Abstract

We analyze adaptation processes responsible for eliciting and alleviating flicker response suppression, which is a class of phenomena characterized by the selective reduction of visual response to the ac component of a flickering light. Stimulus conditions were chosen that would allow characteristic features of flicker response suppression to be defined and manipulated systematically. Data are presented to show that reducing the sinusoidal modulation depth of an 11-Hz stimulus can correspond precisely to raising the temporal frequency of a fully modulated stimulus. In each case there is a nonmonotonic relation between flicker response and dc test illuminance. The nonmonotonic relation cannot be explained by adaptation models that postulate multiplicative and subtractive adaptation processes followed by a single static saturating nonlinearity, even when temporal frequency filters are incorporated into such models. A satisfactory explanation requires an additional contrast gain-control process. This process enhances flicker response at progressively lower temporal response contrasts as the illuminance of a surrounding adaptation field increases.

© 1998 Optical Society of America

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  1. D. H. Kelly, “Flicker” in Handbook of Sensory Physiology, Vol. 7, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972), pp. 273–302.
  2. P. Lennie, J. Pokorny, V. C. Smith, “Luminance,” J. Opt. Soc. Am. A 10, 1283–1293 (1993).
    [CrossRef] [PubMed]
  3. A. B. Watson, “Temporal sensitivity,” in Sensory Processes and Perception, Vol. I of Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 6-1–6-43.
  4. S. A. Burns, A. E. Elsner, M. R. Kreitz, “Analysis of nonlinearities in the flicker ERG,” Optom. Vis. Sci. 69, 95–105 (1992).
    [CrossRef] [PubMed]
  5. A. Eisner, “Suppression of flicker response with increasing test illuminance: roles of temporal waveform, modulation depth, and frequency,” J. Opt. Soc. Am. A 12, 214–224 (1995).
    [CrossRef]
  6. S. H. Goldberg, T. E. Frumkes, R. W. Nygaard, “Inhibi-tory influence of unstimulated rods in the human retina: evidence provided by examining cone flicker,” Science 221, 180–182 (1983).
    [CrossRef] [PubMed]
  7. K. R. Alexander, G. A. Fishman, “Rod influence on cone flicker detection: variation with retinal eccentricity,” Vision Res. 26, 827–834 (1986).
    [CrossRef] [PubMed]
  8. N. J. Coletta, A. J. Adams, “Spatial extent of rod–cone and cone–cone interactions for flicker detection,” Vision Res. 26, 917–925 (1986).
    [CrossRef]
  9. G. Lange, N. Denny, T. F. Frumkes, “Suppressive rod–cone interactions: evidence for separate retinal (temporal) and extraretinal (spatial) mechanisms in achromatic vision,” J. Opt. Soc. Am. A 14, 2487–2498 (1997).
    [CrossRef]
  10. A. Eisner, D. I. A. MacLeod, “Flicker photometric study of chromatic adaptation: selective suppression of cone inputs by colored backgrounds,” J. Opt. Soc. Am. 71, 705–718 (1981).
    [CrossRef] [PubMed]
  11. C. F. Stromeyer, A. Chaparo, A. S. Tolias, R. E. Kronauer, “Colour adaptation modifies the long-wave versus middle-wave cone weights and temporal phases in human luminance (but not red–green) mechanism,” J. Physiol. (London) 499, 227–254 (1997).
  12. G. B. Arden, C. R. Hogg, “Absence of rod–cone interaction and analysis of retinal disease,” Br. J. Ophthalmol. 69, 404–415 (1985).
    [CrossRef] [PubMed]
  13. M. Horiguchi, T. Eysteinsson, G. B. Arden, “Temporal and spatial properties of suppressive rod–cone interaction,” Invest. Ophthalmol. Visual Sci. 32, 575–581 (1991).
  14. G. B. Arden, T. E. Frumkes, “Stimulation of rods can increase cone flicker ERGs in man,” Vision Res. 26, 711–721 (1986).
    [CrossRef] [PubMed]
  15. I. D. Cadenas, E. S. Reifsnider, D. Tranchina, “Modulation of synaptic transfer between retinal cones and horizontal cells by spatial contrast,” J. Gen. Physiol. 104, 567–591 (1994).
    [CrossRef] [PubMed]
  16. R. Nelson, R. Pflug, S. M. Baer, “Background-induced flicker enhancement in cat retinal horizontal cells. II. Spatial properties,” J. Neurophysiol. 64, 326–340 (1990).
    [PubMed]
  17. T. E. Frumkes, T. Eysteinsson, “The cellular basis for suppressive rod-cone interaction,” Visual Neurosci. 1263–273 (1988).
    [CrossRef]
  18. N. S. Peachey, K. R. Alexander, D. J. Derlacki, G. A. Fishman, “Light adaptation, rods and the human flicker ERG,” Visual Neurosci. 8145–150 (1992).
    [CrossRef]
  19. A. Eisner, “Losses of flicker sensitivity during dark adaptation: effects of test size and wavelength,” Vision Res. 32, 1975–1986 (1992).
    [CrossRef] [PubMed]
  20. N. S. Peachey, K. R. Alexander, D. J. Derlacki, “Spatial properties of rod–cone interactions in flicker and hue detection,” Vision Res. 30, 1205–1210 (1990).
    [CrossRef]
  21. A. Eisner, “Nonmonotonic effects of test illuminance on flicker detection: a study of foveal light adaptation with annular surrounds,” J. Opt. Soc. Am. A 11, 33–47 (1994).
    [CrossRef]
  22. N. Graham, D. C. Hood, “Modeling the dynamics of light adaptation: the merging of two traditions,” Vision Res. 32, 1373–1393 (1992).
    [CrossRef] [PubMed]
  23. M. M. Hayhoe, M. E. Levin, R. J. Koshel, “Subtractive processes in light adaptation,” Vision Res. 32, 323–333 (1992).
    [CrossRef] [PubMed]
  24. M. M. Hayhoe, N. I. Benimoff, D. C. Hood, “The time-course of multiplicative and subtractive adaptation process,” Vision Res. 27, 1981–1996 (1987).
    [CrossRef] [PubMed]
  25. T. E. von Wiegand, D. C. Hood, N. Graham, “Testing a computational model of light-adaptation dynamics,” Vision Res. 35, 3037–3051 (1995).
    [CrossRef] [PubMed]
  26. D. C. Hood, N. Graham, T. E. von Wiegand, V. M. Chase, “Probed-sinewave paradigm: a test of models of light-adaptation dynamics,” Vision Res. 37, 1177–1191 (1997).
    [CrossRef] [PubMed]
  27. S. Wu, S. A. Burns, A. E. Elsner, R. T. Eskew, J. He, “Rapid sensitivity changes on flickering backgrounds: tests of models of light adaptation,” J. Opt. Soc. Am. A 14, 2367–2378 (1997).
    [CrossRef]
  28. T. E. Frumkes, S. M. Wu, “Independent influences on cone-mediated responses to light onset and offset in distal retinal neurons,” J. Neurophysiol. 64, 1043–1054 (1990).
    [PubMed]
  29. A. Eisner, “Losses of foveal flicker sensitivity during dark adaptation following extended bleaches,” Vision Res. 29, 1401–1423 (1989).
    [CrossRef] [PubMed]
