Abstract

Earlier studies have reported that grating resolution is sampling-limited in peripheral vision but that letter acuity is generally poorer than grating acuity. These results suggest that peripheral resolution of objects with rich Fourier spectra may be limited by some factor other than neural sampling. To examine this suggestion we formulated and tested the hypothesis that letter acuity in the periphery is sampling-limited, just as it is for extended and truncated gratings. We tested this hypothesis with improved methodology to avoid the confounding factors of target similarity, alphabet size, individual variation, peripheral refractive error, and stimulus size. Acuity was measured for an orientation-discrimination task (horizontal versus vertical) for a three-bar resolution target and for a block-E letter in which all strokes have the same length. We confirmed previous reports in the literature that acuity for these targets is worse than for extended sinusoidal gratings. To account for these results quantitatively, we used difference-spectrum analysis to identify those frequency components of the targets that might form a basis for performing the visual discrimination task. We find that discrimination performance for the three-bar targets and the block-E letters can be accounted for by a sampling-limited model, provided that the limited number of cycles that are present in the characteristic frequency of the stimulus is taken into account. Quantitative differences in acuity for discriminating other letter pairs (e.g., right versus left letters E or characters with short central strokes) could not be attributed to undersampling of either the characteristic frequency or the frequency of maximum energy in the difference spectrum. These results suggest additional tests of the sampling theory of visual resolution, which are the subject of a companion paper [J. Opt. Soc. Am. A. 16, 2334–2342 (1999)].

© 1999 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  50. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).
  51. 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]
  52. J. Pokorny, “The effect of target area on grating acuity,” Vision Res. 8, 543–554 (1968).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  56. R. Hilz, C. R. Cavonius, “Functional organization of the peripheral retina: sensitivity to periodic stimuli,” Vision Res. 14, 1333–1338 (1974).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  59. P. J. Bennett, M. S. Banks, “Sensitivity loss in odd-symmetric mechanisms and phase anomalies in peripheral vision,” Nature (London) 326, 873–876 (1987).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

1999 (2)

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Invest. Ophthalmol. Visual Sci. 40, S809 (1999).

R. S. Anderson, L. N. Thibos, “Sampling limits and critical bandwidth for letter discrimination in peripheral vision,” J. Opt. Soc. Am. A 16, 2334–2342 (1999).
[CrossRef]

1997 (7)

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]

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

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

K. R. Alexander, W. Xie, D. J. Derlacki, “Visual acuity and contrast sensitivity for individual Sloan letters,” Vision Res. 37, 813–819 (1997).
[CrossRef] [PubMed]

Y. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

1996 (5)

K. E. Higgins, A. Arditi, K. Knoblauch, “Detection and identification or mirror-image letter pairs in central and peripheral vision,” Vision Res. 36, 331–337 (1996).
[CrossRef] [PubMed]

R. S. Anderson, “The selective effect of optical defocus on detection and resolution acuity in peripheral vision,” Curr. Eye Res. 15, 351–353 (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 nonveridical 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]

1995 (2)

R. S. Anderson, P. Detkova, C. O'Brien, “Effect of temporal frequency and contrast on peripheral grating resolution,” Curr. Eye Res. 14, 1031–1033 (1995).
[CrossRef] [PubMed]

P. Artal, A. M. Derrington, E. Colombo, “Refraction, aliasing, and the absence of motion reversals in peripheral vision,” Vision Res. 35, 939–947 (1995).
[CrossRef] [PubMed]

1994 (3)

R. F. Hess, J. McCarthy, “Topological disorder in peripheral vision,” Visual Neurosci. 11, 1033–1036 (1994).
[CrossRef]

K. R. Alexander, W. Xie, D. J. Derlacki, “Spatial-frequency characteristics of letter identification,” J. Opt. Soc. Am. A 11, 2373–2382 (1994).
[CrossRef]

D. M. Levi, S. A. Klein, H. Wang, “Amblyopic and peripheral vernier acuity: a test-pedestal approach,” Vision Res. 34, 3265–3292 (1994).
[CrossRef] [PubMed]

1993 (3)

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]

N. J. Coletta, P. Segu, C. L. M. Tiana, “An oblique effect in parafoveal motion perception,” Vision Res. 33, 2747–2756 (1993).
[CrossRef] [PubMed]

