Abstract

High-contrast luminance gratings stabilized on the retina with a Purkinje image eyetracker do not disappear completely. This could be due to small errors of stabilization, or the visual system could include mechanisms capable of responding to temporally constant images. We examined the visual system’s sensitivity to small movements of gratings. We (1) replicated previous measurements of contrast sensitivity for gratings with controlled retinal-drift velocities, (2) developed a method for calculating sensitivity to small oscillations of gratings using thresholds for flickering stabilized gratings, and (3) examined the calculations empirically. We calculated that movements of only 8 sec of arc peak to peak produce detectable temporal changes. Since existent stabilization systems cannot eliminate movements this small, residual stabilized-grating detectability does not require detectors sensitive to temporally constant images.

© 1986 Optical Society of America

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References

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  1. U. T. Keesey, R. M. Jones, “The effect of micromovements of the eye and exposure duration on contrast sensitivity,” Vision Res. 16, 481–488 (1976).
    [Crossref]
  2. D. H. Kelly, “Motion and vision. I. Stabilized images of stationary gratings,”J. Opt. Soc. Am. 69, 1266–1274 (1979).
    [Crossref] [PubMed]
  3. D. H. Kelly, “Motion and vision. II. Stabilized spatiotemporal threshold surface,”J. Opt. Soc. Am. 69, 1340–1349 (1979).
    [Crossref] [PubMed]
  4. C. A. Burbeck, D. H. Kelly, “Role of local adaptation in fading of stabilized images,” J. Opt. Soc. Am. A 1, 216–220 (1984).
    [Crossref] [PubMed]
  5. H. J. M. Gerrits, B. de Haan, A. J. H. Vendrik, “Experiments with retinal stabilized images. Relations between the observations and neural data,” Vision Res. 6, 427–440 (1966).
    [Crossref] [PubMed]
  6. A. L. Yarbus, Eye Movements and Vision (Plenum, New York, 1967).
  7. In this paper this is the only property attributed to static psychophysical detectors. The term dynamic detector will similarly be used only to indicate a detector that has zero sensitivity at 0 Hz, i.e., one that requires temporal modulation on the retina, generated by movement of all or part of the retinal image or modulation of the external image. We make no physiological reference whatsoever and intentionally base our entire analysis on psychophysical evidence alone.
  8. R. M. Jones, U. T. Keesey, “Accuracy of image stabilization by an optical-electronic feedback system,” Vision Res. 15, 57–61 (1975).
    [Crossref] [PubMed]
  9. C. H. Graham, Vision and Visual Perception (Wiley, New York, 1965).
  10. At this velocity the maximum local temporal rate of luminance change is 0.002 log unit/sec. For comparison, a pupil change from 2 to 2.0045 mm would produce a 0.002-log-unit luminance increase over the entire image.
  11. H. D. Crane, T. N. Cornsweet, “Ocular focus stimulator,”J. Opt. Soc. Am. 60, 577 (1970).
  12. A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980).
    [Crossref] [PubMed]
  13. L. E. Arend, “Temporal determinants of the form of the spatial contrast threshold MTF,” Vision Res. 16, 1035–1042 (1976).
    [Crossref] [PubMed]
  14. E. Levinson, R. Sekuler, “The independence of channels in human vision selective for direction of movement,”J. Physiol. (London) 250, 347–366 (1975).
  15. Subject AS adopted a conservative criterion for appearance during the 5-sec interval and therefore had lower sensitivities.
  16. J. J. Koenderink, A. J. van Doorn, “Visibility of unpredictably flickering lights,”J. Opt. Soc. Am. 64, 1517–1522 (1974).
    [Crossref] [PubMed]
  17. L. E. Arend, A. Skavenski, “Free scanning of gratings produces patterned retinal exposure,” Vision Res. 19, 1413–1419 (1979).
    [Crossref] [PubMed]
  18. A new contact-lens coil system developed at the University of Maryland may be capable of the required precision (R. Steinman, Department of Psychology, University of Maryland, College Park, Maryland 20742, personal communication).
  19. D. H. Kelly, “Spatiotemporal variation of chromatic and achromatic contrast thresholds,”J. Opt. Soc. Am. 73, 742–750 (1983).
    [Crossref] [PubMed]
  20. C. Burbeck, D. H. Kelly, “Eliminating transient artifacts in stabilized-image contrast thresholds,”J. Opt. Soc. Am. 72, 1238–1243 (1982).
    [Crossref] [PubMed]
  21. A lateral shift of pupil entry by 0.5 mm produces a Stiles–Crawford effect of 0.002 log unit [Y. LeGrand, Light, Colour, and Vision (Chapman and Hall, London, 1968)].