  30. We do not know whether the uppermost flicker thresholds remain mediated by MWS cones at surround illuminances for which the uppermost flicker thresholds have systematically decreased. It is possible that at those relatively high surround illuminances, subthreshold MWS and LWS responses combined to produce a suprathreshold flicker response.
  31. The fixed modulation depth was set at 99.5% rather than 100% to avoid potential artifacts resulting from the use of pulse-density modulation, as discussed previously.5 The choices of temporal frequency were constrained by the need to obtain flicker tvi curves with abrupt decreases and by the intent to induce abrupt decreases with changes of surround illuminance that were on the order of several tenths of a log unit for 0.1-log-unit decrements of modulation depth. The upper limits of the variable temporal frequency sequence were constrained mainly by the long duration of individual testing sessions, particularly for TQN. For JAM we sought to collect data over temporal frequency and modulation depth ranges that were as comparable to TQN’s as feasible.
  32. M. M. Hayhoe, “Spatial interactions and models of adaptation,” Vision Res. 30, 957–965 (1990).
    [CrossRef] [PubMed]
  33. J. Kremers, B. B. Lee, J. Pokorny, V. C. Smith, “Responses of macaque ganglion cells and human observers to compound periodic waveforms,” Vision Res. 33, 1997–2011 (1993).
    [CrossRef] [PubMed]
  34. There is a bound on how negative (i.e., how much below baseline) the trough response can become at the input to the saturating nonlinearity. As this trough response approaches -σn, the saturating nonlinearity approaches a singularity. If the subbaseline response at the input to the saturating nonlinearity cannot reach -σn then there will be no singularity.
  35. The nonmonotonicity can be steeper yet if s(I)≠kg(I)I but instead s(I)=k(I)g(I)I, with k(I) being a decreasing function of I rather than a constant. However, the degree of steepening is severely constrained if F(I)=g(I)I-s(I) is constrained to be a positive compressive function of I.
  36. In fact, the illuminance level at the threshold for the disappearance of flicker would exceed the illuminance level of a stimulus for which flicker visibility would equal that at the threshold for the initial appearance of flicker. This is because the threshold for the initial appearance of flicker is based on a three-or-more-of-four detection criterion whereas the threshold for the disappearance of flicker is equivalent to a one-or-fewer-of-four detection criterion. Therefore the distance between the thresholds for the initial appearance and subsequent disappearance of flicker would exceed the distance between two equally visible threshold-level flickering stimuli.
  37. R. W. Massof, S. Marcus, G. Dagnelie, D. Choy, J. S. Sunness, A. Albert, “Theoretical interpretation and derivation of flash-on-flash threshold parameters in visual system diseases,” Appl. Opt. 27, 1014–1024 (1988).
    [CrossRef] [PubMed]
  38. We assume that gI and gI-s are smooth compressively nonlinear positive functions of I. We define g′ to be a stronger multiplicative adaptation function than g if g′I<gI and d(g′I)/dI<d(gI)/dI. Similarly, we define s′ to be a stronger subtractive adaptation function than s if gI-s′<gI-s and d(gI-s′)/dI<d(gI-s)/dI or, equivalently, if s′>s and ds′/dI>ds/dI.
  39. An alternative solution, one in which flicker response would be enhanced at progressively higher test illuminances as surround illuminance increased, is ruled out by the failure of subject TQN’s corner data to shift to higher test illuminances across relatively dim surround illuminances.
  40. E. A. Benardete, E. Kaplan, B. W. Knight, “Contrast gain control in the primate retina: P cells are not X-like, some M cells are,” Visual Neurosci 8, 483–486 (1992).
    [CrossRef]
  41. B. B. Lee, J. Pokorny, V. C. Smith, J. Kremers, “Re-sponses to pulses and sinusoids in macaque ganglion cells,” Vision Res. 34, 3081–3096 (1994).
    [CrossRef] [PubMed]
  42. B. B. Lee, “Receptive field structure in the primate retina,” Vision Res. 36, 631–644 (1996).
    [CrossRef] [PubMed]
  43. Proof that the ratio of ac:dc response decreases with increasing dc test illuminance I for any pathway that responds instantaneously and compressively to dc stimuli: We denote the dc response output by the pathway as r(I). The ac:dc ratio is given by [r(I+mI)-r(I-mI)]/r(I), where m signifies modulation depth. Since r is compressive, r(I+mI)/r(I) decreases with I. Similarly, r(I)/r(I-mI) decreases with I, which implies that -r(I-mI)/r(I) also decreases with I. Therefore [r(I+mI)-r(I-mI)]/r(I), decreases with I.
  44. Specifically, at a dc test illuminance 0.4 log unit above the threshold for a 99.5% modulation depth test and at a surround illuminance 0.1 log unit above that which elicited an abrupt decrease of the flicker threshold to that 99.5% modulation depth stimulus, 80% modulation depth flicker remained invisible at every flash for a period of at least 2 min, whereas the 99.5% modulation depth flicker remained visible for at least 30 s before becoming invisible for even a single flash. This experiment was conducted with 18-Hz stimuli for two subjects (TQN plus one other subject; JAM was not tested). In contrast, at surround illuminances 0.1 log unit below that which elicited an abrupt decrease of the flicker threshold, flicker often was visible for one or two out of four flashes at test illuminances that corresponded to flicker threshold at the higher surround illuminances. This observation was made for TQN and JAM.
  45. N. Denny, T. E. Frumkes, S. H. Goldberg, “Comparison of summatory and suppressive rod–cone interaction,” Clin. Vision Sci. 5, 27–36 (1990).
  46. J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fasicularis,” J. Physiol. (London) 427, 681–713 (1990).
  47. D. C. Hood, D. G. Birch, “Phototransduction in human cones measured using the a-wave of the ERG,” Vision Res. 35, 2801–2810 (1995).
    [CrossRef] [PubMed]

1997

G. Lange, N. Denny, T. F. Frumkes, “Suppressive rod–cone interactions: evidence for separate retinal (temporal) and extraretinal (spatial) mechanisms in achromatic vision,” J. Opt. Soc. Am. A 14, 2487–2498 (1997).
[CrossRef]

C. F. Stromeyer, A. Chaparo, A. S. Tolias, R. E. Kronauer, “Colour adaptation modifies the long-wave versus middle-wave cone weights and temporal phases in human luminance (but not red–green) mechanism,” J. Physiol. (London) 499, 227–254 (1997).

