Abstract

We develop and test two functional hypotheses based on the sampling theory of visual resolution that might account for letter acuity in peripheral vision. First, a letter smaller than the acuity limit provides insufficient veridical energy for performing the task, and, second, the available veridical energy is masked by increased amounts of visible but aliased energy. These two hypotheses make opposite predictions about the effect of low-pass filtering on letter acuity, which we tested experimentally by using filtered letters from the tumbling-E alphabet. Our results reject the masking hypothesis in favor of the energy insufficiency hypothesis. Additional experiments in which high-pass-filtered letters were used permitted the isolation of a critical band of spatial frequencies, which is necessary and sufficient for achieving maximum visual acuity. This critical band varied with the particular pair of letters to be discriminated but was in the range 0.9–2.2 cycles per letter.

© 1999 Optical Society of America

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  1. A. P. Ginsburg, “Specifying relevant spatial information for image evaluation and display designs: an explanation of how we see certain objects,” Proc. Soc. Inf. Displ. 21, 219–227 (1980).
  2. G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. 1. Normal vision,” Vision Res. 25, 239–252 (1985).
    [CrossRef]
  3. D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
    [CrossRef]
  4. J. A. Solomon, D. G. Pelli, “The visual filter mediating letter identification,” Nature 369, 395–397 (1994).
    [CrossRef] [PubMed]
  5. V. M. Bondarko, M. V. Danilova, “What spatial frequency do we use to detect the orientation of a Landolt C?” Vision Res. 37, 2153–2156 (1997).
    [CrossRef] [PubMed]
  6. S. T. L. Chung, G. E. Legge, “Spatial-frequency dependence of letter recognition in central and peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, S639 (1997).
  7. K. R. Alexander, W. Xie, D. J. Derlacki, “Spatial-frequency characteristics of letter identification,” J. Opt. Soc. Am. A 11, 2375–2382 (1994).
    [CrossRef]
  8. D. R. Williams, “Aliasing in human foveal vision,” Vision Res. 25, 195–205 (1985).
    [CrossRef] [PubMed]
  9. D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
    [CrossRef] [PubMed]
  10. L. N. Thibos, D. L. Still, A. Bradley, “Characterization of spatial aliasing and contrast sensitivity in peripheral vision,” Vision Res. 36, 249–258 (1996).
    [CrossRef] [PubMed]
  11. L. N. Thibos, D. J. Walsh, F. E. Cheney, “Vision beyond the resolution limit: aliasing in the periphery,” Vision Res. 27, 2193–2197 (1987).
    [CrossRef] [PubMed]
  12. Y. Z. Wang, L. N. Thibos, A. Bradley, “Undersampling produces non-veridical motion perception, but not necessarily motion reversal, in peripheral vision,” Vision Res. 36, 1737–1744 (1996).
    [CrossRef] [PubMed]
  13. Y. Wang, A. Bradley, L. N. Thibos, “Aliased frequencies enable the discrimination of compound gratings in peripheral vision,” Vision Res. 37, 283–290 (1997).
    [CrossRef] [PubMed]
  14. Y. Z. Wang, A. Bradley, L. N. Thibos, “Interaction between sub- and supra-Nyquist spatial frequencies in peripheral vision,” Vision Res. 37, 2545–2552 (1997).
    [CrossRef] [PubMed]
  15. S. J. Galvin, D. R. Williams, “No aliasing at edges in normal viewing,” Vision Res. 32, 2251–2259 (1992).
    [CrossRef] [PubMed]
  16. R. S. Anderson, L. N. Thibos, “The relationship between acuity for gratings and for tumbling-E letters in peripheral vision,” J. Opt. Soc. Am. A 16, 2321–2333 (1999).
    [CrossRef]
  17. L. N. Thibos, “Acuity perimetry and the sampling theory of visual resolution,” Optom. Vision Sci. 75, 399–406 (1997).
    [CrossRef]
  18. J. Rovamo, V. Virsu, P. Laurinen, L. Hyvarinen, “Resolution of gratings oriented along and across meridians in peripheral vision,” Invest. Ophthalmol. Visual Sci. 23, 666–670 (1982).
  19. L. A. Temme, L. Malcus, W. K. Noell, “Peripheral visual field is radially organized,” Am. J. Optom. Physiol. Opt. 62, 545–554 (1985).
    [CrossRef] [PubMed]
  20. R. S. Anderson, M. O. Wilkinson, L. N. Thibos, “Psychophysical localization of the human visual streak,” Optom. Vision Sci. 69, 171–174 (1992).
    [CrossRef]
  21. D. R. Williams, N. J. Coletta, “Cone spacing and the visual resolution limit,” J. Opt. Soc. Am. A 4, 1514–1523 (1987).
    [CrossRef] [PubMed]
  22. Our experimental method for blurring letters is qualitatively different from the blurring of an eye chart by uncorrected refractive error. The effect of optical blur depends on the retinal frequency (cycles per deg), not on the object frequency (c/let). Therefore the loss of high object frequencies in small letters caused by optical blurring may be recovered by increasing the size of the letters. However, no such recovery is possible when letters are filtered according to their object frequency.
  23. R. S. Anderson, D. W. Evans, L. N. Thibos, “Effect of window size on detection acuity and resolution acuity for sinusoidal gratings in central and peripheral vision,” J. Opt. Soc. Am. A 13, 697–706 (1996).
    [CrossRef]
  24. P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature 326, 873–876 (1987).
    [CrossRef] [PubMed]
  25. D. M. Levi, S. A. Klein, “The role of separation and eccentricity in encoding position,” Vision Res. 30, 557–585 (1990).
    [CrossRef] [PubMed]
  26. R. F. Hess, D. Field, “Is the increased spatial uncertainty in the normal periphery due to spatial undersampling or uncalibrated disarray?” Vision Res. 33, 2663–2670 (1993).
    [CrossRef] [PubMed]

