Abstract

We studied photoreceptors in the locust (Schistocerca americanus) visual system to determine the extent to which quantal noise and intrinsic neural noise limit temporal sensitivity. Typical computational models of the temporal contrast sensitivity function are deterministic, reflect only filter characteristics, and lack explicit noise sources [J. Opt. Soc. Am. 58, 1133 (1968); Vision Res. 32, 1373 (1992)]. We report here that the temporal contrast sensitivity function, at low light levels, is not simply the reflection of a filter function. Our evidence suggests that, at low backgrounds, noise, in conjunction with temporal filtering, plays a role in shaping the temporal contrast sensitivity function. At a given low adaptation level, quantal noise limits sensitivity at low temporal frequencies, while intrinsic noise limits sensitivity at relatively higher temporal frequencies.

© 1999 Optical Society of America

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1998 (1)

C. Montell, “TRP trapped in fly signaling web,” Curr. Opin. Neurobiol. 8, 389–397 (1998).
[CrossRef] [PubMed]

1997 (1)

E. P. Hornstein, D. R. Pope, T. E. Cohn, “Effects of early noise on the shape of the temporal contrast sensitivity function,” Invest. Ophthalmol. Visual Sci. Suppl. 38, 1795 (1997).

1996 (6)

J. Rovamo, A. Raninen, S. Lukkarinen, K. Donner, “Flicker sensitivity as a function of spectral density of external white temporal noise,” Vision Res. 36, 3767–3774 (1996).
[CrossRef] [PubMed]

R. R. de Ruyter van Steveninck, S. B. Laughlin, “Light adaptation and reliability in blowfly photoreceptors,” Int. J. Neural Syst. 7, 437–444 (1996).
[CrossRef] [PubMed]

C. S. Zucker, “The biology of vision in Drosophila,” Proc. Natl. Acad. Sci. USA 93, 571–576 (1996).
[CrossRef]

D. A. Baylor, “How photons start vision,” Proc. Natl. Acad. Sci. USA 93, 560–565 (1996).
[CrossRef] [PubMed]

Y. Koutalos, K.-W. Yau, “Regulation of sensitivity in vertebrate rod photoreceptors by calcium,” Trends Neurosci. 19, 73–81 (1996).
[CrossRef] [PubMed]

K. Donner, S. Hemila, “Modelling the spatio-temporal modulation response of ganglion cells with difference-of-Gaussians receptive fields: relation to photoreceptor response kinetics,” Visual Neurosci. 13, 173–186 (1996).
[CrossRef]

1995 (2)

R. Ranganathan, D. M. Malicki, C. S. Zucker, “Signal transduction in Drosophila photoreceptors,” Annu. Rev. Neurosci. 18, 283–317 (1995).
[CrossRef] [PubMed]

K. Donner, A. Koskelainen, K. Djupsund, S. Hemila, “Changes in retinal time scale under background light: observations on rods and ganglion cells in the frog retina,” Vision Res. 35, 2255–2266 (1995).
[CrossRef] [PubMed]

1994 (1)

K.-W. Yau, “Phototransduction mechanisms in retinal rods and cones. The Friedenwald lecture,” Invest. Ophthalmol. Visual Sci. 35, 9–32 (1994).

1993 (2)

E. N. Pugh, T. D. Lamb, “Amplification and kinetics of the activation steps in phototransduction,” Biochem. Biophys. Acta 1141, 111–149 (1993).
[PubMed]

R. B. Barlow, R. R. Birge, E. Kaplan, J. R. Tallent, “On the molecular origin of photoreceptor noise,” Nature (London) 366, 64–66 (1993).
[CrossRef]

1992 (2)

N. Graham, D. C. Hood, “Quantal noise and decision rules in dynamic models of light adaptation,” Vision Res. 32, 779–787 (1992).
[CrossRef] [PubMed]

N. Graham, D. C. Hood, “Modeling the dynamics of light adaptation: the merging of two traditions,” Vision Res. 32, 1373–1393 (1992).
[CrossRef] [PubMed]

1990 (3)

K. Purpura, D. Tranchina, E. Kaplan, R. M. Shapley, “Light adaptation in the primate retina: analysis of changes in gain and dynamics of monkey retinal ganglion cells,” Visual Neurosci. 4, 75–93 (1990).
[CrossRef]