D. C. Hood, N. Graham, T. E. von Wiegand, V. M. Chase, “Probed-sinewave paradigm: a test of models of light-adaptation dynamics,” Vision Res. 37, 1177–1191 (1997).
[CrossRef] [PubMed]

S. Wu, S. A. Burns, A. E. Elsner, R. T. Eskew, J. He, “Rapid sensitivity changes on flickering backgrounds: tests of models of light adaptation,” J. Opt. Soc. Am. A 14, 2367–2378 (1997).
[CrossRef]

1996

B. B. Lee, “Receptive field structure in the primate retina,” Vision Res. 36, 631–644 (1996).
[CrossRef] [PubMed]

1995

T. E. von Wiegand, D. C. Hood, N. Graham, “Testing a computational model of light-adaptation dynamics,” Vision Res. 35, 3037–3051 (1995).
[CrossRef] [PubMed]

A. Eisner, “Suppression of flicker response with increasing test illuminance: roles of temporal waveform, modulation depth, and frequency,” J. Opt. Soc. Am. A 12, 214–224 (1995).
[CrossRef]

D. C. Hood, D. G. Birch, “Phototransduction in human cones measured using the a-wave of the ERG,” Vision Res. 35, 2801–2810 (1995).
[CrossRef] [PubMed]

1994

I. D. Cadenas, E. S. Reifsnider, D. Tranchina, “Modulation of synaptic transfer between retinal cones and horizontal cells by spatial contrast,” J. Gen. Physiol. 104, 567–591 (1994).
[CrossRef] [PubMed]

B. B. Lee, J. Pokorny, V. C. Smith, J. Kremers, “Re-sponses to pulses and sinusoids in macaque ganglion cells,” Vision Res. 34, 3081–3096 (1994).
[CrossRef] [PubMed]

A. Eisner, “Nonmonotonic effects of test illuminance on flicker detection: a study of foveal light adaptation with annular surrounds,” J. Opt. Soc. Am. A 11, 33–47 (1994).
[CrossRef]

1993

J. Kremers, B. B. Lee, J. Pokorny, V. C. Smith, “Responses of macaque ganglion cells and human observers to compound periodic waveforms,” Vision Res. 33, 1997–2011 (1993).
[CrossRef] [PubMed]

P. Lennie, J. Pokorny, V. C. Smith, “Luminance,” J. Opt. Soc. Am. A 10, 1283–1293 (1993).
[CrossRef] [PubMed]

1992

S. A. Burns, A. E. Elsner, M. R. Kreitz, “Analysis of nonlinearities in the flicker ERG,” Optom. Vis. Sci. 69, 95–105 (1992).
[CrossRef] [PubMed]

N. S. Peachey, K. R. Alexander, D. J. Derlacki, G. A. Fishman, “Light adaptation, rods and the human flicker ERG,” Visual Neurosci. 8145–150 (1992).
[CrossRef]

A. Eisner, “Losses of flicker sensitivity during dark adaptation: effects of test size and wavelength,” Vision Res. 32, 1975–1986 (1992).
[CrossRef] [PubMed]

E. A. Benardete, E. Kaplan, B. W. Knight, “Contrast gain control in the primate retina: P cells are not X-like, some M cells are,” Visual Neurosci 8, 483–486 (1992).
[CrossRef]

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

M. M. Hayhoe, M. E. Levin, R. J. Koshel, “Subtractive processes in light adaptation,” Vision Res. 32, 323–333 (1992).
[CrossRef] [PubMed]

1991

M. Horiguchi, T. Eysteinsson, G. B. Arden, “Temporal and spatial properties of suppressive rod–cone interaction,” Invest. Ophthalmol. Visual Sci. 32, 575–581 (1991).

1990

N. S. Peachey, K. R. Alexander, D. J. Derlacki, “Spatial properties of rod–cone interactions in flicker and hue detection,” Vision Res. 30, 1205–1210 (1990).
[CrossRef]

R. Nelson, R. Pflug, S. M. Baer, “Background-induced flicker enhancement in cat retinal horizontal cells. II. Spatial properties,” J. Neurophysiol. 64, 326–340 (1990).
[PubMed]

T. E. Frumkes, S. M. Wu, “Independent influences on cone-mediated responses to light onset and offset in distal retinal neurons,” J. Neurophysiol. 64, 1043–1054 (1990).
[PubMed]

N. Denny, T. E. Frumkes, S. H. Goldberg, “Comparison of summatory and suppressive rod–cone interaction,” Clin. Vision Sci. 5, 27–36 (1990).

J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fasicularis,” J. Physiol. (London) 427, 681–713 (1990).

M. M. Hayhoe, “Spatial interactions and models of adaptation,” Vision Res. 30, 957–965 (1990).
[CrossRef] [PubMed]

1989

A. Eisner, “Losses of foveal flicker sensitivity during dark adaptation following extended bleaches,” Vision Res. 29, 1401–1423 (1989).
[CrossRef] [PubMed]

1988

1987

M. M. Hayhoe, N. I. Benimoff, D. C. Hood, “The time-course of multiplicative and subtractive adaptation process,” Vision Res. 27, 1981–1996 (1987).
[CrossRef] [PubMed]

1986

G. B. Arden, T. E. Frumkes, “Stimulation of rods can increase cone flicker ERGs in man,” Vision Res. 26, 711–721 (1986).
[CrossRef] [PubMed]

K. R. Alexander, G. A. Fishman, “Rod influence on cone flicker detection: variation with retinal eccentricity,” Vision Res. 26, 827–834 (1986).
[CrossRef] [PubMed]

N. J. Coletta, A. J. Adams, “Spatial extent of rod–cone and cone–cone interactions for flicker detection,” Vision Res. 26, 917–925 (1986).
[CrossRef]

1985

G. B. Arden, C. R. Hogg, “Absence of rod–cone interaction and analysis of retinal disease,” Br. J. Ophthalmol. 69, 404–415 (1985).
[CrossRef] [PubMed]

1983

S. H. Goldberg, T. E. Frumkes, R. W. Nygaard, “Inhibi-tory influence of unstimulated rods in the human retina: evidence provided by examining cone flicker,” Science 221, 180–182 (1983).
[CrossRef] [PubMed]

1981

Adams, A. J.

N. J. Coletta, A. J. Adams, “Spatial extent of rod–cone and cone–cone interactions for flicker detection,” Vision Res. 26, 917–925 (1986).
[CrossRef]

Albert, A.

Alexander, K. R.