L. N. Thibos, A. Bradley, “New methods for discriminating neural and optical losses of vision,” Optom. Vision Sci. 70, 279–287 (1993).
[CrossRef]

1992 (2)

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

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

1991 (4)

H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast thresholds for identification of numeric characters in direct and eccentric view,” Percept. Psychophys. 49, 495–508 (1991).
[CrossRef] [PubMed]

N. A. P. Brown, J. M. Sparrow, G. A. Shun-Shin, S. L. Franklin, “The acuityscope: a resolution test target projection ophthalmoscope,” Int. Ophthalmol. 15, 139–142 (1991).
[CrossRef] [PubMed]

C. M. E. Stephenson, A. J. Knapp, O. J. Braddick, “Discrimination of spatial phase shows a qualitative difference between foveal and peripheral processing,” Vision Res. 31, 1315–1326 (1991).
[CrossRef] [PubMed]

S. J. Anderson, K. T. Mullen, R. F. Hess, “Human peripheral spatial resolution for achromatic and chromatic stimuli—limits imposed by optical and retinal factors,” J. Physiol. (London) 442, 47–64 (1991).

1990 (4)

S. J. Anderson, R. F. Hess, “Post-receptoral undersampling in normal human peripheral vision,” Vision Res. 30, 1507–1515 (1990).
[CrossRef] [PubMed]

N. J. Coletta, D. R. Williams, C. L. M. Tiana, “Consequences of spatial sampling for human motion perception,” Vision Res. 30, 1631–1648 (1990).
[CrossRef] [PubMed]

F. Thorn, F. Schwartz, “Effects of dioptric blur on Snellen and grating acuity,” Optom. Vision Sci. 67, 3–7 (1990).
[CrossRef]

S. J. Anderson, R. F. Hess, “Spatial undersampling causes both motion cessation and reversal phenomena in human peripheral vision,” Invest. Ophthalmol. Visual Sci. 31, 495 (1990).

1987 (7)

1986 (1)

T. E. Cohn, D. J. Lasley, “Visual sensitivity,” Annu. Rev. Psychol. 37, 495–521 (1986).
[CrossRef] [PubMed]

1985 (3)

D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
[CrossRef] [PubMed]

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]

D. R. Williams, “Visibility of interference fringes near the resolution limit,” J. Opt. Soc. Am. A 2, 1087–1093 (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).

1981 (2)

R. Hilz, I. Rentschler, H. Brettel, “Insensitivity of peripheral vision to spatial phase,” Exp. Brain Res. 43, 111–114 (1981).
[CrossRef] [PubMed]

O. J. Braddick, “Is spatial phase degraded in peripheral vision and visual pathology?” Doc. Ophthal. Proc. Ser. 30, 255–262 (1981).

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).

1979 (1)

G. Westheimer, “Scaling of visual acuity,” Arch. Ophthalmol. (Chicago) 97, 327–330 (1979).
[CrossRef]

1978 (2)

J. J. Koenderink, A. J. van Doorn, “Visual detection of spatial contrast; influence of location in the visual field, target extent and illuminance level,” Biol. Cybern. 30, 157–167 (1978).
[CrossRef] [PubMed]

J. Rovamo, V. Virsu, R. Nasanen, “Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision,” Nature (London) 271, 54–56 (1978).
[CrossRef]

1977 (1)

G. L. Kandel, P. E. Grattan, H. E. Bedell, “Monocular fixation and acuity in amblyopic and normal eyes,” Am. J. Optom. Physiol. Opt. 54, 598–608 (1977).
[CrossRef] [PubMed]

1976 (1)

I. Bailey, J. Lovie, “New design principles for visual acuity letter charts,” Am. J. Optom. Physiol. Opt. 53, 740–745 (1976).
[CrossRef] [PubMed]

1974 (2)

R. Hilz, C. R. Cavonius, “Functional organization of the peripheral retina: sensitivity to periodic stimuli,” Vision Res. 14, 1333–1338 (1974).
[CrossRef] [PubMed]

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[CrossRef] [PubMed]

1971 (1)

J. L. Kerr, “Visual resolution in the periphery,” Percept. Psychophys. 9, 375–378 (1971).
[CrossRef]

1968 (3)

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

J. Pokorny, “The effect of target area on grating acuity,” Vision Res. 8, 543–554 (1968).
[CrossRef] [PubMed]

J. Pokorny, C. H. Graham, R. N. Lanson, “The effect of wavelength on foveal grating acuity,” J. Opt. Soc. Am. 58, 1410–1414 (1968).
[CrossRef] [PubMed]

1965 (1)

1941 (1)

E. Ludvigh, “Extrafoveal visual acuity as measured with Snellen letters,” Am. J. Ophthalmol. 24, 303–310 (1941).

Aitsebaomo, A. P.