A. B. Watson, “Gain, noise, and contrast sensitivity of linear visual neurons,” Visual Neurosci. 4, 147–157 (1990).
[CrossRef]

W. Bialek, W. G. Owen, “Temporal filtering in retinal bipolar cells: elements of an optimal computation?” Biophys. J. 58, 1227–1233 (1990).
[CrossRef] [PubMed]

1988 (1)

A.-C. Aho, K. Donner, C. Hyden, L. O. Larsen, T. Reuter, “Low retinal noise in animals with low body temperature allows high visual sensitivity,” Nature (London) 334, 348–350 (1988).
[CrossRef]

1987 (4)

W. Bialek, “Physical limits to sensation and perception,” Annu. Rev. Biophys. Biophys. Chem. 16, 455–478 (1987).
[CrossRef] [PubMed]

D. R. Copenhagen, K. Donner, T. Reuter, “Ganglion cell performance at absolute threshold in toad retina: effects of dark events in rods,” J. Physiol. (London) 393, 667–680 (1987).

W. G. Owen, “Ionic conductances in rod photoreceptors,” Annu. Rev. Physiol. 49, 743–764 (1987).
[CrossRef] [PubMed]

S. B. Laughlin, J. Howard, B. Blakeslee, “Synaptic limitations to contrast coding in the retina of the blowfly Calliphora,” Proc. R. Soc. London Ser. B 231, 437–467 (1987).
[CrossRef]

1986 (2)

T. Cohn, D. Lasley, “Visual sensitivity,” Annu. Rev. Psychol. 37, 495–521 (1986).
[CrossRef] [PubMed]

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

1985 (1)

R. D. Bodoia, P. B. Detwiler, “Patch-clamp recordings of the light-sensitive dark noise in retinal rods from lizard and frog,” J. Physiol. (London) 367, 183–216 (1985).

1984 (1)

D. Tranchina, J. Gordon, R. M. Shapley, “Retinal light adaptation—evidence for a feedback mechanism,” Nature (London) 310, 314–316 (1984).
[CrossRef]

1983 (2)

T. E. Cohn, “Receiver operating characteristic analysis of photoreceptor sensitivity,” IEEE Trans. Syst. Man Cybern. SMC-13, 873–881 (1983).
[CrossRef]

W. R. Levick, L. N. Thibos, T. E. Cohn, D. Catanzaro, H. B. Barlow, “Performance of cat retinal ganglion cells at low light levels,” J. Gen. Physiol. 82, 405–426 (1983).
[CrossRef] [PubMed]

1982 (1)

1981 (1)

P. G. Lillywhite, “Multiplicative intrinsic noise and the limits to visual performance,” Vision Res. 21, 291–296 (1981).
[CrossRef] [PubMed]

1980 (2)

F. Wong, B. W. Knight, F. A. Dodge, “Dispersion of latencies in photoreceptors of Limulus and the adapting bump model,” J. Gen. Physiol. 76, 517–537 (1980).
[CrossRef] [PubMed]

D. A. Baylor, G. Matthews, K. W. Yau, “Two components of electrical dark noise in toad retinal rod outer segments,” J. Physiol. (London) 309, 591–621 (1980).

1979 (2)

P. G. Lillywhite, S. B. Laughlin, “Transducer noise in a photoreceptor,” Nature (London) 277, 569–572 (1979).
[CrossRef]

L. N. Thibos, W. R. Levick, T. E. Cohn, “Receiver operating characteristic curves for Poisson signals,” Biol. Cybern. 33, 57–61 (1979).
[CrossRef]

1978 (1)

D. H. Kelly, “Human flicker sensitivity: two stages of retinal diffusion,” Science 202, 896–899 (1978).
[CrossRef] [PubMed]

1977 (2)

T. E. Cohn, “Receiver operating characteristic analysis of sensitivity in neural systems,” Proc. IEEE 65, 781–786 (1977).
[CrossRef]

P. G. Lillywhite, “Single photon signals and transduction in an insect eye,” J. Comp. Physiol. 122, 189–200 (1977).
[CrossRef]

