Abstract

The stabilized contrast-sensitivity function measured at a constant retinal velocity is tuned to a particular spatial frequency, which is inversely related to the velocity chosen. The Fourier transforms of these constant-velocity passbands have the same form as retinal receptive fields of various sizes. At low velocities, in the range of the natural drift motions of the eye, the stabilized contrast-sensitivity function matches the normal, unstabilized result. At higher velocities (corresponding to motions of objects in the environment), this curve maintains the same shape but shifts toward lower spatialfrequencies. The constant-velocity passband is displaced across the spatio-temporal frequency domain in a manner that is almost symmetric about the constant-velocity plane at v = 2 deg/s. Interpolating these diagonal profiles by a suitable analytic expression, we construct the spatio-temporal threshold surface for stabilized vision, and display its properties in terms of the usual frequency parameters; e.g., at low spatial frequencies, the temporal response becomes nearly independent of spatial frequency, while at low temporal frequencies, the spatial response becomes independent of temporal frequency.

© 1979 Optical Society of America

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  1. D. H. Kelly, "Motion and vision. I. Stabilized images of stationary mgratings," J. Opt. Soc. Am. 69, 1266–1274 (1979).
  2. D. H. Kelly, "J0 stimulus patterns for visual research," J. Opt. Soc. Am. 50, 1115–1116 (1960).
  3. D. H. Kelly, Ph.D. thesis, University of California at Los Angeles (1960) (unpublished).
  4. H. Kelly, "New stimuli in vision," in Abbilden utnd Sehen, Proceedings of the 6th meeting of the International Commission for Optics, edited by H. Schober and R. Röhler (Munich, 1962), pp. 119–126.
  5. H. deLange, "Experiments on flicker and some calculations on an electrical analogue of the fovea systems," Physica 18, 935–950 (1952). See also H. deLange, "Research into the dynamic nature of the human fovea-cortex systems with intermittent and modulated light," J. Opt. Soc. Am. 48, 777–789 (1958).
  6. O. H. Schade, "Electro-optical characteristics of television systems. I. Characteristics of vision and visual systems," RCA Review 9, 5–37 (1948).
  7. References 2–4 also proposed the use of circular standing waves, which require two-dimensional analysis. Here we treat only the simpler, one-dimensional case of rectilinear, sine-wave patterns.
  8. D. H. Kelly, "Frequency doubling in visual responses," J. Opt. Soc. Am. 56, 1628–1633 (1966).
  9. J. G. Robson, "Spatial and temporal contrast sensitivity functions of the visual system," J. Opt. Soc. Am. 56, 1141–1142 (1966).
  10. In logarithmic coordinates.
  11. F. L. van Nes, J. J. Koenderink, H. Nas, and M. A. Bouman, "Spatiotemporal modulation transfer in the human eye," J. Opt. Soc. Am. 57, 1082–1088 (1967).
  12. In Ref. 11, horizontal gratings moved vertically, while our vertical gratings moved horizontally. However, there seems to be no evidence of a significant difference between the horizontal and vertical motion thresholds.
  13. E. Levinson and R. Sekular, "The independence of channels in human vision selective for direction of movement," J. Physiol. (Lond.) 250, 347–366 (1975).
  14. D. H. Kelly, "Visual contrast sensitivity," Opt. Acta 24, 107–129 (1977); see Fig. 16.
  15. D. H. Kelly, "Adaptation effects on spatio-temporal sine-wave thresholds," Vision Res. 12, 89–101 (1972).
  16. If the spatial frequency is low enough, the ratio of traveling-wave to standing-wave sensitivity must depend on the phase of the standing wave; e.g., if an antinode of the standing wave fills the visual field, the two sensitivities must be equal. At a node, on the other hand, the standing-wave sensitivity must be zero. Normally the sensitivity ratio falls between these two extreme cases, so there must be some kind of spatial averaging across the standing wave.
  17. Since our flicker and motion signals were derived from different sources, they could not be phase-locked in the present apparatus (see Ref. 1); i.e., we were unable to maintain υ = ω/α exactly. As a result, neither component was perfectly stabilized during this experiment, and the residual destabilization probably increased the thresholds in Fig. 5.
  18. E. M. Levinson (personal communication).
  19. See Ref. 14, Fig. 12.
  20. The zero-velocity data are similar to those given in Ref. 1, Figs. 6–9(d). The question of whether these sustained responses are significantly affected by residual motions in the stabilization apparatus apparatus was discussed in Sec. III of Ref. 1.
  21. A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, "Spatial sine-wave responses of the human visual system," Vision Res. 8, 1245–1263 (1968). See their Fig. 11 (but note that some velocities are identified incorrectly in the figure caption).
  22. L. E. Arend, Jr., "Temporal determinants of the form of the spatial contrast threshold MTF," Vision Res. 16, 1035–1042 (1976). Data are given for three velocities of the fixation point (including zero), in Fig. 5.
  23. R. W. Ditchburn, Eye-movements and Visual Perception (Clarendon, Oxford, 1973), p. 367 et seq.
  24. D. H. Kelly, "Spatial frequency selectivity in the retina"' Vision Res. 15, 665–672 (1975).
  25. D. H. Kelly, "Diffusion model of linear flicker responses," J. Opt. Soc. Am. 59, 1665–1670 (1969).
  26. H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).
  27. J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).
  28. M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).
  29. For example, see B. Fischer, "Overlap of receptive field centers and representation of the visual field in the cat's optic tract," Vision Res. 13, 2113–2120 (1973).
  30. 1f the maximum sensitivity in Figs. 9 and 10 did not vary with velocity, i.e., if k were exactly constant in Eqs. (5) et seq., this area would be exactly constant.
  31. T. H. Harding and C. Enroth-Cugell, "Absolute dark sensitivity and center size in cat retinal ganglion cells," Brain Res. 153, 157–162 (1978), summarizes a number of studies by Enroth-Cugell and her collaborators that confirm this conclusion.
  32. J. J. Koenderink and A. J. van Doorn, "Spatiotemporal contrast detection threshold surface is bimodal," Opt. Lett. 4, 32–34 (1979).
  33. D. H. Kelly and H. S. Magnuski, "Pattern detection and the twodimensional Fourier transform: Circular targets," Vision Res. 15, 911–915 (1975).
  34. J. J. Koenderink (personal communications).
  35. F. W. Campbell and J. G. Robson, "Application of Fourier analysis to the visibility of gratings," J. Physiol. (Lond.) 197, 551–566 (1968).
  36. N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models," Vision Res. 11, 251–259 (1970).
  37. 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. (Lond.) 203, 237–260 (1969).