D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
[CrossRef] [PubMed]

Alexander, K. R.

K. R. Alexander, W. Xie, D. J. Derlacki, “Visual acuity and contrast sensitivity for individual Sloan letters,” Vision Res. 37, 813–819 (1997).
[CrossRef] [PubMed]

K. R. Alexander, W. Xie, D. J. Derlacki, “Spatial-frequency characteristics of letter identification,” J. Opt. Soc. Am. A 11, 2373–2382 (1994).
[CrossRef]

Anderson, R. S.

R. S. Anderson, L. N. Thibos, “Sampling limits and critical bandwidth for letter discrimination in peripheral vision,” J. Opt. Soc. Am. A 16, 2334–2342 (1999).
[CrossRef]

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, “The selective effect of optical defocus on detection and resolution acuity in peripheral vision,” Curr. Eye Res. 15, 351–353 (1996).
[CrossRef] [PubMed]

R. S. Anderson, P. Detkova, C. O'Brien, “Effect of temporal frequency and contrast on peripheral grating resolution,” Curr. Eye Res. 14, 1031–1033 (1995).
[CrossRef] [PubMed]

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

R. S. Anderson, “Spatial and retinal factors limiting acuity across the visual field,” Ph.D. dissertation (Indiana University, Bloomington, Ind., 1994).

Anderson, S. J.

S. J. Anderson, K. T. Mullen, R. F. Hess, “Human peripheral spatial resolution for achromatic and chromatic stimuli—limits imposed by optical and retinal factors,” J. Physiol. (London) 442, 47–64 (1991).

S. J. Anderson, R. F. Hess, “Spatial undersampling causes both motion cessation and reversal phenomena in human peripheral vision,” Invest. Ophthalmol. Visual Sci. 31, 495 (1990).

S. J. Anderson, R. F. Hess, “Post-receptoral undersampling in normal human peripheral vision,” Vision Res. 30, 1507–1515 (1990).
[CrossRef] [PubMed]

Arditi, A.

K. E. Higgins, A. Arditi, K. Knoblauch, “Detection and identification or mirror-image letter pairs in central and peripheral vision,” Vision Res. 36, 331–337 (1996).
[CrossRef] [PubMed]

Artal, P.

P. Artal, A. M. Derrington, E. Colombo, “Refraction, aliasing, and the absence of motion reversals in peripheral vision,” Vision Res. 35, 939–947 (1995).
[CrossRef] [PubMed]

Bailey, I.

I. Bailey, J. Lovie, “New design principles for visual acuity letter charts,” Am. J. Optom. Physiol. Opt. 53, 740–745 (1976).
[CrossRef] [PubMed]

Banks, M. S.

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

Bedell, H. E.

G. L. Kandel, P. E. Grattan, H. E. Bedell, “Monocular fixation and acuity in amblyopic and normal eyes,” Am. J. Optom. Physiol. Opt. 54, 598–608 (1977).
[CrossRef] [PubMed]

Bennett, P. J.

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

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]

Braddick, O. J.

C. M. E. Stephenson, A. J. Knapp, O. J. Braddick, “Discrimination of spatial phase shows a qualitative difference between foveal and peripheral processing,” Vision Res. 31, 1315–1326 (1991).
[CrossRef] [PubMed]

O. J. Braddick, “Is spatial phase degraded in peripheral vision and visual pathology?” Doc. Ophthal. Proc. Ser. 30, 255–262 (1981).

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. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

Y. Z. Wang, L. N. Thibos, A. Bradley, “Undersampling produces nonveridical 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]

L. N. Thibos, A. Bradley, “New methods for discriminating neural and optical losses of vision,” Optom. Vision Sci. 70, 279–287 (1993).
[CrossRef]

Brettel, H.

