Abstract

Humans can detect vernier displacements of two abutted lines that are 30 times smaller than the bar spacings that determine their grating acuity. Since vernier acuity tasks, and hyperacuity tasks in general, reveal such drastically improved sensitivity, it has been traditionally assumed that the detection mechanisms responsible for hyperacuity are fundamentally different from those underlying ordinary spatial acuity. The need for unusual mechanisms is reinforced by the observation that hyperacuity is weakly affected by changes in suprathreshold contrast, whereas ordinary acuity is strongly influenced by contrast. Nevertheless, we argue that many hyperacuity tasks can be understood without resorting to special mechanisms. We have taken a previously developed contrast-detection model, based on spatial-frequency channels, and have applied it directly to a set of hyperacuity experiments. Hyperacuity performance is readily predicted without modification of the model. In addition, the model correctly predicts the insensitivity of hyperacuity to suprathreshold contrast as well as the measured result that moderate low-pass filtering of hyperacuity images does not significantly decrease hyperacuity performance.

© 1985 Optical Society of America

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References

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  1. E. A. Wulfing, “Uber den kleinsten Gesichtswinkel,” Z. Biol. 29, 199–202 (1892).
  2. G. Westheimer, “Proctor Lecture: the spatial sense of the eye,” Invest. Ophthalmol. Visual Sci. 18, 893–912 (1979).
  3. G. Westheimer, S. P. McKee, “Spatial configurations for visual hyperacuity,” Vision Res. 17, 941–947 (1977).
    [CrossRef] [PubMed]
  4. K. E. Baker, “Some variables influencing vernier acuity. I. Illumination and exposure time; II. Wave-length of illumination,” J. Opt. Soc. Am. 39, 567–576 (1949).
    [CrossRef]
  5. R. N. Berry, “Quantitative relations among vernier, real depth, and steroscopic depth acuities,” J. Exp. Psychol. 38, 708–721 (1948).
    [CrossRef] [PubMed]
  6. L. Matin, “Eye movements and perceived visual direction,” In Handbook of Sensory Physiology, D. Jameson, L. Hurrich, eds. (Springer-Verlag, New York, 1972), Vol. VII/4, pp. 331–380.
    [CrossRef]
  7. G. Westheimer, S. P. McKee, “Visual acuity in the presence of retinal image motion,” J. Opt. Soc. Am. 65, 847–850 (1975).
    [CrossRef] [PubMed]
  8. F. Hering, “Uber die Grenzen der Sehscharfe,” Ber. Verh. Saechs. Akad. Wiss. Leipzig Math-Phys. Kl. pp. 16–24 (1899).
  9. S. A. Klein, D. M. Levi, R. E. Manny, “Localization thresholds of less than one second,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).
  10. R. F. Quick, “System theory and vision: a review of models and applications,” Proc. Soc. Inf. Displ. 21, 209–217 (1980).
  11. G. Westheimer, “Spatial frequency and light-spread descriptions of visual acuity and hyperacuity,” J. Opt. Soc. Am. 67, 207–212 (1977).
    [CrossRef] [PubMed]
  12. C. R. Carlson, “A simple model for vernier acuity,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).
  13. C. R. Carlson, “Thresholds for perceived image sharpness,” Photogr. Sci. Eng. J. 22, 69–71 (1978).
  14. R. W. Cohen, “Applying psychophysics to display design,” Photogr. Sci. Eng. J. 22, 56–59 (1978).
  15. C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).
  16. C. R. Carlson, R. W. Cohen, Visibility of Displayed Information, Tech. Rep. to U. S. Office of Naval Research, Contract No. N00014-74-C-0184 (January1978).
  17. C. R. Carlson, “Application of psychophysics to display evaluation,” in Proceedings of the 3rd International Display Conference (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 1–9.
  18. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
  19. H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units revealed by oblique masking,” Vision Res. 23, 873–882 (1983).
    [CrossRef]
  20. A. Watson, A. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Vis. Sci. Suppl. 24, 47 (1983).
  21. H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
    [CrossRef] [PubMed]
  22. W. S. Geisler, “Physical limits of acuity and hyperacuity,” J. Opt. Soc. Am. A 1, 775–782 (1984).
    [CrossRef] [PubMed]
  23. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–556 (1968).
  24. M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
    [CrossRef] [PubMed]
  25. N. Graham, “Visual detection of periodic spatial stimuli by probability summation among narrowband channels,” Vision Res. 17, 637–652 (1977).
    [CrossRef]
  26. C. Blakemore, F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. (London) 200, 11–13 (1968).
  27. C. Blakemore, F. W. Campbell, “On the existance of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).
  28. N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
    [CrossRef] [PubMed]
  29. H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171–178 (1980).
    [CrossRef] [PubMed]
  30. A. F. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
    [CrossRef] [PubMed]
  31. J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
    [CrossRef] [PubMed]
  32. C. R. Carlson, R. W. Klopfenstein, C. H. Anderson, “Spatially inhomogenous scaled transforms for vision and pattern recognition,” Opt. Lett. 6, 386–388 (1981).
    [CrossRef] [PubMed]
  33. R. W. Klopfenstein, C. R. Carlson, “Theory of shape-invariant imaging systems,” J. Opt. Soc. Am. A 1, 1040–1053 (1984).
    [CrossRef] [PubMed]
  34. J. Hoekstra, D. P. J. van der Goot, G. van der Brink, F. A. Bilsen, “The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns,” Vision Res. 14, 365–368 (1974).
    [CrossRef] [PubMed]
  35. R. L. Savoy, J. J. McCann, “Visibility of low-spatial frequency sine-wave targets: dependence on number of cycles,” J. Opt. Soc. Am. 65, 343–350 (1975).
    [CrossRef] [PubMed]
  36. C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Rev. 43, 675–683 (1982).