1999 (1)

1997 (5)

Y. Wang, A. Bradley, L. N. Thibos, “Aliased frequencies enable the discrimination of compound gratings in peripheral vision,” Vision Res. 37, 283–290 (1997).
[CrossRef] [PubMed]

Y. Z. Wang, A. Bradley, L. N. Thibos, “Interaction between sub- and supra-Nyquist spatial frequencies in peripheral vision,” Vision Res. 37, 2545–2552 (1997).
[CrossRef] [PubMed]

V. M. Bondarko, M. V. Danilova, “What spatial frequency do we use to detect the orientation of a Landolt C?” Vision Res. 37, 2153–2156 (1997).
[CrossRef] [PubMed]

S. T. L. Chung, G. E. Legge, “Spatial-frequency dependence of letter recognition in central and peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, S639 (1997).

L. N. Thibos, “Acuity perimetry and the sampling theory of visual resolution,” Optom. Vision Sci. 75, 399–406 (1997).
[CrossRef]

1996 (4)

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

L. N. Thibos, D. L. Still, A. Bradley, “Characterization of spatial aliasing and contrast sensitivity in peripheral vision,” Vision Res. 36, 249–258 (1996).
[CrossRef] [PubMed]

Y. Z. Wang, L. N. Thibos, A. Bradley, “Undersampling produces non-veridical motion perception, but not necessarily motion reversal, in peripheral vision,” Vision Res. 36, 1737–1744 (1996).
[CrossRef] [PubMed]

R. S. Anderson, D. W. Evans, L. N. Thibos, “Effect of window size on detection acuity and resolution acuity for sinusoidal gratings in central and peripheral vision,” J. Opt. Soc. Am. A 13, 697–706 (1996).
[CrossRef]

1994 (2)

1993 (1)

R. F. Hess, D. Field, “Is the increased spatial uncertainty in the normal periphery due to spatial undersampling or uncalibrated disarray?” Vision Res. 33, 2663–2670 (1993).
[CrossRef] [PubMed]

1992 (2)

R. S. Anderson, M. O. Wilkinson, L. N. Thibos, “Psychophysical localization of the human visual streak,” Optom. Vision Sci. 69, 171–174 (1992).
[CrossRef]