N. S. Peachey, K. R. Alexander, D. J. Derlacki, G. A. Fishman, “Light adaptation, rods and the human flicker ERG,” Visual Neurosci. 8145–150 (1992).
[CrossRef]

N. S. Peachey, K. R. Alexander, D. J. Derlacki, “Spatial properties of rod–cone interactions in flicker and hue detection,” Vision Res. 30, 1205–1210 (1990).
[CrossRef]

K. R. Alexander, G. A. Fishman, “Rod influence on cone flicker detection: variation with retinal eccentricity,” Vision Res. 26, 827–834 (1986).
[CrossRef] [PubMed]

Arden, G. B.

M. Horiguchi, T. Eysteinsson, G. B. Arden, “Temporal and spatial properties of suppressive rod–cone interaction,” Invest. Ophthalmol. Visual Sci. 32, 575–581 (1991).

G. B. Arden, T. E. Frumkes, “Stimulation of rods can increase cone flicker ERGs in man,” Vision Res. 26, 711–721 (1986).
[CrossRef] [PubMed]

G. B. Arden, C. R. Hogg, “Absence of rod–cone interaction and analysis of retinal disease,” Br. J. Ophthalmol. 69, 404–415 (1985).
[CrossRef] [PubMed]

Baer, S. M.

R. Nelson, R. Pflug, S. M. Baer, “Background-induced flicker enhancement in cat retinal horizontal cells. II. Spatial properties,” J. Neurophysiol. 64, 326–340 (1990).
[PubMed]

Baylor, D. A.

J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fasicularis,” J. Physiol. (London) 427, 681–713 (1990).

Benardete, E. A.

E. A. Benardete, E. Kaplan, B. W. Knight, “Contrast gain control in the primate retina: P cells are not X-like, some M cells are,” Visual Neurosci 8, 483–486 (1992).
[CrossRef]

Benimoff, N. I.

M. M. Hayhoe, N. I. Benimoff, D. C. Hood, “The time-course of multiplicative and subtractive adaptation process,” Vision Res. 27, 1981–1996 (1987).
[CrossRef] [PubMed]

Birch, D. G.

D. C. Hood, D. G. Birch, “Phototransduction in human cones measured using the a-wave of the ERG,” Vision Res. 35, 2801–2810 (1995).
[CrossRef] [PubMed]

Burns, S. A.

Cadenas, I. D.

I. D. Cadenas, E. S. Reifsnider, D. Tranchina, “Modulation of synaptic transfer between retinal cones and horizontal cells by spatial contrast,” J. Gen. Physiol. 104, 567–591 (1994).
[CrossRef] [PubMed]

Chaparo, A.

C. F. Stromeyer, A. Chaparo, A. S. Tolias, R. E. Kronauer, “Colour adaptation modifies the long-wave versus middle-wave cone weights and temporal phases in human luminance (but not red–green) mechanism,” J. Physiol. (London) 499, 227–254 (1997).

Chase, V. M.

D. C. Hood, N. Graham, T. E. von Wiegand, V. M. Chase, “Probed-sinewave paradigm: a test of models of light-adaptation dynamics,” Vision Res. 37, 1177–1191 (1997).
[CrossRef] [PubMed]

Choy, D.

Coletta, N. J.

N. J. Coletta, A. J. Adams, “Spatial extent of rod–cone and cone–cone interactions for flicker detection,” Vision Res. 26, 917–925 (1986).
[CrossRef]

Dagnelie, G.

Denny, N.

Derlacki, D. J.

N. S. Peachey, K. R. Alexander, D. J. Derlacki, G. A. Fishman, “Light adaptation, rods and the human flicker ERG,” Visual Neurosci. 8145–150 (1992).
[CrossRef]

N. S. Peachey, K. R. Alexander, D. J. Derlacki, “Spatial properties of rod–cone interactions in flicker and hue detection,” Vision Res. 30, 1205–1210 (1990).
[CrossRef]

Eisner, A.

Elsner, A. E.

Eskew, R. T.

Eysteinsson, T.

M. Horiguchi, T. Eysteinsson, G. B. Arden, “Temporal and spatial properties of suppressive rod–cone interaction,” Invest. Ophthalmol. Visual Sci. 32, 575–581 (1991).

T. E. Frumkes, T. Eysteinsson, “The cellular basis for suppressive rod-cone interaction,” Visual Neurosci. 1263–273 (1988).
[CrossRef]

Fishman, G. A.

N. S. Peachey, K. R. Alexander, D. J. Derlacki, G. A. Fishman, “Light adaptation, rods and the human flicker ERG,” Visual Neurosci. 8145–150 (1992).
[CrossRef]

K. R. Alexander, G. A. Fishman, “Rod influence on cone flicker detection: variation with retinal eccentricity,” Vision Res. 26, 827–834 (1986).
[CrossRef] [PubMed]

Frumkes, T. E.

N. Denny, T. E. Frumkes, S. H. Goldberg, “Comparison of summatory and suppressive rod–cone interaction,” Clin. Vision Sci. 5, 27–36 (1990).

T. E. Frumkes, S. M. Wu, “Independent influences on cone-mediated responses to light onset and offset in distal retinal neurons,” J. Neurophysiol. 64, 1043–1054 (1990).
[PubMed]

T. E. Frumkes, T. Eysteinsson, “The cellular basis for suppressive rod-cone interaction,” Visual Neurosci. 1263–273 (1988).
[CrossRef]

G. B. Arden, T. E. Frumkes, “Stimulation of rods can increase cone flicker ERGs in man,” Vision Res. 26, 711–721 (1986).
[CrossRef] [PubMed]

S. H. Goldberg, T. E. Frumkes, R. W. Nygaard, “Inhibi-tory influence of unstimulated rods in the human retina: evidence provided by examining cone flicker,” Science 221, 180–182 (1983).
[CrossRef] [PubMed]

Frumkes, T. F.

Goldberg, S. H.

N. Denny, T. E. Frumkes, S. H. Goldberg, “Comparison of summatory and suppressive rod–cone interaction,” Clin. Vision Sci. 5, 27–36 (1990).

S. H. Goldberg, T. E. Frumkes, R. W. Nygaard, “Inhibi-tory influence of unstimulated rods in the human retina: evidence provided by examining cone flicker,” Science 221, 180–182 (1983).
[CrossRef] [PubMed]

Graham, N.

D. C. Hood, N. Graham, T. E. von Wiegand, V. M. Chase, “Probed-sinewave paradigm: a test of models of light-adaptation dynamics,” Vision Res. 37, 1177–1191 (1997).
[CrossRef] [PubMed]

T. E. von Wiegand, D. C. Hood, N. Graham, “Testing a computational model of light-adaptation dynamics,” Vision Res. 35, 3037–3051 (1995).
[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]

Hayhoe, M. M.