1984 (3)

1983 (4)

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units revealed by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef]

A. Watson, A. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Vis. Sci. Suppl. 24, 47 (1983).

C. R. Carlson, “A simple model for vernier acuity,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).

S. A. Klein, D. M. Levi, R. E. Manny, “Localization thresholds of less than one second,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).

1982 (1)

C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Rev. 43, 675–683 (1982).

1981 (2)

C. R. Carlson, R. W. Klopfenstein, C. H. Anderson, “Spatially inhomogenous scaled transforms for vision and pattern recognition,” Opt. Lett. 6, 386–388 (1981).
[CrossRef] [PubMed]

A. F. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

1980 (3)

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171–178 (1980).
[CrossRef] [PubMed]

R. F. Quick, “System theory and vision: a review of models and applications,” Proc. Soc. Inf. Displ. 21, 209–217 (1980).

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).

1979 (1)

G. Westheimer, “Proctor Lecture: the spatial sense of the eye,” Invest. Ophthalmol. Visual Sci. 18, 893–912 (1979).

1978 (3)

C. R. Carlson, R. W. Cohen, Visibility of Displayed Information, Tech. Rep. to U. S. Office of Naval Research, Contract No. N00014-74-C-0184 (January1978).

C. R. Carlson, “Thresholds for perceived image sharpness,” Photogr. Sci. Eng. J. 22, 69–71 (1978).

R. W. Cohen, “Applying psychophysics to display design,” Photogr. Sci. Eng. J. 22, 56–59 (1978).

1977 (3)

G. Westheimer, S. P. McKee, “Spatial configurations for visual hyperacuity,” Vision Res. 17, 941–947 (1977).
[CrossRef] [PubMed]

G. Westheimer, “Spatial frequency and light-spread descriptions of visual acuity and hyperacuity,” J. Opt. Soc. Am. 67, 207–212 (1977).
[CrossRef] [PubMed]

N. Graham, “Visual detection of periodic spatial stimuli by probability summation among narrowband channels,” Vision Res. 17, 637–652 (1977).
[CrossRef]

1975 (2)

1974 (2)

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, F. A. Bilsen, “The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns,” Vision Res. 14, 365–368 (1974).
[CrossRef] [PubMed]

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

1971 (2)

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
[CrossRef] [PubMed]

1969 (1)

C. Blakemore, F. W. Campbell, “On the existance of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

1968 (2)

C. Blakemore, F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. (London) 200, 11–13 (1968).

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–556 (1968).

1949 (1)

1948 (1)

R. N. Berry, “Quantitative relations among vernier, real depth, and steroscopic depth acuities,” J. Exp. Psychol. 38, 708–721 (1948).
[CrossRef] [PubMed]

1899 (1)

F. Hering, “Uber die Grenzen der Sehscharfe,” Ber. Verh. Saechs. Akad. Wiss. Leipzig Math-Phys. Kl. pp. 16–24 (1899).

1892 (1)

E. A. Wulfing, “Uber den kleinsten Gesichtswinkel,” Z. Biol. 29, 199–202 (1892).

Ahumada, A.

A. Watson, A. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Vis. Sci. Suppl. 24, 47 (1983).

Anderson, C. H.

