Abstract

It has been known for some time that both foveal and peripheral visual acuity are higher for single letters than for letters in a row. Early work showed that this was due to the destructive interaction of adjacent contours (termed contour interaction). It has been assumed to have a neural basis, and a number of competing explanations have been advanced that implicate either high-level or low-level stages of visual processing. Our previous results for foveal vision suggested a much simpler explanation, one determined primarily by the physics of the stimulus rather than the physiology of the visual system. We show that, under conditions of contour interaction or crowding, the most relevant physical spatial-frequency band of the letter is displaced to higher spatial frequencies and that foveal vision tracks this change in spatial scale. In the periphery, however, beyond 5°, the physical explanation is not sufficient. Here we show that there are genuine physiological lateral spatial interactions, which are due to changes in the spatial scale of analysis.

© 2000 Optical Society of America

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References

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  1. P. Muller, “Über das Schen der Amblyopen,” Ophthalmologica 121, 143–149 (1951).
    [CrossRef] [PubMed]
  2. M. C. Flom, F. W. Weymouth, D. Kahneman, “Visual resolution and contour interaction,” J. Opt. Soc. Am. 53, 1026–1032 (1963).
    [CrossRef] [PubMed]
  3. J. M. Loomis, “Lateral masking in foveal and eccentric vision,” Vision Res. 18, 335–338 (1978).
    [CrossRef] [PubMed]
  4. H. Strasburger, L. O. Harvey, I. Rentschler, “Contrast thresholds for the identification of numeric charters in direct and eccentric view,” Percept. Psychophys. 49, 495–508 (1991).
    [CrossRef] [PubMed]
  5. R. J. Jacobs, “Visual resolution and contour interaction in the fovea and periphery,” Vision Res. 19, 1187–1195 (1979).
    [CrossRef] [PubMed]
  6. M. C. Flom, G. Heath, E. Takahashi, “Crowding interaction and visual resolution: contralateral effects,” Science 142, 979–980 (1963).
    [CrossRef] [PubMed]
  7. W. K. Estes, D. H. Allmeyer, S. M. Reder, “Serial position functions for letter identification at brief and extended exposure periods,” Percept. Psychophys. 19, 1–15 (1976).
    [CrossRef]
  8. M. C. Flom, “Contour interaction and the crowding effect,” Prob. Optom. 3, 237–257 (1991).
  9. A. J. Simmers, L. S. Gray, P. V. McGraw, B. Winn, “Contour interaction for high and low contrast optotypes in normal and amblyopic observers,” Ophthalmic Physiol. Opt. 19, 253–260 (1999).
    [CrossRef]
  10. J. Wagner, “Experimentelle Beitrage zur Psychologie des Lesens,” Z. Psychol. 80, 1–75 (1918).
  11. C. D. Gilbert, T. N. Wiesel, “Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex,” J. Neurosci. 9, 2432–2442 (1989).
    [PubMed]
  12. D. Y. T’so, C. D. Gilbert, “The organization of chromatic and spatial interactions in the primate striate cortex,” J. Neurosci. 8, 1712–1727 (1988).
  13. R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Vision Res. 20, 365–370 (2000).
    [CrossRef]
  14. S. J. Leat, K. Epp, “Crowding in central and eccentric vision: the effects of contour interaction and attention,” Invest. Ophthalmol. Visual Sci. 40, 504–512 (1999).
  15. D. H. Brainard, “The psychophysics toolbox,” Spatial Vision 10, 433–446 (1997).
    [CrossRef] [PubMed]
  16. D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1347 (1991).
    [CrossRef] [PubMed]
  17. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).
  18. V. M. Bondarko, M. V. Danilova, “What spatial frequencies do we use to detect the orientation of a Landolt C?” Vision Res. 37, 2153–2156 (1997).
    [CrossRef] [PubMed]
  19. F. L. Kooi, A. Toet, S. P. Tripathy, D. M. Levi, “The effect of similarity and duration on spatial interactions in peripheral vision,” Spatial Vis. 8, 255–279 (1994).
    [CrossRef]
  20. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  21. J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
    [CrossRef]
  22. R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
    [CrossRef] [PubMed]
  23. R. F. Hess, A. Hayes, “The coding of spatial position by the human visual system: effects of spatial scale and retinal eccentricity,” Vision Res. 34, 625–643 (1994).
    [CrossRef] [PubMed]

2000

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Vision Res. 20, 365–370 (2000).
[CrossRef]

1999

S. J. Leat, K. Epp, “Crowding in central and eccentric vision: the effects of contour interaction and attention,” Invest. Ophthalmol. Visual Sci. 40, 504–512 (1999).