1976 (2)

T. E. Cohn, “Quantum fluctuation limit in foveal vision,” Vision Res. 16, 573–579 (1976).
[CrossRef] [PubMed]

D. H. Kelly, R. M. Boynton, W. S. Baron, “Primate flicker sensitivity: psychophysics and electrophysiology,” Science 194, 1077–1079 (1976).
[CrossRef] [PubMed]

1975 (1)

T. E. Cohn, D. G. Green, W. P. Tanner, “Receiver operating characteristic analysis. Application to the study of quantum fluctuation effects in optic nerve of Rana pipiens,” J. Gen. Physiol. 66, 583–616 (1975).
[CrossRef] [PubMed]

1974 (1)

D. A. Baylor, A. L. Hodgkin, T. D. Lamb, “Reconstruction of the electrical responses of turtle cones to flashes and steps of light,” J. Physiol. (London) 242, 759–791 (1974).

1972 (1)

D. H. Kelly, “Adaptation effects on spatio-temporal sine-wave thresholds,” Vision Res. 12, 89–101 (1972).
[CrossRef] [PubMed]

1969 (1)

1968 (3)

1967 (1)

M. M. Taylor, C. D. Creelman, “PEST: efficient estimates on probability functions,” J. Acoust. Soc. Am. 41, 782–787 (1967).
[CrossRef]

1964 (1)

G. F. Fuortes, A. L. Hodgkin, “Changes in time scale and sensitivity in the ommatidia of Limulus,” J. Physiol. (London) 172, 239–263 (1964).

1961 (1)

1958 (3)

H. De Lange Dzn, “Research into the dynamic nature of the human fovea→cortex systems with intermittent and modulated light. I. Attenuation characteristics with white and colored light,” J. Opt. Soc. Am. 48, 777–784 (1958).
[CrossRef]

S. Yeandle, “Evidence of quantized slow potentials in the eye of Limulus,” Am. J. Ophthalmol. 46, 82–87 (1958).

H. B. Barlow, “Temporal and spatial summation in human vision at different background intensities,” J. Physiol. (London) 141, 337–350 (1958).

1956 (1)

1954 (2)

W. W. Peterson, T. G. Birdsall, W. C. Fox, “The theory of signal detectability,” IRE Trans. Inf. Theory PGIT 4, 171–212 (1954).
[CrossRef]

W. P. Tanner, J. A. Swets, “A decision-making theory of visual detection,” Psychol. Rev. 61, 401–409 (1954).
[CrossRef] [PubMed]

1952 (1)

H. De Lange, “Experiments on flicker and some calculations on an electrical analogue of the fovea systems,” Physica 28, 935–950 (1952).
[CrossRef]

1948 (2)

O. H. Shade, “Electro-optical characteristics of television systems. I. Characteristics of vision and visual systems,” RCA Rev. 9, 5–37 (1948).

A. Rose, “The sensitivity performance of the human eye on an absolute scale,” J. Opt. Soc. Am. 38, 196–208 (1948).
[CrossRef] [PubMed]

1943 (1)

H. de Vries, “The quantum character of light and its bearing upon the threshold of vision, the differential sensitivity and acuity of the eye,” Physica 10, 553–564 (1943).
[CrossRef]

1942 (1)

S. Hecht, S. Shlaer, M. H. Pirenne, “Energy, quanta, and vision,” J. Gen. Physiol. 25, 819–840 (1942).
[CrossRef] [PubMed]

Aho, A.-C.

A.-C. Aho, K. Donner, C. Hyden, L. O. Larsen, T. Reuter, “Low retinal noise in animals with low body temperature allows high visual sensitivity,” Nature (London) 334, 348–350 (1988).
[CrossRef]

Barlow, H. B.

W. R. Levick, L. N. Thibos, T. E. Cohn, D. Catanzaro, H. B. Barlow, “Performance of cat retinal ganglion cells at low light levels,” J. Gen. Physiol. 82, 405–426 (1983).
[CrossRef] [PubMed]

H. B. Barlow, “Temporal and spatial summation in human vision at different background intensities,” J. Physiol. (London) 141, 337–350 (1958).