Baker, K. E.

Barlow, H. B.

A. F. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Berry, R. N.

R. N. Berry, “Quantitative relations among vernier, real depth, and steroscopic depth acuities,” J. Exp. Psychol. 38, 708–721 (1948).
[CrossRef] [PubMed]

Bilsen, F. A.

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, F. A. Bilsen, “The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns,” Vision Res. 14, 365–368 (1974).
[CrossRef] [PubMed]

Blakemore, C.

C. Blakemore, F. W. Campbell, “On the existance of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

C. Blakemore, F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. (London) 200, 11–13 (1968).

Burgess, A. F.

A. F. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Campbell, F. W.

C. Blakemore, F. W. Campbell, “On the existance of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

C. Blakemore, F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. (London) 200, 11–13 (1968).

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–556 (1968).

Carlson, C. R.

R. W. Klopfenstein, C. R. Carlson, “Theory of shape-invariant imaging systems,” J. Opt. Soc. Am. A 1, 1040–1053 (1984).
[CrossRef] [PubMed]

C. R. Carlson, “A simple model for vernier acuity,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).

C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Rev. 43, 675–683 (1982).

C. R. Carlson, R. W. Klopfenstein, C. H. Anderson, “Spatially inhomogenous scaled transforms for vision and pattern recognition,” Opt. Lett. 6, 386–388 (1981).
[CrossRef] [PubMed]

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).

C. R. Carlson, “Thresholds for perceived image sharpness,” Photogr. Sci. Eng. J. 22, 69–71 (1978).

C. R. Carlson, R. W. Cohen, Visibility of Displayed Information, Tech. Rep. to U. S. Office of Naval Research, Contract No. N00014-74-C-0184 (January1978).

C. R. Carlson, “Application of psychophysics to display evaluation,” in Proceedings of the 3rd International Display Conference (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 1–9.

Cohen, R. W.

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).

R. W. Cohen, “Applying psychophysics to display design,” Photogr. Sci. Eng. J. 22, 56–59 (1978).

C. R. Carlson, R. W. Cohen, Visibility of Displayed Information, Tech. Rep. to U. S. Office of Naval Research, Contract No. N00014-74-C-0184 (January1978).

Geisler, W. S.

Gelb, D. J.

Graham, N.

N. Graham, “Visual detection of periodic spatial stimuli by probability summation among narrowband channels,” Vision Res. 17, 637–652 (1977).
[CrossRef]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Hering, F.

F. Hering, “Uber die Grenzen der Sehscharfe,” Ber. Verh. Saechs. Akad. Wiss. Leipzig Math-Phys. Kl. pp. 16–24 (1899).

Hoekstra, J.

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, F. A. Bilsen, “The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns,” Vision Res. 14, 365–368 (1974).
[CrossRef] [PubMed]

Jennings, R. J.

A. F. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Klein, S. A.

S. A. Klein, D. M. Levi, R. E. Manny, “Localization thresholds of less than one second,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).

Klopfenstein, R. W.

Levi, D. M.

S. A. Klein, D. M. Levi, R. E. Manny, “Localization thresholds of less than one second,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).

Manny, R. E.

S. A. Klein, D. M. Levi, R. E. Manny, “Localization thresholds of less than one second,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).

Matin, L.

L. Matin, “Eye movements and perceived visual direction,” In Handbook of Sensory Physiology, D. Jameson, L. Hurrich, eds. (Springer-Verlag, New York, 1972), Vol. VII/4, pp. 331–380.
[CrossRef]

McCann, J. J.

McFarlane, D. K.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units revealed by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef]

McKee, S. P.

G. Westheimer, S. P. McKee, “Spatial configurations for visual hyperacuity,” Vision Res. 17, 941–947 (1977).
[CrossRef] [PubMed]

G. Westheimer, S. P. McKee, “Visual acuity in the presence of retinal image motion,” J. Opt. Soc. Am. 65, 847–850 (1975).
[CrossRef] [PubMed]

Nachmias, J.

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
[CrossRef] [PubMed]

Phillips, G. C.

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units revealed by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef]

Quick, R. F.

R. F. Quick, “System theory and vision: a review of models and applications,” Proc. Soc. Inf. Displ. 21, 209–217 (1980).

Robson, J. G.

M. B. Sachs, J. Nachmias, J. G. Robson, “Spatial-frequency channels in human vision,” J. Opt. Soc. Am. 61, 1176–1186 (1971).
[CrossRef] [PubMed]

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–556 (1968).