S. J. Galvin, D. R. Williams, “No aliasing at edges in normal viewing,” Vision Res. 32, 2251–2259 (1992).
[CrossRef] [PubMed]

1991 (1)

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[CrossRef]

1990 (1)

D. M. Levi, S. A. Klein, “The role of separation and eccentricity in encoding position,” Vision Res. 30, 557–585 (1990).
[CrossRef] [PubMed]

1987 (3)

P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature 326, 873–876 (1987).
[CrossRef] [PubMed]

D. R. Williams, N. J. Coletta, “Cone spacing and the visual resolution limit,” J. Opt. Soc. Am. A 4, 1514–1523 (1987).
[CrossRef] [PubMed]

L. N. Thibos, D. J. Walsh, F. E. Cheney, “Vision beyond the resolution limit: aliasing in the periphery,” Vision Res. 27, 2193–2197 (1987).
[CrossRef] [PubMed]

1985 (3)

D. R. Williams, “Aliasing in human foveal vision,” Vision Res. 25, 195–205 (1985).
[CrossRef] [PubMed]

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. 1. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

L. A. Temme, L. Malcus, W. K. Noell, “Peripheral visual field is radially organized,” Am. J. Optom. Physiol. Opt. 62, 545–554 (1985).
[CrossRef] [PubMed]

1982 (1)

J. Rovamo, V. Virsu, P. Laurinen, L. Hyvarinen, “Resolution of gratings oriented along and across meridians in peripheral vision,” Invest. Ophthalmol. Visual Sci. 23, 666–670 (1982).

1980 (1)

A. P. Ginsburg, “Specifying relevant spatial information for image evaluation and display designs: an explanation of how we see certain objects,” Proc. Soc. Inf. Displ. 21, 219–227 (1980).

Alexander, K. R.

Anderson, R. S.

Artal, P.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

Banks, M. S.

P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature 326, 873–876 (1987).
[CrossRef] [PubMed]

Bennett, P. J.

P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature 326, 873–876 (1987).
[CrossRef] [PubMed]

Bondarko, V. M.

V. M. Bondarko, M. V. Danilova, “What spatial frequency do we use to detect the orientation of a Landolt C?” Vision Res. 37, 2153–2156 (1997).
[CrossRef] [PubMed]

Bradley, A.

Y. Wang, A. Bradley, L. N. Thibos, “Aliased frequencies enable the discrimination of compound gratings in peripheral vision,” Vision Res. 37, 283–290 (1997).
[CrossRef] [PubMed]

Y. Z. Wang, A. Bradley, L. N. Thibos, “Interaction between sub- and supra-Nyquist spatial frequencies in peripheral vision,” Vision Res. 37, 2545–2552 (1997).
[CrossRef] [PubMed]

Y. Z. Wang, L. N. Thibos, A. Bradley, “Undersampling produces non-veridical motion perception, but not necessarily motion reversal, in peripheral vision,” Vision Res. 36, 1737–1744 (1996).
[CrossRef] [PubMed]

L. N. Thibos, D. L. Still, A. Bradley, “Characterization of spatial aliasing and contrast sensitivity in peripheral vision,” Vision Res. 36, 249–258 (1996).
[CrossRef] [PubMed]

Brainard, D. H.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

Cheney, F. E.

L. N. Thibos, D. J. Walsh, F. E. Cheney, “Vision beyond the resolution limit: aliasing in the periphery,” Vision Res. 27, 2193–2197 (1987).
[CrossRef] [PubMed]

Chung, S. T. L.

S. T. L. Chung, G. E. Legge, “Spatial-frequency dependence of letter recognition in central and peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, S639 (1997).

Coletta, N. J.

Danilova, M. V.

V. M. Bondarko, M. V. Danilova, “What spatial frequency do we use to detect the orientation of a Landolt C?” Vision Res. 37, 2153–2156 (1997).
[CrossRef] [PubMed]

Derlacki, D. J.

Evans, D. W.

Field, D.