1979

1978

T. H. Harding and C. Enroth-Cugell, "Absolute dark sensitivity and center size in cat retinal ganglion cells," Brain Res. 153, 157–162 (1978), summarizes a number of studies by Enroth-Cugell and her collaborators that confirm this conclusion.

H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).

1977

J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).

D. H. Kelly, "Visual contrast sensitivity," Opt. Acta 24, 107–129 (1977); see Fig. 16.

1976

M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

L. E. Arend, Jr., "Temporal determinants of the form of the spatial contrast threshold MTF," Vision Res. 16, 1035–1042 (1976). Data are given for three velocities of the fixation point (including zero), in Fig. 5.

1975

D. H. Kelly, "Spatial frequency selectivity in the retina"' Vision Res. 15, 665–672 (1975).

D. H. Kelly and H. S. Magnuski, "Pattern detection and the twodimensional Fourier transform: Circular targets," Vision Res. 15, 911–915 (1975).

E. Levinson and R. Sekular, "The independence of channels in human vision selective for direction of movement," J. Physiol. (Lond.) 250, 347–366 (1975).

1973

For example, see B. Fischer, "Overlap of receptive field centers and representation of the visual field in the cat's optic tract," Vision Res. 13, 2113–2120 (1973).

1972

D. H. Kelly, "Adaptation effects on spatio-temporal sine-wave thresholds," Vision Res. 12, 89–101 (1972).

1970

N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models," Vision Res. 11, 251–259 (1970).

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. (Lond.) 203, 237–260 (1969).

D. H. Kelly, "Diffusion model of linear flicker responses," J. Opt. Soc. Am. 59, 1665–1670 (1969).

1968

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

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, "Spatial sine-wave responses of the human visual system," Vision Res. 8, 1245–1263 (1968). See their Fig. 11 (but note that some velocities are identified incorrectly in the figure caption).

1967

1966

1960

1952

H. deLange, "Experiments on flicker and some calculations on an electrical analogue of the fovea systems," Physica 18, 935–950 (1952). See also H. deLange, "Research into the dynamic nature of the human fovea-cortex systems with intermittent and modulated light," J. Opt. Soc. Am. 48, 777–789 (1958).

1948

O. H. Schade, "Electro-optical characteristics of television systems. I. Characteristics of vision and visual systems," RCA Review 9, 5–37 (1948).

Arend, Jr., L. E.

L. E. Arend, Jr., "Temporal determinants of the form of the spatial contrast threshold MTF," Vision Res. 16, 1035–1042 (1976). Data are given for three velocities of the fixation point (including zero), in Fig. 5.

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. (Lond.) 203, 237–260 (1969).

Bouman, M. A.

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. (Lond.) 203, 237–260 (1969).

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

deLange, H.