1984 (1)

1983 (1)

1982 (1)

1980 (1)

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980).
[Crossref] [PubMed]

1979 (3)

1976 (2)

L. E. Arend, “Temporal determinants of the form of the spatial contrast threshold MTF,” Vision Res. 16, 1035–1042 (1976).
[Crossref] [PubMed]

U. T. Keesey, R. M. Jones, “The effect of micromovements of the eye and exposure duration on contrast sensitivity,” Vision Res. 16, 481–488 (1976).
[Crossref]

1975 (2)

R. M. Jones, U. T. Keesey, “Accuracy of image stabilization by an optical-electronic feedback system,” Vision Res. 15, 57–61 (1975).
[Crossref] [PubMed]

E. Levinson, R. Sekuler, “The independence of channels in human vision selective for direction of movement,”J. Physiol. (London) 250, 347–366 (1975).

1974 (1)

1970 (1)

1966 (1)

H. J. M. Gerrits, B. de Haan, A. J. H. Vendrik, “Experiments with retinal stabilized images. Relations between the observations and neural data,” Vision Res. 6, 427–440 (1966).
[Crossref] [PubMed]

Arend, L. E.

L. E. Arend, A. Skavenski, “Free scanning of gratings produces patterned retinal exposure,” Vision Res. 19, 1413–1419 (1979).
[Crossref] [PubMed]

L. E. Arend, “Temporal determinants of the form of the spatial contrast threshold MTF,” Vision Res. 16, 1035–1042 (1976).
[Crossref] [PubMed]

Burbeck, C.

Burbeck, C. A.

Cornsweet, T. N.

Crane, H. D.

de Haan, B.

H. J. M. Gerrits, B. de Haan, A. J. H. Vendrik, “Experiments with retinal stabilized images. Relations between the observations and neural data,” Vision Res. 6, 427–440 (1966).
[Crossref] [PubMed]

Gerrits, H. J. M.

H. J. M. Gerrits, B. de Haan, A. J. H. Vendrik, “Experiments with retinal stabilized images. Relations between the observations and neural data,” Vision Res. 6, 427–440 (1966).
[Crossref] [PubMed]

Graham, C. H.

C. H. Graham, Vision and Visual Perception (Wiley, New York, 1965).

Jones, R. M.

U. T. Keesey, R. M. Jones, “The effect of micromovements of the eye and exposure duration on contrast sensitivity,” Vision Res. 16, 481–488 (1976).
[Crossref]

R. M. Jones, U. T. Keesey, “Accuracy of image stabilization by an optical-electronic feedback system,” Vision Res. 15, 57–61 (1975).
[Crossref] [PubMed]

Keesey, U. T.

U. T. Keesey, R. M. Jones, “The effect of micromovements of the eye and exposure duration on contrast sensitivity,” Vision Res. 16, 481–488 (1976).
[Crossref]

R. M. Jones, U. T. Keesey, “Accuracy of image stabilization by an optical-electronic feedback system,” Vision Res. 15, 57–61 (1975).
[Crossref] [PubMed]

Kelly, D. H.

Koenderink, J. J.

LeGrand, Y.

A lateral shift of pupil entry by 0.5 mm produces a Stiles–Crawford effect of 0.002 log unit [Y. LeGrand, Light, Colour, and Vision (Chapman and Hall, London, 1968)].

Levinson, E.

E. Levinson, R. Sekuler, “The independence of channels in human vision selective for direction of movement,”J. Physiol. (London) 250, 347–366 (1975).

Murphy, B. J.

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980).
[Crossref] [PubMed]

Nachmias, J.

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980).
[Crossref] [PubMed]

Sekuler, R.

E. Levinson, R. Sekuler, “The independence of channels in human vision selective for direction of movement,”J. Physiol. (London) 250, 347–366 (1975).

Skavenski, A.

L. E. Arend, A. Skavenski, “Free scanning of gratings produces patterned retinal exposure,” Vision Res. 19, 1413–1419 (1979).
[Crossref] [PubMed]

Steinman, R.

A new contact-lens coil system developed at the University of Maryland may be capable of the required precision (R. Steinman, Department of Psychology, University of Maryland, College Park, Maryland 20742, personal communication).

Thompson, P. G.

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980).
[Crossref] [PubMed]

van Doorn, A. J.

Vendrik, A. J. H.

H. J. M. Gerrits, B. de Haan, A. J. H. Vendrik, “Experiments with retinal stabilized images. Relations between the observations and neural data,” Vision Res. 6, 427–440 (1966).
[Crossref] [PubMed]

Watson, A. B.

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980).
[Crossref] [PubMed]

Yarbus, A. L.

A. L. Yarbus, Eye Movements and Vision (Plenum, New York, 1967).

J. Opt. Soc. Am. (6)

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

J. Physiol. (London) (1)

E. Levinson, R. Sekuler, “The independence of channels in human vision selective for direction of movement,”J. Physiol. (London) 250, 347–366 (1975).