R. F. Hess, D. Field, “Is the increased spatial uncertainty in the normal periphery due to spatial undersampling or uncalibrated disarray?” Vision Res. 33, 2663–2670 (1993).
[CrossRef] [PubMed]

Galvin, S. J.

S. J. Galvin, D. R. Williams, “No aliasing at edges in normal viewing,” Vision Res. 32, 2251–2259 (1992).
[CrossRef] [PubMed]

Ginsburg, A. P.

A. P. Ginsburg, “Specifying relevant spatial information for image evaluation and display designs: an explanation of how we see certain objects,” Proc. Soc. Inf. Displ. 21, 219–227 (1980).

Hess, R. F.

R. F. Hess, D. Field, “Is the increased spatial uncertainty in the normal periphery due to spatial undersampling or uncalibrated disarray?” Vision Res. 33, 2663–2670 (1993).
[CrossRef] [PubMed]

Hyvarinen, L.

J. Rovamo, V. Virsu, P. Laurinen, L. Hyvarinen, “Resolution of gratings oriented along and across meridians in peripheral vision,” Invest. Ophthalmol. Visual Sci. 23, 666–670 (1982).

Klein, S. A.

D. M. Levi, S. A. Klein, “The role of separation and eccentricity in encoding position,” Vision Res. 30, 557–585 (1990).
[CrossRef] [PubMed]

Laurinen, P.

J. Rovamo, V. Virsu, P. Laurinen, L. Hyvarinen, “Resolution of gratings oriented along and across meridians in peripheral vision,” Invest. Ophthalmol. Visual Sci. 23, 666–670 (1982).

Legge, G. E.

S. T. L. Chung, G. E. Legge, “Spatial-frequency dependence of letter recognition in central and peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, S639 (1997).

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. 1. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

Levi, D. M.

D. M. Levi, S. A. Klein, “The role of separation and eccentricity in encoding position,” Vision Res. 30, 557–585 (1990).
[CrossRef] [PubMed]

Malcus, L.

L. A. Temme, L. Malcus, W. K. Noell, “Peripheral visual field is radially organized,” Am. J. Optom. Physiol. Opt. 62, 545–554 (1985).
[CrossRef] [PubMed]

McMahon, M. J.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

Navarro, R.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

Noell, W. K.

L. A. Temme, L. Malcus, W. K. Noell, “Peripheral visual field is radially organized,” Am. J. Optom. Physiol. Opt. 62, 545–554 (1985).
[CrossRef] [PubMed]

Parish, D. H.

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[CrossRef]

Pelli, D. G.

J. A. Solomon, D. G. Pelli, “The visual filter mediating letter identification,” Nature 369, 395–397 (1994).
[CrossRef] [PubMed]

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. 1. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

Rovamo, J.

J. Rovamo, V. Virsu, P. Laurinen, L. Hyvarinen, “Resolution of gratings oriented along and across meridians in peripheral vision,” Invest. Ophthalmol. Visual Sci. 23, 666–670 (1982).

Rubin, G. S.

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. 1. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

Schleske, M. M.

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. 1. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

Solomon, J. A.

J. A. Solomon, D. G. Pelli, “The visual filter mediating letter identification,” Nature 369, 395–397 (1994).
[CrossRef] [PubMed]

Sperling, G.

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[CrossRef]

Still, D. L.

L. N. Thibos, D. L. Still, A. Bradley, “Characterization of spatial aliasing and contrast sensitivity in peripheral vision,” Vision Res. 36, 249–258 (1996).
[CrossRef] [PubMed]

Temme, L. A.

L. A. Temme, L. Malcus, W. K. Noell, “Peripheral visual field is radially organized,” Am. J. Optom. Physiol. Opt. 62, 545–554 (1985).
[CrossRef] [PubMed]

Thibos, L. N.