H. B. Barlow, “Retinal noise and absolute threshold,” J. Opt. Soc. Am. 46, 634–639 (1956).
[CrossRef] [PubMed]

H. B. Barlow, “Retinal and central factors in human vision limited by noise,” in Vertebrate Photoreception, H. B. Barlow, P. Fatt, eds. (Academic, London, 1977), pp. 337–358.

H. B. Barlow, “The physical limits of visual discrimination,” in Photophysiology, A. C. Giese, ed. (Academic, New York, 1964), pp. 163–202.

Barlow, R. B.

R. B. Barlow, R. R. Birge, E. Kaplan, J. R. Tallent, “On the molecular origin of photoreceptor noise,” Nature (London) 366, 64–66 (1993).
[CrossRef]

Baron, W. S.

D. H. Kelly, R. M. Boynton, W. S. Baron, “Primate flicker sensitivity: psychophysics and electrophysiology,” Science 194, 1077–1079 (1976).
[CrossRef] [PubMed]

Baylor, D. A.

D. A. Baylor, “How photons start vision,” Proc. Natl. Acad. Sci. USA 93, 560–565 (1996).
[CrossRef] [PubMed]

D. A. Baylor, G. Matthews, K. W. Yau, “Two components of electrical dark noise in toad retinal rod outer segments,” J. Physiol. (London) 309, 591–621 (1980).

D. A. Baylor, A. L. Hodgkin, T. D. Lamb, “Reconstruction of the electrical responses of turtle cones to flashes and steps of light,” J. Physiol. (London) 242, 759–791 (1974).

Bialek, W.

W. Bialek, W. G. Owen, “Temporal filtering in retinal bipolar cells: elements of an optimal computation?” Biophys. J. 58, 1227–1233 (1990).
[CrossRef] [PubMed]

W. Bialek, “Physical limits to sensation and perception,” Annu. Rev. Biophys. Biophys. Chem. 16, 455–478 (1987).
[CrossRef] [PubMed]

Birdsall, T. G.

W. W. Peterson, T. G. Birdsall, W. C. Fox, “The theory of signal detectability,” IRE Trans. Inf. Theory PGIT 4, 171–212 (1954).
[CrossRef]

Birge, R. R.

R. B. Barlow, R. R. Birge, E. Kaplan, J. R. Tallent, “On the molecular origin of photoreceptor noise,” Nature (London) 366, 64–66 (1993).
[CrossRef]

Blakeslee, B.

S. B. Laughlin, J. Howard, B. Blakeslee, “Synaptic limitations to contrast coding in the retina of the blowfly Calliphora,” Proc. R. Soc. London Ser. B 231, 437–467 (1987).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Sample trial demonstrating our use of the matched filter algorithm (top, stimulus interval; bottom, no-stimulus interval). T, response template; R, photoreceptor membrane potential; M, scaled output of the matched filter (T multiplied by R). The decision variable (see Section 2) is shown at the right-hand side of each output. The output of the matched filter shows clearly that highly correlated points in time between the template and response waveforms produce a positive output value regardless of the sign of the individual waveforms. Uncorrelated points are randomly distributed about zero.

Fig. 2
Fig. 2

Threshold amplitude sensitivity measurements (1/ΔIt) for mean luminance of 25 effective photons/s (circles) and 250 effective photons/s (squares) with temporal flicker of constant duration and a matched filter computer algorithm that approximates an ideal observer. There is an attenuation in amplitude sensitivity at high frequencies and a flattening at low frequencies for both mean luminance levels tested. Owing to severe attenuation of the signal at high temporal frequencies, the threshold value for the 20-Hz signal at the lowest mean luminance could not be obtained. Error bars represent standard errors (n=7).