M. M. Hayhoe, M. E. Levin, R. J. Koshel, “Subtractive processes in light adaptation,” Vision Res. 32, 323–333 (1992).
[CrossRef] [PubMed]

M. M. Hayhoe, “Spatial interactions and models of adaptation,” Vision Res. 30, 957–965 (1990).
[CrossRef] [PubMed]

M. M. Hayhoe, N. I. Benimoff, D. C. Hood, “The time-course of multiplicative and subtractive adaptation process,” Vision Res. 27, 1981–1996 (1987).
[CrossRef] [PubMed]

He, J.

Hogg, C. R.

G. B. Arden, C. R. Hogg, “Absence of rod–cone interaction and analysis of retinal disease,” Br. J. Ophthalmol. 69, 404–415 (1985).
[CrossRef] [PubMed]

Hood, D. C.

D. C. Hood, N. Graham, T. E. von Wiegand, V. M. Chase, “Probed-sinewave paradigm: a test of models of light-adaptation dynamics,” Vision Res. 37, 1177–1191 (1997).
[CrossRef] [PubMed]

T. E. von Wiegand, D. C. Hood, N. Graham, “Testing a computational model of light-adaptation dynamics,” Vision Res. 35, 3037–3051 (1995).
[CrossRef] [PubMed]

D. C. Hood, D. G. Birch, “Phototransduction in human cones measured using the a-wave of the ERG,” Vision Res. 35, 2801–2810 (1995).
[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]

M. M. Hayhoe, N. I. Benimoff, D. C. Hood, “The time-course of multiplicative and subtractive adaptation process,” Vision Res. 27, 1981–1996 (1987).
[CrossRef] [PubMed]

Horiguchi, M.

M. Horiguchi, T. Eysteinsson, G. B. Arden, “Temporal and spatial properties of suppressive rod–cone interaction,” Invest. Ophthalmol. Visual Sci. 32, 575–581 (1991).

Kaplan, E.

E. A. Benardete, E. Kaplan, B. W. Knight, “Contrast gain control in the primate retina: P cells are not X-like, some M cells are,” Visual Neurosci 8, 483–486 (1992).
[CrossRef]

Kelly, D. H.

D. H. Kelly, “Flicker” in Handbook of Sensory Physiology, Vol. 7, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972), pp. 273–302.

Knight, B. W.

E. A. Benardete, E. Kaplan, B. W. Knight, “Contrast gain control in the primate retina: P cells are not X-like, some M cells are,” Visual Neurosci 8, 483–486 (1992).
[CrossRef]

Koshel, R. J.

M. M. Hayhoe, M. E. Levin, R. J. Koshel, “Subtractive processes in light adaptation,” Vision Res. 32, 323–333 (1992).
[CrossRef] [PubMed]

Kreitz, M. R.

S. A. Burns, A. E. Elsner, M. R. Kreitz, “Analysis of nonlinearities in the flicker ERG,” Optom. Vis. Sci. 69, 95–105 (1992).
[CrossRef] [PubMed]

Kremers, J.

B. B. Lee, J. Pokorny, V. C. Smith, J. Kremers, “Re-sponses to pulses and sinusoids in macaque ganglion cells,” Vision Res. 34, 3081–3096 (1994).
[CrossRef] [PubMed]

J. Kremers, B. B. Lee, J. Pokorny, V. C. Smith, “Responses of macaque ganglion cells and human observers to compound periodic waveforms,” Vision Res. 33, 1997–2011 (1993).
[CrossRef] [PubMed]

Kronauer, R. E.

C. F. Stromeyer, A. Chaparo, A. S. Tolias, R. E. Kronauer, “Colour adaptation modifies the long-wave versus middle-wave cone weights and temporal phases in human luminance (but not red–green) mechanism,” J. Physiol. (London) 499, 227–254 (1997).

Lange, G.

Lee, B. B.

B. B. Lee, “Receptive field structure in the primate retina,” Vision Res. 36, 631–644 (1996).
[CrossRef] [PubMed]

B. B. Lee, J. Pokorny, V. C. Smith, J. Kremers, “Re-sponses to pulses and sinusoids in macaque ganglion cells,” Vision Res. 34, 3081–3096 (1994).
[CrossRef] [PubMed]

J. Kremers, B. B. Lee, J. Pokorny, V. C. Smith, “Responses of macaque ganglion cells and human observers to compound periodic waveforms,” Vision Res. 33, 1997–2011 (1993).
[CrossRef] [PubMed]

Lennie, P.

Levin, M. E.

M. M. Hayhoe, M. E. Levin, R. J. Koshel, “Subtractive processes in light adaptation,” Vision Res. 32, 323–333 (1992).
[CrossRef] [PubMed]

MacLeod, D. I. A.

Marcus, S.

Massof, R. W.

Meister, M.

J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fasicularis,” J. Physiol. (London) 427, 681–713 (1990).

Nelson, R.

R. Nelson, R. Pflug, S. M. Baer, “Background-induced flicker enhancement in cat retinal horizontal cells. II. Spatial properties,” J. Neurophysiol. 64, 326–340 (1990).
[PubMed]

Nunn, B. J.

J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fasicularis,” J. Physiol. (London) 427, 681–713 (1990).

Nygaard, R. W.

S. H. Goldberg, T. E. Frumkes, R. W. Nygaard, “Inhibi-tory influence of unstimulated rods in the human retina: evidence provided by examining cone flicker,” Science 221, 180–182 (1983).
[CrossRef] [PubMed]

Peachey, N. S.

N. S. Peachey, K. R. Alexander, D. J. Derlacki, G. A. Fishman, “Light adaptation, rods and the human flicker ERG,” Visual Neurosci. 8145–150 (1992).
[CrossRef]

N. S. Peachey, K. R. Alexander, D. J. Derlacki, “Spatial properties of rod–cone interactions in flicker and hue detection,” Vision Res. 30, 1205–1210 (1990).
[CrossRef]

Pflug, R.

R. Nelson, R. Pflug, S. M. Baer, “Background-induced flicker enhancement in cat retinal horizontal cells. II. Spatial properties,” J. Neurophysiol. 64, 326–340 (1990).
[PubMed]

Pokorny, J.

B. B. Lee, J. Pokorny, V. C. Smith, J. Kremers, “Re-sponses to pulses and sinusoids in macaque ganglion cells,” Vision Res. 34, 3081–3096 (1994).
[CrossRef] [PubMed]

P. Lennie, J. Pokorny, V. C. Smith, “Luminance,” J. Opt. Soc. Am. A 10, 1283–1293 (1993).
[CrossRef] [PubMed]

J. Kremers, B. B. Lee, J. Pokorny, V. C. Smith, “Responses of macaque ganglion cells and human observers to compound periodic waveforms,” Vision Res. 33, 1997–2011 (1993).
[CrossRef] [PubMed]

Reifsnider, E. S.