A. J. Simmers, L. S. Gray, P. V. McGraw, B. Winn, “Contour interaction for high and low contrast optotypes in normal and amblyopic observers,” Ophthalmic Physiol. Opt. 19, 253–260 (1999).
[CrossRef]

R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
[CrossRef] [PubMed]

1997

D. H. Brainard, “The psychophysics toolbox,” Spatial Vision 10, 433–446 (1997).
[CrossRef] [PubMed]

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

1994

F. L. Kooi, A. Toet, S. P. Tripathy, D. M. Levi, “The effect of similarity and duration on spatial interactions in peripheral vision,” Spatial Vis. 8, 255–279 (1994).
[CrossRef]

R. F. Hess, A. Hayes, “The coding of spatial position by the human visual system: effects of spatial scale and retinal eccentricity,” Vision Res. 34, 625–643 (1994).
[CrossRef] [PubMed]

1991

M. C. Flom, “Contour interaction and the crowding effect,” Prob. Optom. 3, 237–257 (1991).

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1347 (1991).
[CrossRef] [PubMed]

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

1989

C. D. Gilbert, T. N. Wiesel, “Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex,” J. Neurosci. 9, 2432–2442 (1989).
[PubMed]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[CrossRef]

1988

D. Y. T’so, C. D. Gilbert, “The organization of chromatic and spatial interactions in the primate striate cortex,” J. Neurosci. 8, 1712–1727 (1988).

1979

R. J. Jacobs, “Visual resolution and contour interaction in the fovea and periphery,” Vision Res. 19, 1187–1195 (1979).
[CrossRef] [PubMed]

1978

J. M. Loomis, “Lateral masking in foveal and eccentric vision,” Vision Res. 18, 335–338 (1978).
[CrossRef] [PubMed]

1976

W. K. Estes, D. H. Allmeyer, S. M. Reder, “Serial position functions for letter identification at brief and extended exposure periods,” Percept. Psychophys. 19, 1–15 (1976).
[CrossRef]

1965

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).

1963

M. C. Flom, G. Heath, E. Takahashi, “Crowding interaction and visual resolution: contralateral effects,” Science 142, 979–980 (1963).
[CrossRef] [PubMed]

M. C. Flom, F. W. Weymouth, D. Kahneman, “Visual resolution and contour interaction,” J. Opt. Soc. Am. 53, 1026–1032 (1963).
[CrossRef] [PubMed]

1951

P. Muller, “Über das Schen der Amblyopen,” Ophthalmologica 121, 143–149 (1951).
[CrossRef] [PubMed]

1918

J. Wagner, “Experimentelle Beitrage zur Psychologie des Lesens,” Z. Psychol. 80, 1–75 (1918).

Allmeyer, D. H.

W. K. Estes, D. H. Allmeyer, S. M. Reder, “Serial position functions for letter identification at brief and extended exposure periods,” Percept. Psychophys. 19, 1–15 (1976).
[CrossRef]

Bondarko, V. M.

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

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

Brainard, D. H.

D. H. Brainard, “The psychophysics toolbox,” Spatial Vision 10, 433–446 (1997).
[CrossRef] [PubMed]

Campbell, F. W.

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).

Dakin, S. C.

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Vision Res. 20, 365–370 (2000).
[CrossRef]

R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
[CrossRef] [PubMed]

Danilova, M. V.

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

Epp, K.

S. J. Leat, K. Epp, “Crowding in central and eccentric vision: the effects of contour interaction and attention,” Invest. Ophthalmol. Visual Sci. 40, 504–512 (1999).

Estes, W. K.

W. K. Estes, D. H. Allmeyer, S. M. Reder, “Serial position functions for letter identification at brief and extended exposure periods,” Percept. Psychophys. 19, 1–15 (1976).
[CrossRef]

Flom, M. C.

