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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 8 — Aug. 1, 1998
  • pp: 1987–2002

Equivalence between temporal frequency and modulation depth for flicker response suppression: analysis of a three-process model of visual adaptation

Alvin Eisner, Arthur G. Shapiro, and Joel A. Middleton  »View Author Affiliations

JOSA A, Vol. 15, Issue 8, pp. 1987-2002 (1998)

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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

OCIS Codes
(330.1800) Vision, color, and visual optics : Vision - contrast sensitivity
(330.4060) Vision, color, and visual optics : Vision modeling
(330.5510) Vision, color, and visual optics : Psychophysics
(330.6790) Vision, color, and visual optics : Temporal discrimination
(330.7320) Vision, color, and visual optics : Vision adaptation

Original Manuscript: November 13, 1997
Revised Manuscript: March 19, 1998
Manuscript Accepted: March 23, 1998
Published: August 1, 1998

Alvin Eisner, Arthur G. Shapiro, and Joel A. Middleton, "Equivalence between temporal frequency and modulation depth for flicker response suppression: analysis of a three-process model of visual adaptation," J. Opt. Soc. Am. A 15, 1987-2002 (1998)

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  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.
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  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.
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  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.
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  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.
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