R. Hilz, I. Rentschler, H. Brettel, “Insensitivity of peripheral vision to spatial phase,” Exp. Brain Res. 43, 111–114 (1981).
[CrossRef] [PubMed]

Brown, N. A. P.

N. A. P. Brown, J. M. Sparrow, G. A. Shun-Shin, S. L. Franklin, “The acuityscope: a resolution test target projection ophthalmoscope,” Int. Ophthalmol. 15, 139–142 (1991).
[CrossRef] [PubMed]

Campbell, F. W.

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

Cass, R. A.

Cavonius, C. R.

R. Hilz, C. R. Cavonius, “Functional organization of the peripheral retina: sensitivity to periodic stimuli,” Vision Res. 14, 1333–1338 (1974).
[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]

L. N. Thibos, F. E. Cheney, D. J. Walsh, “Retinal limits to the detection and resolution of gratings,” J. Opt. Soc. Am. A 4, 1524–1529 (1987).
[CrossRef] [PubMed]

Chung, S. T. L.

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

Cohn, T. E.

T. E. Cohn, D. J. Lasley, “Visual sensitivity,” Annu. Rev. Psychol. 37, 495–521 (1986).
[CrossRef] [PubMed]

Coletta, N. J.

N. J. Coletta, P. Segu, C. L. M. Tiana, “An oblique effect in parafoveal motion perception,” Vision Res. 33, 2747–2756 (1993).
[CrossRef] [PubMed]

N. J. Coletta, D. R. Williams, C. L. M. Tiana, “Consequences of spatial sampling for human motion perception,” Vision Res. 30, 1631–1648 (1990).
[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]

N. J. Coletta, D. R. Williams, “Psychophysical estimate of extrafoveal cone spacing,” J. Opt. Soc. Am. A 4, 1503–1513 (1987).
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Colombo, E.

P. Artal, A. M. Derrington, E. Colombo, “Refraction, aliasing, and the absence of motion reversals in peripheral vision,” Vision Res. 35, 939–947 (1995).
[CrossRef] [PubMed]

Dakin, S. C.

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Invest. Ophthalmol. Visual Sci. 40, S809 (1999).

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).
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Derlacki, D. J.

K. R. Alexander, W. Xie, D. J. Derlacki, “Visual acuity and contrast sensitivity for individual Sloan letters,” Vision Res. 37, 813–819 (1997).
[CrossRef] [PubMed]

K. R. Alexander, W. Xie, D. J. Derlacki, “Spatial-frequency characteristics of letter identification,” J. Opt. Soc. Am. A 11, 2373–2382 (1994).
[CrossRef]

Derrington, A. M.

P. Artal, A. M. Derrington, E. Colombo, “Refraction, aliasing, and the absence of motion reversals in peripheral vision,” Vision Res. 35, 939–947 (1995).
[CrossRef] [PubMed]

Detkova, P.

R. S. Anderson, P. Detkova, C. O'Brien, “Effect of temporal frequency and contrast on peripheral grating resolution,” Curr. Eye Res. 14, 1031–1033 (1995).
[CrossRef] [PubMed]

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]

Franklin, S. L.

N. A. P. Brown, J. M. Sparrow, G. A. Shun-Shin, S. L. Franklin, “The acuityscope: a resolution test target projection ophthalmoscope,” Int. Ophthalmol. 15, 139–142 (1991).
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S. J. Galvin, D. R. Williams, “No aliasing at edges in normal viewing,” Vision Res. 32, 2251–2259 (1992).
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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).

Graham, C. H.

Grattan, P. E.

G. L. Kandel, P. E. Grattan, H. E. Bedell, “Monocular fixation and acuity in amblyopic and normal eyes,” Am. J. Optom. Physiol. Opt. 54, 598–608 (1977).
[CrossRef] [PubMed]

Harvey, L. O.

H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast thresholds for identification of numeric characters in direct and eccentric view,” Percept. Psychophys. 49, 495–508 (1991).
[CrossRef] [PubMed]

Hess, R. F.

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Invest. Ophthalmol. Visual Sci. 40, S809 (1999).

R. F. Hess, J. McCarthy, “Topological disorder in peripheral vision,” Visual Neurosci. 11, 1033–1036 (1994).
[CrossRef]

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]

S. J. Anderson, K. T. Mullen, R. F. Hess, “Human peripheral spatial resolution for achromatic and chromatic stimuli—limits imposed by optical and retinal factors,” J. Physiol. (London) 442, 47–64 (1991).