M. C. Flom, “Contour interaction and the crowding effect,” Prob. Optom. 3, 237–257 (1991).

M. C. Flom, G. Heath, E. Takahashi, “Crowding interaction and visual resolution: contralateral effects,” Science 142, 979–980 (1963).
[CrossRef] [PubMed]

M. C. Flom, F. W. Weymouth, D. Kahneman, “Visual resolution and contour interaction,” J. Opt. Soc. Am. 53, 1026–1032 (1963).
[CrossRef] [PubMed]

Gilbert, C. D.

C. D. Gilbert, T. N. Wiesel, “Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex,” J. Neurosci. 9, 2432–2442 (1989).
[PubMed]

D. Y. T’so, C. D. Gilbert, “The organization of chromatic and spatial interactions in the primate striate cortex,” J. Neurosci. 8, 1712–1727 (1988).

Gray, L. S.

A. J. Simmers, L. S. Gray, P. V. McGraw, B. Winn, “Contour interaction for high and low contrast optotypes in normal and amblyopic observers,” Ophthalmic Physiol. Opt. 19, 253–260 (1999).
[CrossRef]

Green, D. G.

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).

Harvey, L. O.

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

Hayes, A.

R. F. Hess, A. Hayes, “The coding of spatial position by the human visual system: effects of spatial scale and retinal eccentricity,” Vision Res. 34, 625–643 (1994).
[CrossRef] [PubMed]

Heath, G.

M. C. Flom, G. Heath, E. Takahashi, “Crowding interaction and visual resolution: contralateral effects,” Science 142, 979–980 (1963).
[CrossRef] [PubMed]

Hess, R. F.

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Vision Res. 20, 365–370 (2000).
[CrossRef]

R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
[CrossRef] [PubMed]

R. F. Hess, A. Hayes, “The coding of spatial position by the human visual system: effects of spatial scale and retinal eccentricity,” Vision Res. 34, 625–643 (1994).
[CrossRef] [PubMed]

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[CrossRef]

Jacobs, R. J.

R. J. Jacobs, “Visual resolution and contour interaction in the fovea and periphery,” Vision Res. 19, 1187–1195 (1979).
[CrossRef] [PubMed]

Kahneman, D.

Kapoor, N.

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Vision Res. 20, 365–370 (2000).
[CrossRef]

Kooi, F. L.

F. L. Kooi, A. Toet, S. P. Tripathy, D. M. Levi, “The effect of similarity and duration on spatial interactions in peripheral vision,” Spatial Vis. 8, 255–279 (1994).
[CrossRef]

Leat, S. J.

S. J. Leat, K. Epp, “Crowding in central and eccentric vision: the effects of contour interaction and attention,” Invest. Ophthalmol. Visual Sci. 40, 504–512 (1999).

Levi, D. M.

F. L. Kooi, A. Toet, S. P. Tripathy, D. M. Levi, “The effect of similarity and duration on spatial interactions in peripheral vision,” Spatial Vis. 8, 255–279 (1994).
[CrossRef]

Loomis, J. M.

J. M. Loomis, “Lateral masking in foveal and eccentric vision,” Vision Res. 18, 335–338 (1978).
[CrossRef] [PubMed]

McGraw, P. V.

A. J. Simmers, L. S. Gray, P. V. McGraw, B. Winn, “Contour interaction for high and low contrast optotypes in normal and amblyopic observers,” Ophthalmic Physiol. Opt. 19, 253–260 (1999).
[CrossRef]

Muller, P.

P. Muller, “Über das Schen der Amblyopen,” Ophthalmologica 121, 143–149 (1951).
[CrossRef] [PubMed]

Pelli, D. G.

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1347 (1991).
[CrossRef] [PubMed]

Pointer, J. S.

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[CrossRef]

Reder, S. M.

W. K. Estes, D. H. Allmeyer, S. M. Reder, “Serial position functions for letter identification at brief and extended exposure periods,” Percept. Psychophys. 19, 1–15 (1976).
[CrossRef]

Rentschler, I.

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

Simmers, A. J.

A. J. Simmers, L. S. Gray, P. V. McGraw, B. Winn, “Contour interaction for high and low contrast optotypes in normal and amblyopic observers,” Ophthalmic Physiol. Opt. 19, 253–260 (1999).
[CrossRef]

Strasburger, H.

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

T’so, D. Y.

D. Y. T’so, C. D. Gilbert, “The organization of chromatic and spatial interactions in the primate striate cortex,” J. Neurosci. 8, 1712–1727 (1988).