H. deLange, "Experiments on flicker and some calculations on an electrical analogue of the fovea systems," Physica 18, 935–950 (1952). See also H. deLange, "Research into the dynamic nature of the human fovea-cortex systems with intermittent and modulated light," J. Opt. Soc. Am. 48, 777–789 (1958).

Ditchburn, R. W.

R. W. Ditchburn, Eye-movements and Visual Perception (Clarendon, Oxford, 1973), p. 367 et seq.

Enroth-Cugell, C.

T. H. Harding and C. Enroth-Cugell, "Absolute dark sensitivity and center size in cat retinal ganglion cells," Brain Res. 153, 157–162 (1978), summarizes a number of studies by Enroth-Cugell and her collaborators that confirm this conclusion.

Fischer, B.

For example, see B. Fischer, "Overlap of receptive field centers and representation of the visual field in the cat's optic tract," Vision Res. 13, 2113–2120 (1973).

Graham, N.

N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models," Vision Res. 11, 251–259 (1970).

Harding, T. H.

T. H. Harding and C. Enroth-Cugell, "Absolute dark sensitivity and center size in cat retinal ganglion cells," Brain Res. 153, 157–162 (1978), summarizes a number of studies by Enroth-Cugell and her collaborators that confirm this conclusion.

Hines, M.

M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

Hiwatashi, K.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, "Spatial sine-wave responses of the human visual system," Vision Res. 8, 1245–1263 (1968). See their Fig. 11 (but note that some velocities are identified incorrectly in the figure caption).

Kelly, D. H.

D. H. Kelly, "Motion and vision. I. Stabilized images of stationary mgratings," J. Opt. Soc. Am. 69, 1266–1274 (1979).

D. H. Kelly, "Visual contrast sensitivity," Opt. Acta 24, 107–129 (1977); see Fig. 16.

D. H. Kelly, "Spatial frequency selectivity in the retina"' Vision Res. 15, 665–672 (1975).

D. H. Kelly and H. S. Magnuski, "Pattern detection and the twodimensional Fourier transform: Circular targets," Vision Res. 15, 911–915 (1975).

D. H. Kelly, "Adaptation effects on spatio-temporal sine-wave thresholds," Vision Res. 12, 89–101 (1972).

D. H. Kelly, "Diffusion model of linear flicker responses," J. Opt. Soc. Am. 59, 1665–1670 (1969).

D. H. Kelly, "Frequency doubling in visual responses," J. Opt. Soc. Am. 56, 1628–1633 (1966).

D. H. Kelly, "J0 stimulus patterns for visual research," J. Opt. Soc. Am. 50, 1115–1116 (1960).

D. H. Kelly, Ph.D. thesis, University of California at Los Angeles (1960) (unpublished).

Kelly, H.

H. Kelly, "New stimuli in vision," in Abbilden utnd Sehen, Proceedings of the 6th meeting of the International Commission for Optics, edited by H. Schober and R. Röhler (Munich, 1962), pp. 119–126.

Koenderink, J. J.

Levinson, E.

E. Levinson and R. Sekular, "The independence of channels in human vision selective for direction of movement," J. Physiol. (Lond.) 250, 347–366 (1975).

Levinson, E. M.

E. M. Levinson (personal communication).

Limb, J. O.

J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).

Magnuski, H. S.

D. H. Kelly and H. S. Magnuski, "Pattern detection and the twodimensional Fourier transform: Circular targets," Vision Res. 15, 911–915 (1975).

Mori, T.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, "Spatial sine-wave responses of the human visual system," Vision Res. 8, 1245–1263 (1968). See their Fig. 11 (but note that some velocities are identified incorrectly in the figure caption).

Nachmias, J.

N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models," Vision Res. 11, 251–259 (1970).

Nagata, S.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, "Spatial sine-wave responses of the human visual system," Vision Res. 8, 1245–1263 (1968). See their Fig. 11 (but note that some velocities are identified incorrectly in the figure caption).

Nas, H.

Robson, J. G.

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

J. G. Robson, "Spatial and temporal contrast sensitivity functions of the visual system," J. Opt. Soc. Am. 56, 1141–1142 (1966).

Rubinstein, C. B.

J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).

Schade, O. H.

O. H. Schade, "Electro-optical characteristics of television systems. I. Characteristics of vision and visual systems," RCA Review 9, 5–37 (1948).

Sekular, R.

E. Levinson and R. Sekular, "The independence of channels in human vision selective for direction of movement," J. Physiol. (Lond.) 250, 347–366 (1975).

van Doorn, A. J.

van Nes, F. L.

Watanabe, A.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, "Spatial sine-wave responses of the human visual system," Vision Res. 8, 1245–1263 (1968). See their Fig. 11 (but note that some velocities are identified incorrectly in the figure caption).

Wilson, H. R.

H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).

