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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 2, Iss. 10 — Oct. 1, 1985
  • pp: 1747–1751

Spatial-frequency model for hyperacuity

C. R. Carlson and R. W. Klopfenstein  »View Author Affiliations

JOSA A, Vol. 2, Issue 10, pp. 1747-1751 (1985)

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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

Original Manuscript: July 23, 1984
Manuscript Accepted: May 21, 1985
Published: October 1, 1985

C. R. Carlson and R. W. Klopfenstein, "Spatial-frequency model for hyperacuity," J. Opt. Soc. Am. A 2, 1747-1751 (1985)

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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).

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