R. S. Anderson, L. N. Thibos, “The relationship between acuity for gratings and for tumbling-E letters in peripheral vision,” J. Opt. Soc. Am. A 16, 2321–2333 (1999).
[CrossRef]

L. N. Thibos, “Acuity perimetry and the sampling theory of visual resolution,” Optom. Vision Sci. 75, 399–406 (1997).
[CrossRef]

Y. Z. Wang, A. Bradley, L. N. Thibos, “Interaction between sub- and supra-Nyquist spatial frequencies in peripheral vision,” Vision Res. 37, 2545–2552 (1997).
[CrossRef] [PubMed]

Y. Wang, A. Bradley, L. N. Thibos, “Aliased frequencies enable the discrimination of compound gratings in peripheral vision,” Vision Res. 37, 283–290 (1997).
[CrossRef] [PubMed]

Y. Z. Wang, L. N. Thibos, A. Bradley, “Undersampling produces non-veridical motion perception, but not necessarily motion reversal, in peripheral vision,” Vision Res. 36, 1737–1744 (1996).
[CrossRef] [PubMed]

L. N. Thibos, D. L. Still, A. Bradley, “Characterization of spatial aliasing and contrast sensitivity in peripheral vision,” Vision Res. 36, 249–258 (1996).
[CrossRef] [PubMed]

R. S. Anderson, D. W. Evans, L. N. Thibos, “Effect of window size on detection acuity and resolution acuity for sinusoidal gratings in central and peripheral vision,” J. Opt. Soc. Am. A 13, 697–706 (1996).
[CrossRef]

R. S. Anderson, M. O. Wilkinson, L. N. Thibos, “Psychophysical localization of the human visual streak,” Optom. Vision Sci. 69, 171–174 (1992).
[CrossRef]

L. N. Thibos, D. J. Walsh, F. E. Cheney, “Vision beyond the resolution limit: aliasing in the periphery,” Vision Res. 27, 2193–2197 (1987).
[CrossRef] [PubMed]

Virsu, V.

J. Rovamo, V. Virsu, P. Laurinen, L. Hyvarinen, “Resolution of gratings oriented along and across meridians in peripheral vision,” Invest. Ophthalmol. Visual Sci. 23, 666–670 (1982).

Walsh, D. J.

L. N. Thibos, D. J. Walsh, F. E. Cheney, “Vision beyond the resolution limit: aliasing in the periphery,” Vision Res. 27, 2193–2197 (1987).
[CrossRef] [PubMed]

Wang, Y.

Y. Wang, A. Bradley, L. N. Thibos, “Aliased frequencies enable the discrimination of compound gratings in peripheral vision,” Vision Res. 37, 283–290 (1997).
[CrossRef] [PubMed]

Wang, Y. Z.

Y. Z. Wang, A. Bradley, L. N. Thibos, “Interaction between sub- and supra-Nyquist spatial frequencies in peripheral vision,” Vision Res. 37, 2545–2552 (1997).
[CrossRef] [PubMed]

Y. Z. Wang, L. N. Thibos, A. Bradley, “Undersampling produces non-veridical motion perception, but not necessarily motion reversal, in peripheral vision,” Vision Res. 36, 1737–1744 (1996).
[CrossRef] [PubMed]

Wilkinson, M. O.

R. S. Anderson, M. O. Wilkinson, L. N. Thibos, “Psychophysical localization of the human visual streak,” Optom. Vision Sci. 69, 171–174 (1992).
[CrossRef]

Williams, D. R.

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

S. J. Galvin, D. R. Williams, “No aliasing at edges in normal viewing,” Vision Res. 32, 2251–2259 (1992).
[CrossRef] [PubMed]

D. R. Williams, N. J. Coletta, “Cone spacing and the visual resolution limit,” J. Opt. Soc. Am. A 4, 1514–1523 (1987).
[CrossRef] [PubMed]

D. R. Williams, “Aliasing in human foveal vision,” Vision Res. 25, 195–205 (1985).
[CrossRef] [PubMed]

Xie, W.

Am. J. Optom. Physiol. Opt. (1)

L. A. Temme, L. Malcus, W. K. Noell, “Peripheral visual field is radially organized,” Am. J. Optom. Physiol. Opt. 62, 545–554 (1985).
[CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci. (2)

S. T. L. Chung, G. E. Legge, “Spatial-frequency dependence of letter recognition in central and peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, S639 (1997).