Takahashi, E.

M. C. Flom, G. Heath, E. Takahashi, “Crowding interaction and visual resolution: contralateral effects,” Science 142, 979–980 (1963).
[CrossRef] [PubMed]

Toet, A.

F. L. Kooi, A. Toet, S. P. Tripathy, D. M. Levi, “The effect of similarity and duration on spatial interactions in peripheral vision,” Spatial Vis. 8, 255–279 (1994).
[CrossRef]

Tripathy, S. P.

F. L. Kooi, A. Toet, S. P. Tripathy, D. M. Levi, “The effect of similarity and duration on spatial interactions in peripheral vision,” Spatial Vis. 8, 255–279 (1994).
[CrossRef]

Wagner, J.

J. Wagner, “Experimentelle Beitrage zur Psychologie des Lesens,” Z. Psychol. 80, 1–75 (1918).

Weymouth, F. W.

Wiesel, T. N.

C. D. Gilbert, T. N. Wiesel, “Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex,” J. Neurosci. 9, 2432–2442 (1989).
[PubMed]

Winn, B.

A. J. Simmers, L. S. Gray, P. V. McGraw, B. Winn, “Contour interaction for high and low contrast optotypes in normal and amblyopic observers,” Ophthalmic Physiol. Opt. 19, 253–260 (1999).
[CrossRef]

Zhang, L.

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1347 (1991).
[CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci.

S. J. Leat, K. Epp, “Crowding in central and eccentric vision: the effects of contour interaction and attention,” Invest. Ophthalmol. Visual Sci. 40, 504–512 (1999).

J. Neurosci.

C. D. Gilbert, T. N. Wiesel, “Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex,” J. Neurosci. 9, 2432–2442 (1989).
[PubMed]

D. Y. T’so, C. D. Gilbert, “The organization of chromatic and spatial interactions in the primate striate cortex,” J. Neurosci. 8, 1712–1727 (1988).

J. Opt. Soc. Am.

J. Physiol. (London)

F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).

Ophthalmic Physiol. Opt.

A. J. Simmers, L. S. Gray, P. V. McGraw, B. Winn, “Contour interaction for high and low contrast optotypes in normal and amblyopic observers,” Ophthalmic Physiol. Opt. 19, 253–260 (1999).
[CrossRef]

Ophthalmologica

P. Muller, “Über das Schen der Amblyopen,” Ophthalmologica 121, 143–149 (1951).
[CrossRef] [PubMed]

Percept. Psychophys.

W. K. Estes, D. H. Allmeyer, S. M. Reder, “Serial position functions for letter identification at brief and extended exposure periods,” Percept. Psychophys. 19, 1–15 (1976).
[CrossRef]

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

Prob. Optom.

M. C. Flom, “Contour interaction and the crowding effect,” Prob. Optom. 3, 237–257 (1991).

Science

M. C. Flom, G. Heath, E. Takahashi, “Crowding interaction and visual resolution: contralateral effects,” Science 142, 979–980 (1963).
[CrossRef] [PubMed]

Spatial Vis.

F. L. Kooi, A. Toet, S. P. Tripathy, D. M. Levi, “The effect of similarity and duration on spatial interactions in peripheral vision,” Spatial Vis. 8, 255–279 (1994).
[CrossRef]

Spatial Vision

D. H. Brainard, “The psychophysics toolbox,” Spatial Vision 10, 433–446 (1997).
[CrossRef] [PubMed]

Vision Res.

D. G. Pelli, L. Zhang, “Accurate control of contrast on microcomputer displays,” Vision Res. 31, 1337–1347 (1991).
[CrossRef] [PubMed]

R. F. Hess, S. C. Dakin, N. Kapoor, “Foveal contour interaction: physics or physiology?” Vision Res. 20, 365–370 (2000).
[CrossRef]

R. J. Jacobs, “Visual resolution and contour interaction in the fovea and periphery,” Vision Res. 19, 1187–1195 (1979).
[CrossRef] [PubMed]

J. M. Loomis, “Lateral masking in foveal and eccentric vision,” Vision Res. 18, 335–338 (1978).
[CrossRef] [PubMed]

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

J. S. Pointer, R. F. Hess, “The contrast sensitivity gradient across the human visual field: emphasis on the low spatial frequency range,” Vision Res. 29, 1133–1151 (1989).
[CrossRef]

R. F. Hess, S. C. Dakin, “Contour integration in the peripheral field,” Vision Res. 39, 947–959 (1999).
[CrossRef] [PubMed]

R. F. Hess, A. Hayes, “The coding of spatial position by the human visual system: effects of spatial scale and retinal eccentricity,” Vision Res. 34, 625–643 (1994).
[CrossRef] [PubMed]

Z. Psychol.

J. Wagner, “Experimentelle Beitrage zur Psychologie des Lesens,” Z. Psychol. 80, 1–75 (1918).

Other

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1965).