Brain Res.

T. H. Harding and C. Enroth-Cugell, "Absolute dark sensitivity and center size in cat retinal ganglion cells," Brain Res. 153, 157–162 (1978), summarizes a number of studies by Enroth-Cugell and her collaborators that confirm this conclusion.

J. Opt. Soc. Am.

J. Physiol.

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. (Lond.) 203, 237–260 (1969).

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

E. Levinson and R. Sekular, "The independence of channels in human vision selective for direction of movement," J. Physiol. (Lond.) 250, 347–366 (1975).

Opt. Acta

D. H. Kelly, "Visual contrast sensitivity," Opt. Acta 24, 107–129 (1977); see Fig. 16.

Opt. Lett.

Physica

H. deLange, "Experiments on flicker and some calculations on an electrical analogue of the fovea systems," Physica 18, 935–950 (1952). See also H. deLange, "Research into the dynamic nature of the human fovea-cortex systems with intermittent and modulated light," J. Opt. Soc. Am. 48, 777–789 (1958).

RCA Review

O. H. Schade, "Electro-optical characteristics of television systems. I. Characteristics of vision and visual systems," RCA Review 9, 5–37 (1948).

Vision Res.

A. Watanabe, T. Mori, S. Nagata, and K. Hiwatashi, "Spatial sine-wave responses of the human visual system," Vision Res. 8, 1245–1263 (1968). See their Fig. 11 (but note that some velocities are identified incorrectly in the figure caption).

L. E. Arend, Jr., "Temporal determinants of the form of the spatial contrast threshold MTF," Vision Res. 16, 1035–1042 (1976). Data are given for three velocities of the fixation point (including zero), in Fig. 5.

D. H. Kelly, "Adaptation effects on spatio-temporal sine-wave thresholds," Vision Res. 12, 89–101 (1972).

N. Graham and J. Nachmias, "Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models," Vision Res. 11, 251–259 (1970).

D. H. Kelly and H. S. Magnuski, "Pattern detection and the twodimensional Fourier transform: Circular targets," Vision Res. 15, 911–915 (1975).

D. H. Kelly, "Spatial frequency selectivity in the retina"' Vision Res. 15, 665–672 (1975).

H. R. Wilson, "Quantitative characterization of two types of linespread function near the fovea," Vision Res. 18, 971–981 (1978).

J. O. Limb and C. B. Rubinstein, "A model of threshold vision incorporating inhomogeneity of the visual field," Vision Res. 17, 571–584 (1977).

M. Hines, "Line spread function variation near the fovea," Vision Res. 16, 567–572 (1976).

For example, see B. Fischer, "Overlap of receptive field centers and representation of the visual field in the cat's optic tract," Vision Res. 13, 2113–2120 (1973).

Other

1f the maximum sensitivity in Figs. 9 and 10 did not vary with velocity, i.e., if k were exactly constant in Eqs. (5) et seq., this area would be exactly constant.

J. J. Koenderink (personal communications).

If the spatial frequency is low enough, the ratio of traveling-wave to standing-wave sensitivity must depend on the phase of the standing wave; e.g., if an antinode of the standing wave fills the visual field, the two sensitivities must be equal. At a node, on the other hand, the standing-wave sensitivity must be zero. Normally the sensitivity ratio falls between these two extreme cases, so there must be some kind of spatial averaging across the standing wave.

Since our flicker and motion signals were derived from different sources, they could not be phase-locked in the present apparatus (see Ref. 1); i.e., we were unable to maintain υ = ω/α exactly. As a result, neither component was perfectly stabilized during this experiment, and the residual destabilization probably increased the thresholds in Fig. 5.

E. M. Levinson (personal communication).

See Ref. 14, Fig. 12.

The zero-velocity data are similar to those given in Ref. 1, Figs. 6–9(d). The question of whether these sustained responses are significantly affected by residual motions in the stabilization apparatus apparatus was discussed in Sec. III of Ref. 1.

R. W. Ditchburn, Eye-movements and Visual Perception (Clarendon, Oxford, 1973), p. 367 et seq.

D. H. Kelly, Ph.D. thesis, University of California at Los Angeles (1960) (unpublished).

H. Kelly, "New stimuli in vision," in Abbilden utnd Sehen, Proceedings of the 6th meeting of the International Commission for Optics, edited by H. Schober and R. Röhler (Munich, 1962), pp. 119–126.

References 2–4 also proposed the use of circular standing waves, which require two-dimensional analysis. Here we treat only the simpler, one-dimensional case of rectilinear, sine-wave patterns.

In logarithmic coordinates.

In Ref. 11, horizontal gratings moved vertically, while our vertical gratings moved horizontally. However, there seems to be no evidence of a significant difference between the horizontal and vertical motion thresholds.

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