I. D. Cadenas, E. S. Reifsnider, D. Tranchina, “Modulation of synaptic transfer between retinal cones and horizontal cells by spatial contrast,” J. Gen. Physiol. 104, 567–591 (1994).
[CrossRef] [PubMed]

Schnapf, J. L.

J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fasicularis,” J. Physiol. (London) 427, 681–713 (1990).

Smith, V. C.

B. B. Lee, J. Pokorny, V. C. Smith, J. Kremers, “Re-sponses to pulses and sinusoids in macaque ganglion cells,” Vision Res. 34, 3081–3096 (1994).
[CrossRef] [PubMed]

P. Lennie, J. Pokorny, V. C. Smith, “Luminance,” J. Opt. Soc. Am. A 10, 1283–1293 (1993).
[CrossRef] [PubMed]

J. Kremers, B. B. Lee, J. Pokorny, V. C. Smith, “Responses of macaque ganglion cells and human observers to compound periodic waveforms,” Vision Res. 33, 1997–2011 (1993).
[CrossRef] [PubMed]

Stromeyer, C. F.

C. F. Stromeyer, A. Chaparo, A. S. Tolias, R. E. Kronauer, “Colour adaptation modifies the long-wave versus middle-wave cone weights and temporal phases in human luminance (but not red–green) mechanism,” J. Physiol. (London) 499, 227–254 (1997).

Sunness, J. S.

Tolias, A. S.

C. F. Stromeyer, A. Chaparo, A. S. Tolias, R. E. Kronauer, “Colour adaptation modifies the long-wave versus middle-wave cone weights and temporal phases in human luminance (but not red–green) mechanism,” J. Physiol. (London) 499, 227–254 (1997).

Tranchina, D.

I. D. Cadenas, E. S. Reifsnider, D. Tranchina, “Modulation of synaptic transfer between retinal cones and horizontal cells by spatial contrast,” J. Gen. Physiol. 104, 567–591 (1994).
[CrossRef] [PubMed]

von Wiegand, T. E.

D. C. Hood, N. Graham, T. E. von Wiegand, V. M. Chase, “Probed-sinewave paradigm: a test of models of light-adaptation dynamics,” Vision Res. 37, 1177–1191 (1997).
[CrossRef] [PubMed]

T. E. von Wiegand, D. C. Hood, N. Graham, “Testing a computational model of light-adaptation dynamics,” Vision Res. 35, 3037–3051 (1995).
[CrossRef] [PubMed]

Watson, A. B.

A. B. Watson, “Temporal sensitivity,” in Sensory Processes and Perception, Vol. I of Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 6-1–6-43.

Wu, S.

Wu, S. M.

T. E. Frumkes, S. M. Wu, “Independent influences on cone-mediated responses to light onset and offset in distal retinal neurons,” J. Neurophysiol. 64, 1043–1054 (1990).
[PubMed]

Appl. Opt.

Br. J. Ophthalmol.

G. B. Arden, C. R. Hogg, “Absence of rod–cone interaction and analysis of retinal disease,” Br. J. Ophthalmol. 69, 404–415 (1985).
[CrossRef] [PubMed]

Clin. Vision Sci.

N. Denny, T. E. Frumkes, S. H. Goldberg, “Comparison of summatory and suppressive rod–cone interaction,” Clin. Vision Sci. 5, 27–36 (1990).

Invest. Ophthalmol. Visual Sci.

M. Horiguchi, T. Eysteinsson, G. B. Arden, “Temporal and spatial properties of suppressive rod–cone interaction,” Invest. Ophthalmol. Visual Sci. 32, 575–581 (1991).

J. Gen. Physiol.

I. D. Cadenas, E. S. Reifsnider, D. Tranchina, “Modulation of synaptic transfer between retinal cones and horizontal cells by spatial contrast,” J. Gen. Physiol. 104, 567–591 (1994).
[CrossRef] [PubMed]

J. Neurophysiol.

R. Nelson, R. Pflug, S. M. Baer, “Background-induced flicker enhancement in cat retinal horizontal cells. II. Spatial properties,” J. Neurophysiol. 64, 326–340 (1990).
[PubMed]

T. E. Frumkes, S. M. Wu, “Independent influences on cone-mediated responses to light onset and offset in distal retinal neurons,” J. Neurophysiol. 64, 1043–1054 (1990).
[PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Physiol. (London)

C. F. Stromeyer, A. Chaparo, A. S. Tolias, R. E. Kronauer, “Colour adaptation modifies the long-wave versus middle-wave cone weights and temporal phases in human luminance (but not red–green) mechanism,” J. Physiol. (London) 499, 227–254 (1997).

J. L. Schnapf, B. J. Nunn, M. Meister, D. A. Baylor, “Visual transduction in cones of the monkey Macaca fasicularis,” J. Physiol. (London) 427, 681–713 (1990).

Optom. Vis. Sci.

S. A. Burns, A. E. Elsner, M. R. Kreitz, “Analysis of nonlinearities in the flicker ERG,” Optom. Vis. Sci. 69, 95–105 (1992).
[CrossRef] [PubMed]

Science

S. H. Goldberg, T. E. Frumkes, R. W. Nygaard, “Inhibi-tory influence of unstimulated rods in the human retina: evidence provided by examining cone flicker,” Science 221, 180–182 (1983).
[CrossRef] [PubMed]

Vision Res.

K. R. Alexander, G. A. Fishman, “Rod influence on cone flicker detection: variation with retinal eccentricity,” Vision Res. 26, 827–834 (1986).
[CrossRef] [PubMed]

N. J. Coletta, A. J. Adams, “Spatial extent of rod–cone and cone–cone interactions for flicker detection,” Vision Res. 26, 917–925 (1986).
[CrossRef]

G. B. Arden, T. E. Frumkes, “Stimulation of rods can increase cone flicker ERGs in man,” Vision Res. 26, 711–721 (1986).
[CrossRef] [PubMed]

A. Eisner, “Losses of flicker sensitivity during dark adaptation: effects of test size and wavelength,” Vision Res. 32, 1975–1986 (1992).
[CrossRef] [PubMed]

N. S. Peachey, K. R. Alexander, D. J. Derlacki, “Spatial properties of rod–cone interactions in flicker and hue detection,” Vision Res. 30, 1205–1210 (1990).
[CrossRef]

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

M. M. Hayhoe, M. E. Levin, R. J. Koshel, “Subtractive processes in light adaptation,” Vision Res. 32, 323–333 (1992).
[CrossRef] [PubMed]

M. M. Hayhoe, N. I. Benimoff, D. C. Hood, “The time-course of multiplicative and subtractive adaptation process,” Vision Res. 27, 1981–1996 (1987).
[CrossRef] [PubMed]