J. Rovamo, V. Virsu, P. Laurinen, L. Hyvarinen, “Resolution of gratings oriented along and across meridians in peripheral vision,” Invest. Ophthalmol. Visual Sci. 23, 666–670 (1982).

J. Opt. Soc. Am. A (4)

Nature (2)

P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature 326, 873–876 (1987).
[CrossRef] [PubMed]

J. A. Solomon, D. G. Pelli, “The visual filter mediating letter identification,” Nature 369, 395–397 (1994).
[CrossRef] [PubMed]

Optom. Vision Sci. (2)

L. N. Thibos, “Acuity perimetry and the sampling theory of visual resolution,” Optom. Vision Sci. 75, 399–406 (1997).
[CrossRef]

R. S. Anderson, M. O. Wilkinson, L. N. Thibos, “Psychophysical localization of the human visual streak,” Optom. Vision Sci. 69, 171–174 (1992).
[CrossRef]

Proc. Soc. Inf. Displ. (1)

A. P. Ginsburg, “Specifying relevant spatial information for image evaluation and display designs: an explanation of how we see certain objects,” Proc. Soc. Inf. Displ. 21, 219–227 (1980).

Vision Res. (13)

G. E. Legge, D. G. Pelli, G. S. Rubin, M. M. Schleske, “Psychophysics of reading. 1. Normal vision,” Vision Res. 25, 239–252 (1985).
[CrossRef]

D. H. Parish, G. Sperling, “Object spatial frequencies, retinal spatial frequencies, noise and the efficiency of letter discrimination,” Vision Res. 31, 1399–1415 (1991).
[CrossRef]

V. M. Bondarko, M. V. Danilova, “What spatial frequency do we use to detect the orientation of a Landolt C?” Vision Res. 37, 2153–2156 (1997).
[CrossRef] [PubMed]

D. R. Williams, “Aliasing in human foveal vision,” Vision Res. 25, 195–205 (1985).
[CrossRef] [PubMed]

D. R. Williams, P. Artal, R. Navarro, M. J. McMahon, D. H. Brainard, “Off-axis optical quality and retinal sampling in the human eye,” Vision Res. 36, 1103–1114 (1996).
[CrossRef] [PubMed]

L. N. Thibos, D. L. Still, A. Bradley, “Characterization of spatial aliasing and contrast sensitivity in peripheral vision,” Vision Res. 36, 249–258 (1996).
[CrossRef] [PubMed]

L. N. Thibos, D. J. Walsh, F. E. Cheney, “Vision beyond the resolution limit: aliasing in the periphery,” Vision Res. 27, 2193–2197 (1987).
[CrossRef] [PubMed]

Y. Z. Wang, L. N. Thibos, A. Bradley, “Undersampling produces non-veridical motion perception, but not necessarily motion reversal, in peripheral vision,” Vision Res. 36, 1737–1744 (1996).
[CrossRef] [PubMed]

Y. Wang, A. Bradley, L. N. Thibos, “Aliased frequencies enable the discrimination of compound gratings in peripheral vision,” Vision Res. 37, 283–290 (1997).
[CrossRef] [PubMed]

Y. Z. Wang, A. Bradley, L. N. Thibos, “Interaction between sub- and supra-Nyquist spatial frequencies in peripheral vision,” Vision Res. 37, 2545–2552 (1997).
[CrossRef] [PubMed]

S. J. Galvin, D. R. Williams, “No aliasing at edges in normal viewing,” Vision Res. 32, 2251–2259 (1992).
[CrossRef] [PubMed]

D. M. Levi, S. A. Klein, “The role of separation and eccentricity in encoding position,” Vision Res. 30, 557–585 (1990).
[CrossRef] [PubMed]

R. F. Hess, D. Field, “Is the increased spatial uncertainty in the normal periphery due to spatial undersampling or uncalibrated disarray?” Vision Res. 33, 2663–2670 (1993).
[CrossRef] [PubMed]

Other (1)

Our experimental method for blurring letters is qualitatively different from the blurring of an eye chart by uncorrected refractive error. The effect of optical blur depends on the retinal frequency (cycles per deg), not on the object frequency (c/let). Therefore the loss of high object frequencies in small letters caused by optical blurring may be recovered by increasing the size of the letters. However, no such recovery is possible when letters are filtered according to their object frequency.