S. J. Anderson, R. F. Hess, “Spatial undersampling causes both motion cessation and reversal phenomena in human peripheral vision,” Invest. Ophthalmol. Visual Sci. 31, 495 (1990).

S. J. Anderson, R. F. Hess, “Post-receptoral undersampling in normal human peripheral vision,” Vision Res. 30, 1507–1515 (1990).
[CrossRef] [PubMed]

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K. E. Higgins, A. Arditi, K. Knoblauch, “Detection and identification or mirror-image letter pairs in central and peripheral vision,” Vision Res. 36, 331–337 (1996).
[CrossRef] [PubMed]

Hilz, R.

R. Hilz, I. Rentschler, H. Brettel, “Insensitivity of peripheral vision to spatial phase,” Exp. Brain Res. 43, 111–114 (1981).
[CrossRef] [PubMed]

R. Hilz, C. R. Cavonius, “Functional organization of the peripheral retina: sensitivity to periodic stimuli,” Vision Res. 14, 1333–1338 (1974).
[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).

Kandel, G. L.

G. L. Kandel, P. E. Grattan, H. E. Bedell, “Monocular fixation and acuity in amblyopic and normal eyes,” Am. J. Optom. Physiol. Opt. 54, 598–608 (1977).
[CrossRef] [PubMed]

Kapoor, N.

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Invest. Ophthalmol. Visual Sci. 40, S809 (1999).

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J. L. Kerr, “Visual resolution in the periphery,” Percept. Psychophys. 9, 375–378 (1971).
[CrossRef]

Klein, S.

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[CrossRef] [PubMed]

Klein, S. A.

D. M. Levi, S. A. Klein, H. Wang, “Amblyopic and peripheral vernier acuity: a test-pedestal approach,” Vision Res. 34, 3265–3292 (1994).
[CrossRef] [PubMed]

D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
[CrossRef] [PubMed]

Knapp, A. J.

C. M. E. Stephenson, A. J. Knapp, O. J. Braddick, “Discrimination of spatial phase shows a qualitative difference between foveal and peripheral processing,” Vision Res. 31, 1315–1326 (1991).
[CrossRef] [PubMed]

Knoblauch, K.

K. E. Higgins, A. Arditi, K. Knoblauch, “Detection and identification or mirror-image letter pairs in central and peripheral vision,” Vision Res. 36, 331–337 (1996).
[CrossRef] [PubMed]

Koenderink, J. J.

J. J. Koenderink, A. J. van Doorn, “Visual detection of spatial contrast; influence of location in the visual field, target extent and illuminance level,” Biol. Cybern. 30, 157–167 (1978).
[CrossRef] [PubMed]

Lanson, R. N.

Lasley, D. J.

T. E. Cohn, D. J. Lasley, “Visual sensitivity,” Annu. Rev. Psychol. 37, 495–521 (1986).
[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 depen-dence of letter recognition in central and peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, S639 (1997).

Levi, D. M.

D. M. Levi, S. A. Klein, H. Wang, “Amblyopic and peripheral vernier acuity: a test-pedestal approach,” Vision Res. 34, 3265–3292 (1994).
[CrossRef] [PubMed]

D. M. Levi, S. A. Klein, A. P. Aitsebaomo, “Vernier acuity, crowding and cortical magnification,” Vision Res. 25, 963–977 (1985).
[CrossRef] [PubMed]

Lovie, J.

I. Bailey, J. Lovie, “New design principles for visual acuity letter charts,” Am. J. Optom. Physiol. Opt. 53, 740–745 (1976).
[CrossRef] [PubMed]

Ludvigh, E.

E. Ludvigh, “Extrafoveal visual acuity as measured with Snellen letters,” Am. J. Ophthalmol. 24, 303–310 (1941).

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]

McCarthy, J.

R. F. Hess, J. McCarthy, “Topological disorder in peripheral vision,” Visual Neurosci. 11, 1033–1036 (1994).
[CrossRef]

Merchant, J.

Mullen, K. T.