T. E. von Wiegand, D. C. Hood, N. Graham, “Testing a computational model of light-adaptation dynamics,” Vision Res. 35, 3037–3051 (1995).
[CrossRef] [PubMed]

D. C. Hood, N. Graham, T. E. von Wiegand, V. M. Chase, “Probed-sinewave paradigm: a test of models of light-adaptation dynamics,” Vision Res. 37, 1177–1191 (1997).
[CrossRef] [PubMed]

A. Eisner, “Losses of foveal flicker sensitivity during dark adaptation following extended bleaches,” Vision Res. 29, 1401–1423 (1989).
[CrossRef] [PubMed]

M. M. Hayhoe, “Spatial interactions and models of adaptation,” Vision Res. 30, 957–965 (1990).
[CrossRef] [PubMed]

J. Kremers, B. B. Lee, J. Pokorny, V. C. Smith, “Responses of macaque ganglion cells and human observers to compound periodic waveforms,” Vision Res. 33, 1997–2011 (1993).
[CrossRef] [PubMed]

D. C. Hood, D. G. Birch, “Phototransduction in human cones measured using the a-wave of the ERG,” Vision Res. 35, 2801–2810 (1995).
[CrossRef] [PubMed]

B. B. Lee, J. Pokorny, V. C. Smith, J. Kremers, “Re-sponses to pulses and sinusoids in macaque ganglion cells,” Vision Res. 34, 3081–3096 (1994).
[CrossRef] [PubMed]

B. B. Lee, “Receptive field structure in the primate retina,” Vision Res. 36, 631–644 (1996).
[CrossRef] [PubMed]

Visual Neurosci

E. A. Benardete, E. Kaplan, B. W. Knight, “Contrast gain control in the primate retina: P cells are not X-like, some M cells are,” Visual Neurosci 8, 483–486 (1992).
[CrossRef]

Visual Neurosci.

T. E. Frumkes, T. Eysteinsson, “The cellular basis for suppressive rod-cone interaction,” Visual Neurosci. 1263–273 (1988).
[CrossRef]

N. S. Peachey, K. R. Alexander, D. J. Derlacki, G. A. Fishman, “Light adaptation, rods and the human flicker ERG,” Visual Neurosci. 8145–150 (1992).
[CrossRef]

Other

D. H. Kelly, “Flicker” in Handbook of Sensory Physiology, Vol. 7, D. Jameson, L. M. Hurvich, eds. (Springer-Verlag, New York, 1972), pp. 273–302.

A. B. Watson, “Temporal sensitivity,” in Sensory Processes and Perception, Vol. I of Handbook of Perception and Human Performance, K. R. Boff, L. Kaufman, J. P. Thomas, eds. (Wiley, New York, 1986), pp. 6-1–6-43.

There is a bound on how negative (i.e., how much below baseline) the trough response can become at the input to the saturating nonlinearity. As this trough response approaches -σn, the saturating nonlinearity approaches a singularity. If the subbaseline response at the input to the saturating nonlinearity cannot reach -σn then there will be no singularity.

The nonmonotonicity can be steeper yet if s(I)≠kg(I)I but instead s(I)=k(I)g(I)I, with k(I) being a decreasing function of I rather than a constant. However, the degree of steepening is severely constrained if F(I)=g(I)I-s(I) is constrained to be a positive compressive function of I.

In fact, the illuminance level at the threshold for the disappearance of flicker would exceed the illuminance level of a stimulus for which flicker visibility would equal that at the threshold for the initial appearance of flicker. This is because the threshold for the initial appearance of flicker is based on a three-or-more-of-four detection criterion whereas the threshold for the disappearance of flicker is equivalent to a one-or-fewer-of-four detection criterion. Therefore the distance between the thresholds for the initial appearance and subsequent disappearance of flicker would exceed the distance between two equally visible threshold-level flickering stimuli.

We do not know whether the uppermost flicker thresholds remain mediated by MWS cones at surround illuminances for which the uppermost flicker thresholds have systematically decreased. It is possible that at those relatively high surround illuminances, subthreshold MWS and LWS responses combined to produce a suprathreshold flicker response.

The fixed modulation depth was set at 99.5% rather than 100% to avoid potential artifacts resulting from the use of pulse-density modulation, as discussed previously.5 The choices of temporal frequency were constrained by the need to obtain flicker tvi curves with abrupt decreases and by the intent to induce abrupt decreases with changes of surround illuminance that were on the order of several tenths of a log unit for 0.1-log-unit decrements of modulation depth. The upper limits of the variable temporal frequency sequence were constrained mainly by the long duration of individual testing sessions, particularly for TQN. For JAM we sought to collect data over temporal frequency and modulation depth ranges that were as comparable to TQN’s as feasible.

Proof that the ratio of ac:dc response decreases with increasing dc test illuminance I for any pathway that responds instantaneously and compressively to dc stimuli: We denote the dc response output by the pathway as r(I). The ac:dc ratio is given by [r(I+mI)-r(I-mI)]/r(I), where m signifies modulation depth. Since r is compressive, r(I+mI)/r(I) decreases with I. Similarly, r(I)/r(I-mI) decreases with I, which implies that -r(I-mI)/r(I) also decreases with I. Therefore [r(I+mI)-r(I-mI)]/r(I), decreases with I.

Specifically, at a dc test illuminance 0.4 log unit above the threshold for a 99.5% modulation depth test and at a surround illuminance 0.1 log unit above that which elicited an abrupt decrease of the flicker threshold to that 99.5% modulation depth stimulus, 80% modulation depth flicker remained invisible at every flash for a period of at least 2 min, whereas the 99.5% modulation depth flicker remained visible for at least 30 s before becoming invisible for even a single flash. This experiment was conducted with 18-Hz stimuli for two subjects (TQN plus one other subject; JAM was not tested). In contrast, at surround illuminances 0.1 log unit below that which elicited an abrupt decrease of the flicker threshold, flicker often was visible for one or two out of four flashes at test illuminances that corresponded to flicker threshold at the higher surround illuminances. This observation was made for TQN and JAM.

We assume that gI and gI-s are smooth compressively nonlinear positive functions of I. We define g′ to be a stronger multiplicative adaptation function than g if g′I<gI and d(g′I)/dI<d(gI)/dI. Similarly, we define s′ to be a stronger subtractive adaptation function than s if gI-s′<gI-s and d(gI-s′)/dI<d(gI-s)/dI or, equivalently, if s′>s and ds′/dI>ds/dI.

An alternative solution, one in which flicker response would be enhanced at progressively higher test illuminances as surround illuminance increased, is ruled out by the failure of subject TQN’s corner data to shift to higher test illuminances across relatively dim surround illuminances.