Fig. 3
Fig. 3

ROC analysis of photoreceptor responses to equal luminance increments and decrements from a mean luminance of 22 effective photons/s. (a) Stimulus (150 trials with 500-ms luminance decrements) and no-stimulus (450 trials) response distributions. The ordinate is the frequency of occurrence and the abscissa is the calculated IWR. The vertical line represents one criterion that can be chosen to calculate one hit and false-alarm-rate pair, giving one point on the ROC curve. The area under a distribution to the right-hand side of the criterion (yes response) is either the false-alarm rate (no-stimulus condition) or the hit rate (stimulus condition). (b) ROC curves resulting from ROC analysis of responses to long (500-ms) decrements (circles) and increments (squares), ±72% modulation, from the mean luminance level. The ordinate is the hit rate, and the abscissa is the false-alarm rate. (c) ROC coordinates of (b) transformed to normal deviates. Z-score coordinates are shown. The quantal fluctuation fingerprint can be seen in these ROC curves. The detectability of the decrement (3.11) is greater than that of the increment (1.63), and the slope of the decrement curve (1.07) is greater than 1.0, while the slope of the increment curve (0.92) is less than 1.0. Error bars represent binomial standard errors (for y-axis error bars, n=150; for x-axis error bars, n=450).

Fig. 4
Fig. 4

ROC curves resulting from ROC analysis of responses to short (65-ms) decrements (circles) and increments (squares), ±95% modulation, from the mean luminance level. Detectabilities for the luminance decrements and increments are nearly identical. These results provide little evidence of the quantum fluctuation fingerprint and thus suggest a different sort of predominant noise. Error bars represent binomial standard errors (for y-axis error bars, n=150; for x-axis error bars, n=450).

Fig. 5
Fig. 5

Performance of the ideal observer compared with real performance for the case of long-duration (500-ms) increments (squares) and decrements (circles). (a) Poisson distributions calculated with the Poisson probability formula with means 11 (triangles), 3.08 (circles), and 18.92 (squares) representing the mean number of effective photons/500 ms. (b) ROC curves, calculated from the probability distributions in (a), predicting ideal performance. (c) Comparison of ROC curves calculated from Poisson distributions (filled symbols) and ROC curves calculated from measured response distributions (open symbols). Error bars represent binomial standard errors (for y-axis error bars, n=150; for x-axis error bars, n=450).

Fig. 6
Fig. 6

Performance of the ideal observer compared with real performance for the case of short-duration (65-ms) increments (squares) and decrements (circles). (a) ROC curves calculated from Poisson probability distributions with means 1.43, 0.072, and 2.79, predicting ideal performance. (b) Comparison of ROC curves calculated from Poisson distributions (filled symbols) and those calculated from measured response distributions (open symbols). Error bars for curves from measured response distributions represent binomial standard errors (for y-axis error bars, n=150; for x-axis error bars, n=450).

Fig. 7
Fig. 7

(a), (b) ROC curves calculated from Poisson probability distributions with means 0.72, 1.43, and 2.79 (with added Gaussian variance) generated through Monte Carlo simulations. The standard deviations of the Gaussian random variable added to the Poisson random variable were 0.0, 0.5, 1.0, and 2.0. Each curve is identified in the legend according to the standard deviation (s.d.) of the amount of added variance. ROC curves in (a) are for the case of an increment, and ROC curves in (b) are for the case of a decrement. (c) Comparison of increment (squares) and decrement (circles) ROC curves calculated from measured response distributions (open symbols) and simulated Poisson probability distributions with an added variance with s.d.=0.5 (filled symbols).

Fig. 8
Fig. 8

(a) Schematic of a model for the photoreceptor TCSF. This model is made up of four modules: an input (with quantal noise Q), a temporal filter that acts on the input, wideband intrinsic noise (i) that can be added to the filtered input, and an output. (b) The output characteristic of the model without (case 1) and with (case 2) intrinsic noise. Each output is interpreted by an ideal observer (matched filter in the time domain), thus leading to a TCSF as shown on the right-hand side. The resultant TCSF for the case of quantal noise only (diamonds) is flat, while for the case of quantal noise and intrinsic noise (squares) it is low pass in nature. The filter function (triangles) is also plotted, for reference, to demonstrate that the photoreceptor TCSF is not simply the reflection of a filter function. Curves were generated with a computer simulation of this model.

Fig. 9
Fig. 9

Comparison of a normalized gain function (circles) and a TCSF (squares), both measured from a photoreceptor to illustrate shape differences.

Tables (1)

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Table 1 Detectability Ratios (Decrement d/Incrementd) Calculated from Photoreceptor Responses to Long- and Short-Duration Stimuli

Metrics