Sachs, M. B.

Sansbury, R. V.

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

Savoy, R. L.

Swets, J. A.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

van der Brink, G.

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, F. A. Bilsen, “The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns,” Vision Res. 14, 365–368 (1974).
[CrossRef] [PubMed]

van der Goot, D. P. J.

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, F. A. Bilsen, “The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns,” Vision Res. 14, 365–368 (1974).
[CrossRef] [PubMed]

Wagner, R. F.

A. F. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Watson, A.

A. Watson, A. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Vis. Sci. Suppl. 24, 47 (1983).

Westheimer, G.

G. Westheimer, “Proctor Lecture: the spatial sense of the eye,” Invest. Ophthalmol. Visual Sci. 18, 893–912 (1979).

G. Westheimer, S. P. McKee, “Spatial configurations for visual hyperacuity,” Vision Res. 17, 941–947 (1977).
[CrossRef] [PubMed]

G. Westheimer, “Spatial frequency and light-spread descriptions of visual acuity and hyperacuity,” J. Opt. Soc. Am. 67, 207–212 (1977).
[CrossRef] [PubMed]

G. Westheimer, S. P. McKee, “Visual acuity in the presence of retinal image motion,” J. Opt. Soc. Am. 65, 847–850 (1975).
[CrossRef] [PubMed]

Wilson, H. R.

H. R. Wilson, D. J. Gelb, “Modified line-element theory for spatial-frequency and width discrimination,” J. Opt. Soc. Am. A 1, 124–131 (1984).
[CrossRef] [PubMed]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units revealed by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef]

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171–178 (1980).
[CrossRef] [PubMed]

Wulfing, E. A.

E. A. Wulfing, “Uber den kleinsten Gesichtswinkel,” Z. Biol. 29, 199–202 (1892).

Ber. Verh. Saechs. Akad. Wiss. Leipzig Math-Phys. Kl. (1)

F. Hering, “Uber die Grenzen der Sehscharfe,” Ber. Verh. Saechs. Akad. Wiss. Leipzig Math-Phys. Kl. pp. 16–24 (1899).

Biol. Cybern. (1)

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171–178 (1980).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. Suppl. (2)

S. A. Klein, D. M. Levi, R. E. Manny, “Localization thresholds of less than one second,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).

C. R. Carlson, “A simple model for vernier acuity,” Invest. Ophthalmol. Vis. Sci. Suppl. 24, 276 (1983).

Invest. Ophthalmol. Visual Sci. (1)

G. Westheimer, “Proctor Lecture: the spatial sense of the eye,” Invest. Ophthalmol. Visual Sci. 18, 893–912 (1979).

Invest. Opthalmol. Vis. Sci. Suppl. (1)

A. Watson, A. Ahumada, “A model of spatial contrast vision,” Invest. Opthalmol. Vis. Sci. Suppl. 24, 47 (1983).

J. Exp. Psychol. (1)

R. N. Berry, “Quantitative relations among vernier, real depth, and steroscopic depth acuities,” J. Exp. Psychol. 38, 708–721 (1948).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (3)

J. Physiol. (London) (3)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–556 (1968).

C. Blakemore, F. W. Campbell, “Adaptation to spatial stimuli,” J. Physiol. (London) 200, 11–13 (1968).

C. Blakemore, F. W. Campbell, “On the existance of neurones in the human visual system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).

Opt. Lett. (1)

Photogr. Sci. Eng. J. (2)

C. R. Carlson, “Thresholds for perceived image sharpness,” Photogr. Sci. Eng. J. 22, 69–71 (1978).

R. W. Cohen, “Applying psychophysics to display design,” Photogr. Sci. Eng. J. 22, 56–59 (1978).

Proc. Soc. Inf. Displ. (2)

C. R. Carlson, R. W. Cohen, “A simple psychophysical model for predicting the visibility of displayed information,” Proc. Soc. Inf. Displ. 21, 229–246 (1980).

R. F. Quick, “System theory and vision: a review of models and applications,” Proc. Soc. Inf. Displ. 21, 209–217 (1980).

RCA Rev. (1)

C. R. Carlson, “Sine-wave threshold contrast-sensitivity function: dependence on display size,” RCA Rev. 43, 675–683 (1982).

Science (1)

A. F. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Visibility of Displayed Information (1)

C. R. Carlson, R. W. Cohen, Visibility of Displayed Information, Tech. Rep. to U. S. Office of Naval Research, Contract No. N00014-74-C-0184 (January1978).