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Figures (7)

Fig. 1
Fig. 1

Flicker tvi curve for 11-Hz, 40% modulation depth sinusoidally modulated flicker for subject TQN. The lower branch (open squares) is comprised of thresholds for the initial appearance of flicker. The upper branch (crosses) is comprised of thresholds either for the initial appearance of flicker at low surround illuminances or else for the reappearance of flicker at higher surround illuminances. [The absence of a cross at a surround illuminance of 1.0 log td is due to light level limitations in the test channel.] The middle branch (filled squares) is comprised of thresholds for the disappearance of flicker. The region of flicker tvi stimulus space for which flicker response is suppressed and for which flicker consequently is invisible is represented by the shaded area. Appearance corner and disappearance corner terminology is defined in the text.

Fig. 2
Fig. 2

Corner data curves (see text for definition) for the initial appearance (open symbols) and disappearance (filled symbols) of flicker. Data are presented from four consecutive testing sessions, numbered sequentially. Squares, data from the modulation depth sequence; circles, data from the temporal frequency sequence. The fixed modulation depth for the temporal frequency sequence was 99.5%. (a) Results for subject TQN. The temporal frequency at which this sequence began was 14 Hz, and the incremental units were 1 Hz. The fixed temporal frequency for the modulation depth sequence was 11 Hz, the modulation depth at which this sequence began was 51%, and the decremental units were approximately 0.1 log unit. (b) Same as (a) but for subject JAM. The temporal frequency sequence began at 16 Hz, the modulation depth sequence began at 40%, and the maximum dc test illuminance possible was 3.0 log td.

Fig. 3
Fig. 3

Corresponding log modulation depths and log temporal frequencies, derived from the four sets of corner data in Fig. 2(a) (see text for definition of “correspondence”). For each temporal frequency, error bars are standard deviations about the mean of the corresponding log modulation depths. (a) Results for subject TQN. The solid line represents the least-squares linear regression line through all the data, from 14–20 Hz; the solid circle on the upper axis represents 11-Hz, 99.5% modulation depth. (b) Same as (a), except that correspondences are derived from the data in Fig. 2(b) and are for subject JAM, and data are from 16–21 Hz.

Fig. 4
Fig. 4

Schematic diagram of the MUSNOL model for flicker. The front end of this model is given by a distal temporal frequency response filter μ in tandem with a multiplicative adaptation process g (for gain). A subtractive feed-forward adaptation process s is interspersed between the front end and a static saturating nonlinearity, assumed to be of the Michaelis–Menton or Naka–Rushton type with half-saturation constant σ and exponent n. There is a final temporal frequency filter T. The variable I represents the illuminance of the dc component of the test stimulus. The peak-to-trough response difference, R(I), that determines the flicker signal is given by R(I)=[gI(1+μ)-s]n/{[gI(1+μ)-s]n+σn}-[gI(1-μ)-s]n/{[(gI(1-μ)-s]n+σn}.

Fig. 5
Fig. 5

The solid curve represents a hypothetical graph of the dc response output from a saturating nonlinearity as function of dc illuminance I. The intersections of each pair of vertical lines with the abscissa define the ac excursion at a fixed modulation depth about each of three test illuminances: low (I1), intermediate (I2), and high (I3). The intersections of each pair of horizontal lines with the ordinate define the corresponding peak-to-trough response excursions, R1, R2, and R3, output by the saturating nonlinearity. The peak-to-trough response excursion is greatest for the intermediate dc test illuminance. For simplicity, the abscissa in this graph represents dc test illuminance and the ac excursion is for incomplete physical contrast, i.e., for a temporal modulation depth <100%. Equivalently, the abscissa could have represented the response output by the model’s front end, in which case the ac excursion would represent the physiologic modulation of the front end’s response, which would be incomplete even if the modulation depth of the physical stimulus were 100%.

Fig. 6
Fig. 6

Peak-to-trough flicker responses generated by the MUSNOL model. The different curves represent the peak-to-trough flicker response function for different values of μ. To derive the curve for μ=70% in (b), we needed to extend the nonlinearity in the MUSNOL model so that it was defined for negative (i.e., subbaseline) stimuli. We did this by creating an odd-symmetric mirror image across the origin of the same instantaneous nonlinearity that we used for positive stimuli. For μ=80%, the peak-to-trough response function would have become undefined at high enough I. The parameters or functions were (a) g(I)=I/(I+100 td), s=0, n=1, σ=25; (b) g(I)=I/(I+100 td), s=0.5[g(I)]I, n=1, σ=25.

Fig. 7
Fig. 7

The top graphs collectively represent a family of hypothetical flicker response versus dc test illuminance functions for a test stimulus of fixed modulation depth at a series of progressively higher surround illuminances, given by A, B, and C. The horizontal dashed lines represent the flicker response at threshold. The bottom graph portrays an idealized flicker tvi curve with the three surround illuminances, A, B, and C, noted on the abscissa. The region of flicker tvi stimulus space for which flicker response is suppressed and for which flicker consequently is invisible is represented by the shaded area.

Equations (14)

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R(I)={gI(1+μ)/[gI(1+μ)+σ]}-{gI(1-μ)/[(gI(1-μ)+σ]}.
R(I)=2σgIμ/[g2I2(1-μ2)+2σgI+σ2].
0=[d(gI)/dI][(σ2-g2I2(1-μ2)]/[g2I2(1-μ2)+2σgI+σ2]2.
I0=σ/[g(1-μ2)1/2],
R(I)=[gI(1+μ)]n/{[gI(1+μ)]n+σn}-[gI(1-μ)]n/{[gI(1-μ)]n+σn}.
R(I)=σn(gI)nz/[(gI)2n(1-μ2)n+σn(gI)ny+σ2n].
dR/dI=(σnz)[d(gI)n/dI][σ2n-(gI)2n(1-μ2)n]/[(gI)2n(1-μ2)n+σn(gI)ny+σ2n]2.
0=[d(gI)n/dI][σ2n-(gI)2n(1-μ2)n],
R(I)=[gI(1+μ)-s]/[gI(1+μ)-s+σ]-[gI(1-μ)-s]/[(gI(1-μ)-s+σ].
h(I)I=g(I)I-s(I)=g(I)I-kg(I)I.
μs=μ/(1-k).
R(I)=hI(1+μs)/[hI(1+μs)+σ]-hI(1-μs)/[hI(1-μs)+σ],
R(I)=[gI(1+μ)-s]n/{[gI(1+μ)-s]n+σn}-[gI(1-μ)-s]n/{[gI(1-μ)-s]n+σn},
R(I)=[hI(1+μs)]n/{[hI(1+μs)]n+σn}-[hI(1-μs)]n/{[hI(1-μs)]n+σn},

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