S. J. Anderson, K. T. Mullen, R. F. Hess, “Human peripheral spatial resolution for achromatic and chromatic stimuli—limits imposed by optical and retinal factors,” J. Physiol. (London) 442, 47–64 (1991).

Nasanen, R.

V. Virsu, R. Nasanen, K. Osmoviita, “Cortical magnification and peripheral vision,” J. Opt. Soc. Am. A 4, 1568–1578 (1987).
[CrossRef] [PubMed]

J. Rovamo, V. Virsu, R. Nasanen, “Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision,” Nature (London) 271, 54–56 (1978).
[CrossRef]

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]

O'Brien, C.

R. S. Anderson, P. Detkova, C. O'Brien, “Effect of temporal frequency and contrast on peripheral grating resolution,” Curr. Eye Res. 14, 1031–1033 (1995).
[CrossRef] [PubMed]

Osmoviita, K.

Pokorny, J.

Rentschler, I.

H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast thresholds for identification of numeric characters in direct and eccentric view,” Percept. Psychophys. 49, 495–508 (1991).
[CrossRef] [PubMed]

R. Hilz, I. Rentschler, H. Brettel, “Insensitivity of peripheral vision to spatial phase,” Exp. Brain Res. 43, 111–114 (1981).
[CrossRef] [PubMed]

Robson, J. G.

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

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).

J. Rovamo, V. Virsu, R. Nasanen, “Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision,” Nature (London) 271, 54–56 (1978).
[CrossRef]

Schwartz, F.

F. Thorn, F. Schwartz, “Effects of dioptric blur on Snellen and grating acuity,” Optom. Vision Sci. 67, 3–7 (1990).
[CrossRef]

Segu, P.

N. J. Coletta, P. Segu, C. L. M. Tiana, “An oblique effect in parafoveal motion perception,” Vision Res. 33, 2747–2756 (1993).
[CrossRef] [PubMed]

Shun-Shin, G. A.

N. A. P. Brown, J. M. Sparrow, G. A. Shun-Shin, S. L. Franklin, “The acuityscope: a resolution test target projection ophthalmoscope,” Int. Ophthalmol. 15, 139–142 (1991).
[CrossRef] [PubMed]

Smith, R. A.

Sparrow, J. M.

N. A. P. Brown, J. M. Sparrow, G. A. Shun-Shin, S. L. Franklin, “The acuityscope: a resolution test target projection ophthalmoscope,” Int. Ophthalmol. 15, 139–142 (1991).
[CrossRef] [PubMed]

Stephenson, C. M. E.

C. M. E. Stephenson, A. J. Knapp, O. J. Braddick, “Discrimination of spatial phase shows a qualitative difference between foveal and peripheral processing,” Vision Res. 31, 1315–1326 (1991).
[CrossRef] [PubMed]

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]

Strasburger, H.

H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast thresholds for identification of numeric characters in direct and eccentric view,” Percept. Psychophys. 49, 495–508 (1991).
[CrossRef] [PubMed]

Stromeyer, C. F.

C. F. Stromeyer, S. Klein, “Spatial frequency channels in human vision as asymmetric (edge) mechanisms,” Vision Res. 14, 1409–1420 (1974).
[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, “Sampling limits and critical bandwidth for letter discrimination in peripheral vision,” J. Opt. Soc. Am. A 16, 2334–2342 (1999).
[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, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

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]

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

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 nonveridical 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]

L. N. Thibos, A. Bradley, “New methods for discriminating neural and optical losses of vision,” Optom. Vision Sci. 70, 279–287 (1993).
[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, F. E. Cheney, D. J. Walsh, “Retinal limits to the detection and resolution of gratings,” J. Opt. Soc. Am. A 4, 1524–1529 (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]

Thorn, F.

F. Thorn, F. Schwartz, “Effects of dioptric blur on Snellen and grating acuity,” Optom. Vision Sci. 67, 3–7 (1990).
[CrossRef]

Tiana, C. L. M.

N. J. Coletta, P. Segu, C. L. M. Tiana, “An oblique effect in parafoveal motion perception,” Vision Res. 33, 2747–2756 (1993).
[CrossRef] [PubMed]

N. J. Coletta, D. R. Williams, C. L. M. Tiana, “Consequences of spatial sampling for human motion perception,” Vision Res. 30, 1631–1648 (1990).
[CrossRef] [PubMed]

van Doorn, A. J.