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Figures (10)

Fig. 1
Fig. 1

Peripheral-vision model of visual acuity based on the difference in Fourier spectra of letters to be discriminated. (a) At the acuity limit, critical frequency components in the difference spectrum lie just inside the Nyquist ring. (b) As letters shrink below the acuity limit, the Fourier spectrum expands, causing stimulus energy to escape the Nyquist ring. This prevents letter discrimination for either of two possible reasons: (1) there is insufficient veridical energy available to support the discrimination task or (2) signal energy outside the Nyquist ring is undersampled, which produces aliasing that can mask the visibility of remaining veridical components inside the Nyquist ring. (c) A shrinking target causes individual frequency components to shift to higher spatial frequencies, which will lead to contrast insufficiency when the component crosses the Nyquist boundary (filled symbols) or when it crosses the threshold for contrast detection (open symbols).

Fig. 2
Fig. 2

Amplitude spectrum of a short-stroke E. The circular window shows the filter cutoff frequency. Frequencies outside the window were removed to low-pass filter, and frequencies within the window were removed to high-pass filter.

Fig. 3
Fig. 3

Appearance of a short-stroke E, unfiltered and low-pass filtered at different cutoff frequencies.

Fig. 4
Fig. 4

Appearance of a short-stroke E, unfiltered and high-pass filtered at different cutoff frequencies.

Fig. 5
Fig. 5

Threshold letter size versus cutoff frequency for long-stroke E’s that were low-pass filtered at different cutoff frequencies. Symbols show the means of two settings, and error bars represent one standard deviation of two threshold measures. The standard deviation of the staircase reversal values on any given run averaged ∼10% of the mean. Arrows indicate that the subject was unable to identify even the largest letter (80 arc min) that could be displayed on the computer monitor. Inset, difference spectra for the R vs. U configuration (upper row of spectra) and the R vs. L configuration (lower row). Cutoff frequencies represented by the four difference spectra (from left to right) are 1.25, 1.9, and 2.5 c/let and unfiltered. Labels “RSA” and “LNT” identify the observers here and in subsequent figures.

Fig. 6
Fig. 6

Threshold letter size versus cutoff frequency for short-stroke E’s that were low-pass filtered at different cutoff frequencies. The middle panel in Figs. 68 illustrates the difference spectra for the R vs. U configuration (upper row of spectra) and the R. vs. L configuration (lower row). Cutoff frequencies represented by the four difference spectra (from left to right) are 1.25, 1.9, and 2.5 c/let and unfiltered.

Fig. 7
Fig. 7

Threshold letter size versus cutoff frequency for long-stroke E’s that were high-pass filtered at different cutoff frequencies. Cutoff frequencies represented by the four difference spectra (from left to right) are unfiltered and 0.9, 1.6, and 2.5 c/let.

Fig. 8
Fig. 8

Threshold letter size versus cutoff frequency for short-stroke E’s that were high-pass filtered at different cutoff frequencies. Cutoff frequencies represented by the four difference spectra (from left to right) are unfiltered and 0.9, 1.6, and 2.5 c/let.

Fig. 9
Fig. 9

Threshold letter size versus cutoff frequency for long-stroke E’s that were low-pass and high-pass filtered at several cutoff frequencies (mean of both subjects). Shaded areas indicate the bands of frequencies that are necessary and sufficient for supporting normal visual acuity at the test location.

Fig. 10
Fig. 10

Threshold letter size versus cutoff frequency for short-stroke E’s that were low-pass and high-pass filtered at different cutoff frequencies (mean of both subjects). Shaded areas indicate the band of frequencies that are necessary and sufficient for supporting normal visual acuity at the test location.

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