Fig. 7.

Peak response of a ganglion cell in the retina of a cat as a function of test spot luminance at six different adapting luminances. The ordinate shows the rate of discharge during the first 50 ms of stimulation, less the maintained discharge. The adapting luminance is indicated by the arrows at the top (except that the adapting luminance for the leftmost set of data lies off the scale). The curves fitted by eye represent the Naka–Ruston equation and differ between different adapting luminances solely by a lateral shift (with respect to log luminance). Data from [23].

Fig. 8.
Fig. 8.

Simultaneous contrast. The four small squares are all 50% black. (See [52].)

Fig. 9.
Fig. 9.

Interval histogram of maintained discharge from an on-center ganglion cell in the retina of a cat in darkness. The bin widths are 2 ms. Data from [57].

Fig. 10.
Fig. 10.

Auditory “thresholds” for a 0.4 deg test spot and an annulus with internal diameter 2.1 deg centered on the receptive field of a ganglion cell in the retina of a cat. The adapting field was 5×104cd/m2 with, in addition, an adapting disc at 5×102cd/m2, again centered on the receptive field. The haloes mark those “thresholds” for which [37] published a PST histogram. Data from [37].

Tables (1)

Tables Icon

Table 1. Interpretation of the Parameters in Eqs. (3), (4), and (16) in Terms of the Standard Deviations of the Components of the Receptive Field

Equations (16)

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

L(u)=L0{1+Ccos2πgu},
Ltransg2.
logΔL=3.73log(1exp{0.935a2}).
logΔL=2.74log(exp(0.329a2)exp(0.935a2)+0.22(2exp(0.329a2)exp(0.935a2))/(4π)).
g=constant.
Ltrans=g2Ilim.
L(u)=L0{1+(4C/π)r=0(2r+1)1sin2π(2r+1)gu}.
R=Rmax(L/(L+Ls)),
R=Rmax(exp(lnL)/(exp(lnL)+exp(lnLs))),
R=(GL/(GL+Ls))Rmax,
ΔR=Rmax[La/2π+pLLa/2π+pL+LsLa/2πLa/2π+Ls]=Rmax[pLpL+La/2π+Ls]×LsLa/2π+Ls.
0t/δt1[1{βexp(βti)+α}δt]=exp{0t/δt1ln[1{βexp(βti)+α}δt]}=exp{0t{βeβt+α}dt}=exp{αt(1eβt)}.
f(t)=[α+βeβt]exp{αt(1eβt)}.
log{f(t)}=0.4343[αt+(1eβt)]+log[α+βeβt].
log{4979f(t)}=1.32.7t+1.45e21t
logΔL=1.35+0.5log[2.02exp(0.329a2)exp(0.935a2)].

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