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Figures (7)

Fig. 1
Fig. 1

Subset of the stimuli used in the contour interaction task.

Fig. 2
Fig. 2

Illustration of the effects of bandpass filtering of an unflanked Landolt C at (c) 0.7, (b) 1.6, and (a) 5.6 c/lett.

Fig. 3
Fig. 3

Percent correct for the identification of the position (up, down, left, right) of a gap in a Landolt C is plotted as a function of the distance of lateral contours (see Fig. 1). Results are displayed for foveal and near periphery and for same (open symbols) and reverse contrast polarity flanking contours (solid symbols). Typical error bars [2 standard deviations (SD)] are displayed in frame A.

Fig. 4
Fig. 4

Foveal bandpass-filter filtering functions for Landolt C identification for three subjects (open circles) for unflanked [(a), (e), and (i)], same polarity flanks at five-barwidth separation [(b), (f), and (j)] and same [(c), (g), and (k)] and opposite polarity [(d), (h), and (l)] flanks at one-barwidth separation. Percent correct is plotted against the peak spatial frequency of the passband in cycles per degree. The horizontal dashed line gives the unfiltered performance, whereas the vertical dashed lines give the predictions for the peak filtering location based solely on the difference spectra (see text). The predictions when converted from cycles per letter to cycles per degree differ slightly for each subject because their absolute acuity is not the same. The physical predictions (vertical lines) match the peak locations in the filtering functions. The minimum angle of resolution in the unflanked case was 0.024° for RFH, 0.019° for NK, and 0.017° for MT. Typical error bars (2 SD) are displayed in frame A.

Fig. 5
Fig. 5

Percent correct for the identification of the position (up, down, left, right) of a gap in a Landolt C is plotted as a function of the distance of lateral contours (see Fig. 1). Results are displayed for midperiphery and for same (open symbols) and reverse-contrast polarity flanking contours (solid symbols). Typical error bars (2 SD) are displayed in frame A.

Fig. 6
Fig. 6

Near-peripheral bandpass-filter filtering functions for Landolt-C identification for three subjects (open circles) for unflanked [(a), (e), and (i)], same polarity flanks at five-barwidth separation [(b), (f), and (j)] and same [(c), (g), and (k)] and opposite polarity [(d), (h), and (l)] flanks at one barwidth separation. Percent correct is plotted against the peak spatial frequency of the passband in cycles per degree. The horizontal dashed line gives the unfiltered performance, whereas the vertical dashed lines give the predictions for the peak filtering location based solely on the difference spectra (see text). The predictions when converted from cycles per letter to cycles per degree differ slightly for each subject because their absolute acuity is not the same. The physical predictions (vertical lines) roughly match the peak locations in the filtering functions. Typical error bars (2 SD) are displayed in frame A.

Fig. 7
Fig. 7

Peripheral bandpass-filter filtering functions for Landolt C identification for three subjects (open circles) for unflanked [(a), (e), and (i)], same polarity flanks at five-barwidth separation [(b), (f), and (j)] and same [(c), (g), and (k)] and opposite polarity[(d), (h), and (l)] flanks at one barwidth separation. Percent correct is plotted against the peak spatial frequency of the passband in cycles per degree. The horizontal dashed line gives the unfiltered performance, whereas the vertical dashed lines give the predictions for the peak filtering location based solely on the difference spectra (see text). The predictions when converted from cycles per letter to cycles per degree differ slightly for each subject because their absolute acuity is not the same. The physical predictions (vertical lines) do not match the peak locations in the filtering functions. Typical error bars (2 SD) are displayed in frame A.

Equations (1)

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2G(σ)=1-x2+y22σ2exp-x2+y22σ2.

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