Vision Res. (6)

G. Westheimer, S. P. McKee, “Spatial configurations for visual hyperacuity,” Vision Res. 17, 941–947 (1977).
[CrossRef] [PubMed]

J. Nachmias, R. V. Sansbury, “Grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
[CrossRef] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channel models,” Vision Res. 11, 251–259 (1971).
[CrossRef] [PubMed]

N. Graham, “Visual detection of periodic spatial stimuli by probability summation among narrowband channels,” Vision Res. 17, 637–652 (1977).
[CrossRef]

H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units revealed by oblique masking,” Vision Res. 23, 873–882 (1983).
[CrossRef]

J. Hoekstra, D. P. J. van der Goot, G. van der Brink, F. A. Bilsen, “The influence of the number of cycles upon the visual contrast threshold for spatial sine-wave patterns,” Vision Res. 14, 365–368 (1974).
[CrossRef] [PubMed]

Z. Biol. (1)

E. A. Wulfing, “Uber den kleinsten Gesichtswinkel,” Z. Biol. 29, 199–202 (1892).

Other (3)

L. Matin, “Eye movements and perceived visual direction,” In Handbook of Sensory Physiology, D. Jameson, L. Hurrich, eds. (Springer-Verlag, New York, 1972), Vol. VII/4, pp. 331–380.
[CrossRef]

C. R. Carlson, “Application of psychophysics to display evaluation,” in Proceedings of the 3rd International Display Conference (Institute of Electrical and Electronics Engineers, New York, 1982), pp. 1–9.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

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Figures (7)

Fig. 1
Fig. 1

Four images whose hyperacuity thresholds, ΔS, are roughly 6 sec of arc. The background luminance of each image is Ī, and the contrast of each image is ΔI/Ī.

Fig. 2
Fig. 2

Relative amplitude spectra of the image shown in Fig. 1(b). The line separations, S, were taken to be 120 and 130 sec of arc, respectively.

Fig. 3
Fig. 3

Schematic representation of the visual signal-detection model.

Fig. 4
Fig. 4

Measured change in contrast, Δm, as a function of the initial contrast, mi, for a 3-cycle-per-degree sine-wave grating.31 The solid curve is the theoretical fit to the data using the indicated values of threshold contrast, mT, and signal-to-noise ratio parameter, k.

Fig. 5
Fig. 5

Measured hyperacuity thresholds, ΔS, as a function of S for the parallel line image shown on the figure. The solid line represents the theoretical prediction of the signal-detection model, assuming ΔI/Ī = 1 and d = 1/3 min of arc. The predicted curve does not go below S = 1/3 min of arc, since at this point the two lines touch.

Fig. 6
Fig. 6

Predicted hyperacuity thresholds, ΔS, as a function of line separation, S, with ΔI/Ī a parameter. The linewidth, d, is taken to be 1 min of arc.

Fig. 7
Fig. 7

Predicted critical spatial frequency where the signal-detection model predicts the hyperacuity threshold, ΔS, exhibited as a function of S. The different curves represent different line contrasts, ΔI/Ī.

Tables (1)

Tables Icon

Table 1 Parameters for the Human Visual System Used in the Signal-Detection Modela

Equations (10)

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Δ = P f ( ν ) d ν P i ( ν ) d ν = k ( ν 0 ) [ N υ ( ν ) d ν + P i ( ν ) d ν ] ,
Î ( ν ) = W ( ν θ ) I ( θ ) exp ( i 2 π ν θ ) d θ ,
P ( ν ) = | Î ( ν ) | 2 .
W ( ν θ ) = exp ( | ν θ | / γ ) ,
I ( θ ) = Ī [ 1 + m sin ( 2 π ν 0 θ ) ] ,
P ( ν ) d ν ½ m 2 Ī 2 l ( ν 0 ) ,
½ m T 2 Ī 2 l ( ν 0 ) = k ( ν 0 ) N υ ( ν ) d ν .
m f 2 ( ν 0 ) m i 2 ( ν 0 ) = m T 2 ( ν 0 ) + k ( ν 0 ) m i 2 ( ν 0 ) .
½ m i , f 2 ( ν ) Ī 2 l ( ν ) = P i , f ( ν ) d ν .
m i , f 2 ( ν 0 ) = 16 d 2 l ( ν 0 ) ( Δ I Ī ) 2 ν 1 ν 2 sin 2 ( π d ν ) ( π d ν ) 2 cos 2 ( π s ν ) d ν ,

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