J. J. Koenderink, A. J. van Doorn, “Visual detection of spatial contrast; influence of location in the visual field, target extent and illuminance level,” Biol. Cybern. 30, 157–167 (1978).
[CrossRef] [PubMed]

Virsu, V.

V. Virsu, R. Nasanen, K. Osmoviita, “Cortical magnification and peripheral vision,” J. Opt. Soc. Am. A 4, 1568–1578 (1987).
[CrossRef] [PubMed]

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. Rovamo, V. Virsu, R. Nasanen, “Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision,” Nature (London) 271, 54–56 (1978).
[CrossRef]

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]

L. N. Thibos, F. E. Cheney, D. J. Walsh, “Retinal limits to the detection and resolution of gratings,” J. Opt. Soc. Am. A 4, 1524–1529 (1987).
[CrossRef] [PubMed]

Wang, H.

D. M. Levi, S. A. Klein, H. Wang, “Amblyopic and peripheral vernier acuity: a test-pedestal approach,” Vision Res. 34, 3265–3292 (1994).
[CrossRef] [PubMed]

Wang, Y.

Y. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

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 nonveridical motion perception, but not necessarily motion reversal, in peripheral vision,” Vision Res. 36, 1737–1744 (1996).
[CrossRef] [PubMed]

Westheimer, G.

G. Westheimer, “Scaling of visual acuity,” Arch. Ophthalmol. (Chicago) 97, 327–330 (1979).
[CrossRef]

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]

M. O. Wilkinson, “Neural basis of photopic and scotopic visual acuity,” Ph.D. dissertation (Indiana University, Bloomington, Ind., 1994).

Williams, D. R.

Xie, W.

K. R. Alexander, W. Xie, D. J. Derlacki, “Visual acuity and contrast sensitivity for individual Sloan letters,” Vision Res. 37, 813–819 (1997).
[CrossRef] [PubMed]

K. R. Alexander, W. Xie, D. J. Derlacki, “Spatial-frequency characteristics of letter identification,” J. Opt. Soc. Am. A 11, 2373–2382 (1994).
[CrossRef]

Am. J. Ophthalmol. (1)

E. Ludvigh, “Extrafoveal visual acuity as measured with Snellen letters,” Am. J. Ophthalmol. 24, 303–310 (1941).

Am. J. Optom. Physiol. Opt. (3)

G. L. Kandel, P. E. Grattan, H. E. Bedell, “Monocular fixation and acuity in amblyopic and normal eyes,” Am. J. Optom. Physiol. Opt. 54, 598–608 (1977).
[CrossRef] [PubMed]

I. Bailey, J. Lovie, “New design principles for visual acuity letter charts,” Am. J. Optom. Physiol. Opt. 53, 740–745 (1976).
[CrossRef] [PubMed]

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]

Annu. Rev. Psychol. (1)

T. E. Cohn, D. J. Lasley, “Visual sensitivity,” Annu. Rev. Psychol. 37, 495–521 (1986).
[CrossRef] [PubMed]

Arch. Ophthalmol. (Chicago) (1)

G. Westheimer, “Scaling of visual acuity,” Arch. Ophthalmol. (Chicago) 97, 327–330 (1979).
[CrossRef]

Biol. Cybern. (1)

J. J. Koenderink, A. J. van Doorn, “Visual detection of spatial contrast; influence of location in the visual field, target extent and illuminance level,” Biol. Cybern. 30, 157–167 (1978).
[CrossRef] [PubMed]

Curr. Eye Res. (2)

R. S. Anderson, “The selective effect of optical defocus on detection and resolution acuity in peripheral vision,” Curr. Eye Res. 15, 351–353 (1996).
[CrossRef] [PubMed]

R. S. Anderson, P. Detkova, C. O'Brien, “Effect of temporal frequency and contrast on peripheral grating resolution,” Curr. Eye Res. 14, 1031–1033 (1995).
[CrossRef] [PubMed]

Doc. Ophthal. Proc. Ser. (1)

O. J. Braddick, “Is spatial phase degraded in peripheral vision and visual pathology?” Doc. Ophthal. Proc. Ser. 30, 255–262 (1981).