Vision Res. (6)

L. E. Arend, A. Skavenski, “Free scanning of gratings produces patterned retinal exposure,” Vision Res. 19, 1413–1419 (1979).
[Crossref] [PubMed]

U. T. Keesey, R. M. Jones, “The effect of micromovements of the eye and exposure duration on contrast sensitivity,” Vision Res. 16, 481–488 (1976).
[Crossref]

H. J. M. Gerrits, B. de Haan, A. J. H. Vendrik, “Experiments with retinal stabilized images. Relations between the observations and neural data,” Vision Res. 6, 427–440 (1966).
[Crossref] [PubMed]

A. B. Watson, P. G. Thompson, B. J. Murphy, J. Nachmias, “Summation and discrimination of gratings moving in opposite directions,” Vision Res. 20, 341–348 (1980).
[Crossref] [PubMed]

L. E. Arend, “Temporal determinants of the form of the spatial contrast threshold MTF,” Vision Res. 16, 1035–1042 (1976).
[Crossref] [PubMed]

R. M. Jones, U. T. Keesey, “Accuracy of image stabilization by an optical-electronic feedback system,” Vision Res. 15, 57–61 (1975).
[Crossref] [PubMed]

Other (7)

C. H. Graham, Vision and Visual Perception (Wiley, New York, 1965).

At this velocity the maximum local temporal rate of luminance change is 0.002 log unit/sec. For comparison, a pupil change from 2 to 2.0045 mm would produce a 0.002-log-unit luminance increase over the entire image.

A. L. Yarbus, Eye Movements and Vision (Plenum, New York, 1967).

In this paper this is the only property attributed to static psychophysical detectors. The term dynamic detector will similarly be used only to indicate a detector that has zero sensitivity at 0 Hz, i.e., one that requires temporal modulation on the retina, generated by movement of all or part of the retinal image or modulation of the external image. We make no physiological reference whatsoever and intentionally base our entire analysis on psychophysical evidence alone.

A lateral shift of pupil entry by 0.5 mm produces a Stiles–Crawford effect of 0.002 log unit [Y. LeGrand, Light, Colour, and Vision (Chapman and Hall, London, 1968)].

A new contact-lens coil system developed at the University of Maryland may be capable of the required precision (R. Steinman, Department of Psychology, University of Maryland, College Park, Maryland 20742, personal communication).

Subject AS adopted a conservative criterion for appearance during the 5-sec interval and therefore had lower sensitivities.

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Figures (5)

Fig. 1
Fig. 1

Mean log sensitivities for stabilized gratings with superimposed constant-velocity drifts. Drift velocity in degrees of arc per second is shown to the right of each curve. (a) Subject LA. Error bars show ±1 standard error of the mean. (b) Corresponding data from Kelly,3 shown for comparison.

Fig. 2
Fig. 2

Mean log sensitivities for drifting (filled symbols) and counterphase flickering (open symbols) gratings. Drift velocity varied as a function of spatial frequency to produce the same 4.4-Hz local temporal modulation as the counterphase flicker. Gratings were either stabilized (squares) or unstabilized (circles). Error bars are 1 standard error of the mean. Subject LA.

Fig. 3
Fig. 3

(a) Mean log sensitivities for stabilized (S) and unstabilized (U) gratings determined using a modified ascending method of limits to reduce exposure to suprathreshold gratings. For comparison, the stabilized (0.0-deg-of-arc/sec) curve from Fig. 1(a) is shown (bottom curve). Subject LA. (b) Subject AS. (c) Difference between unstabilized and stabilized sensitivities from (a) and (b). Circles, subject LA; squares, subject AS.

Fig. 4
Fig. 4

Displacements (γ, sec of arc rms) calculated from eye-tracker-stabilized contrast sensitivities, using Eq. (2). Open circles: Subject DK, luminance contrast, 4-Hz flicker (Ref. 3). Filled circles: Subject DK, chromatic contrast, 4-Hz flicker (Ref. 19). Open triangles: subject DK, luminance contrast, 12 Hz (Ref. 3). Filled triangles: Subject LA, luminance contrast, 4 Hz.

Fig. 5
Fig. 5

Mean log sensitivities for stabilized 1-c/deg gratings temporally modulated by two methods. Top curve (FLICKER) represents sensitivities for counterphase-flickering gratings. Lower curve (MOTION) represents the inverse of the threshold contrast of the local counterphase modulation on the retina produced by l-c/deg gratings moving sinusoidally 3.33 min of arc peak to peak. These contrasts were calculated from the measured thresholds for detecting the moving gratings, using Eq. (2). Subject LA.

Equations (6)

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

L ( x , t ) L M [ 1 + C s sin 2 π f x + ( C s 2 π f γ ) ( cos 2 π ν t ) ( cos 2 π f x ) ] ,
C ν , f = C s 2 π f γ ,
γ = C ν , f / C s 2 π f = 0.014 / 4 π = 0.0011 - deg amplitude ,
L ( x , t ) = L M { 1 + C s sin [ 2 π f ( x + γ cos 2 π ν t ) ] } ,
sin ( A + B ) = sin A ( 1 - ( B 2 / 2 ! ) + ) + cos A [ B - ( B 3 / 3 ! ) + ] .
sin ( A + B ) sin A + B cos A .

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