Exp. Brain Res. (1)

R. Hilz, I. Rentschler, H. Brettel, “Insensitivity of peripheral vision to spatial phase,” Exp. Brain Res. 43, 111–114 (1981).
[CrossRef] [PubMed]

Int. Ophthalmol. (1)

N. A. P. Brown, J. M. Sparrow, G. A. Shun-Shin, S. L. Franklin, “The acuityscope: a resolution test target projection ophthalmoscope,” Int. Ophthalmol. 15, 139–142 (1991).
[CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci. (5)

S. J. Anderson, R. F. Hess, “Spatial undersampling causes both motion cessation and reversal phenomena in human peripheral vision,” Invest. Ophthalmol. Visual Sci. 31, 495 (1990).

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).

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

Y. Wang, L. N. Thibos, A. Bradley, “Effects of refractive error on detection acuity and resolution acuity in peripheral vision,” Invest. Ophthalmol. Visual Sci. 38, 2134–2143 (1997).

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Invest. Ophthalmol. Visual Sci. 40, S809 (1999).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (9)

J. Physiol. (London) (2)

S. J. Anderson, K. T. Mullen, R. F. Hess, “Human peripheral spatial resolution for achromatic and chromatic stimuli—limits imposed by optical and retinal factors,” J. Physiol. (London) 442, 47–64 (1991).

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

Nature (London) (2)

J. Rovamo, V. Virsu, R. Nasanen, “Cortical magnification factor predicts the photopic contrast sensitivity of peripheral vision,” Nature (London) 271, 54–56 (1978).
[CrossRef]

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

Optom. Vision Sci. (4)

L. N. Thibos, A. Bradley, “New methods for discriminating neural and optical losses of vision,” Optom. Vision Sci. 70, 279–287 (1993).
[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]

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Figures (7)

Fig. 1
Fig. 1

Contrast spectra for patches of a square-wave grating containing A, 32 stimulus cycles or B, 2.5 stimulus cycles. Both targets are assumed to have the same physical spatial frequency, which lies just below the Nyquist frequency of a neural sampling array. Spectral dispersion causes stimulus energy in the fundamental Fourier component in B to leak into the aliasing zone, whereas no such leakage occurs in A.

Fig. 2
Fig. 2

Five stimulus pairs used for measuring discrimination acuity.

Fig. 3
Fig. 3

Threshold letter size and grating period versus eccentricity for long-stroke letters E and three-bar gratings. The labels RSA and LNT refer to the observers and in Fig. 4.

Fig. 4
Fig. 4

Threshold letter size and grating period versus eccentricity for short-stroke letters E and three-bar gratings.

Fig. 5
Fig. 5

Contrast spectra for the long- and short-stroke tumbling E's. Spectral resolution in this and other figures is 0.3125 c/let. In the two-dimensional spectra the abscissa and the ordinate represent spatial frequencies in the horizontal and the vertical directions, respectively, and contrast of individual frequency components is encoded by the intensity of the corresponding pixels. One-dimensional spectra below and to the side are cross sections of the two-dimensional spectra taken through the origin. The characteristic frequency in both examples is 2.5 c/let (ordinate), and a prominent second peak occurs also at 1.25 c/let.

Fig. 6
Fig. 6

Determination of the difference spectrum. The images of the horizontal and vertical three-bar gratings are subtracted in the spatial domain to give the difference image. A fast Fourier transform is then performed on the difference image, and the magnitude of the result is displayed as the difference spectrum. Calibration in physical units is for a target at the resolution threshold (34-arc-min target width) for subject RSA, 30° eccentricity.

Fig. 7
Fig. 7

Difference spectra for test targets when letter size is at psychophysical threshold for discrimination (subject RSA, 30° eccentricity). The Nyquist frequency estimated from a previous paper12 is shown by a circle centered on the origin. Notice that the most prominent components of the difference spectrum (marked by arrows) vary with the letter pair being discriminated but in every case fall inside the Nyquist ring. Spatial-frequency calibration is provided in terms of object frequency (cycles per letter) and physical frequency (cycles per degree).

Tables (2)

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Table 1 Refractive Error at Several Eccentricities for both Subjects

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Table 2 Foveal MAR (in arc min) and Linear Regression Parametersa

Equations (2)

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fccyclesdegree=fccyclesletter 1letterθarc min 60arc mindegree.
fN(c/let)fN(c/deg)=fcc/letfc c/deg.

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