Abstract

The maximum spatial frequency for the detection and resolution of sinusoidal gratings was determined as a function of stimulus location across the visual field. Stimuli were produced directly on the retina as interference fringes, thus avoiding possible loss of image quality, which may occur when the optical system of the eye is used to form the retinal image. Contrary to earlier reports, we found that subjects could detect gratings with spatial frequencies much higher than the resolution limit. At 5° of eccentricity from the fovea, the detection limit was about three times the resolution limit, and this factor increased to about 10 as the test stimulus was moved 35° into the periphery. Quantitative comparison of the data with retinal anatomy and physiology suggests that pattern resolution is limited by the spacing of primate beta (midget) retinal ganglion cells, whereas pattern detection is limited by the size of individual cones.

© 1987 Optical Society of America

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  1. R. Hiltz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1338 (1974).
    [CrossRef]
  2. V. Virsu and J. Rovamo, "Visual resolution, contrast sensitivity and the cortical magnification factor," Exp. Brain Res. 37, 475–494 (1979).
    [CrossRef]
  3. Th. Wertheim, "Peripheral visual acuity" (1894) [translated by I. L. Dunsky, Am. J. Optom. Physiol. Opt. 57, 919–924 (1980)]. Wertheim's normalized eccentricity curves (Table 2) were put on an absolute scale by using the data from a second experiment (Table 1).
  4. F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).
    [PubMed]
  5. D. G. Green, "Regional variations in the visual acuity for interference fringes on the retina," J. Physiol. (London) 207, 351–356 (1970).
  6. J. L. Kerr, "Visual resolution in the periphery," Percept. Psychophys. 9, 375–378 (1971).
    [CrossRef]
  7. J. M. Enoch and G. M. Hope, "Interferometric resolution determinations in the fovea and parafovea," Doc. Ophthalmol. 34, 143–156 (1973).
    [CrossRef] [PubMed]
  8. L. Frisen and A. Glansholm, "Optical and neural resolution in peripheral vision," Invest. Ophthalmol. 14, 528–536 (1975).
    [PubMed]
  9. J. Rovamo, V. Virsu, P. Laurinen, and L. Hyvarinen, "Resolution of gratings oriented along and across meridians in peripheral vision," Invest. Opthalmol. Vis. Sci. 23, 666–670 (1982).
  10. D. R. Williams, "Visibility of interference fringes near the resolution limit," J. Opt. Soc. Am. A 2, 1087–1093 (1985).
    [CrossRef] [PubMed]
  11. D. R. Williams, "Aliasing in human foveal vision," Vision Res. 25, 195–205 (1985).
    [CrossRef] [PubMed]
  12. L. N. Thibos and D. J. Walsh, "Detection of high frequency gratings in the periphery," J. Opt. Soc. Am. A 2, P64 (1985).
  13. F. W. Campbell and R. W. Gubish, "Optical quality of the human eye," J. Physiol. (London) 186, 558–578 (1966).
  14. M. Millodot, A. L. Johnson, A. Lamont, and H. W. Leibowitz, "Effect of dioptrics on peripheral visual acuity," Vision Res. 15, 1357–1362 (1975).
    [CrossRef] [PubMed]
  15. A. W. Snyder, T. R. J. Bossomaier, and A. Hughes, "Optical image quality and the cone mosaic," Science 231, 499–501 (1986).
    [CrossRef] [PubMed]
  16. D. R. Williams, "Seeing through the photoreceptor mosaic," Trends Neurosci. 9, 193–198 (1986).
    [CrossRef]
  17. L. N. Thibos, D. J. Walsh, and F. E. Cheney, "Vision beyond the resolution limit: aliasing in the periphery," submitted to Vision Res.
  18. W. Lotmar, "Apparatus for the measurement of retinal visual acuity by moiré fringes," Invest. Ophthalmol. Vis. Sci. 19, 393–400 (1980).
    [PubMed]
  19. Y. Le Grand, "La formation des images retiniennes. Sur un mode de vision eliminant les defauts optiques de l'oeil," presented at the 2e Reunion de l'lnstitut d'Optique, Paris, 1937.
  20. G. Westheimer, "Modulation thresholds for sinusoidal light distributions on the retina," J. Physiol. (London) 152, 67–74 (1960).
  21. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  22. L. N. Thibos, "Calculation of the influence of lateral chromaticaberration on image quality across the visual field," J. Opt. Soc. Am. A 4, 1673–1680 (1987).
    [CrossRef] [PubMed]
  23. L. N. Thibos, A. Bradley, D. Still, and P. Henderson, "Do white-light interferometers bypass the eye's optics? Clinical implications of decentering the optical beam in the pupil," in Digest of the Conference on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1987), pp. 80–82.
  24. F. E. Cheney, "The effect of lateral chromatic aberration on the detection of gratings in peripheral vision," M.S. thesis (Indiana University, Bloomington, Ind., 1987).
  25. A. Hughes, "New perspectives in retinal organisation," Prog. Retinal Res. 4, 243–313 (1985).
    [CrossRef]
  26. The center-to-center spacing of an hexagonal array of density D is given by the formula S2 = 2/(D√3). The MAR of such an array is MAR = 0.5S√3 Combining these formulas leads to the result MAR = 0.93/√D, which is not much different from Eq. (1).
  27. N. Drasdo, "The neural representation of visual space," Nature 266, 54–556 (1977).
    [CrossRef] [PubMed]
  28. E. T. Rolls and A. Cowey, "Topography of the retina and striate cortex and its relationship to visual acuity in rhesus monkeys and squirrel monkeys," Exp. Brain Res. 10, 298–310 (1970),
    [CrossRef] [PubMed]
  29. V. H. Perry, R. Oehler, and A. Cowey, "Retinal ganglion cells that project to the dorsal lateral geniculate nucleus in the macaque monkey," Neuroscience 12, 111–1123 (1984).
    [CrossRef] [PubMed]
  30. S. L. Pdlyak, The Retina (U. Chicago Press, Chicago, 1941).
  31. A. Hughes, "Cat retina and the sampling theorem; the relation of transient and sustained brisk-unit cut-off frequency to alpha-and beta-mode cell density," Exp. Brain Res. 42, 196–202 (1981).
    [CrossRef]
  32. H. Wassle, B. B. Boycott, and R. B. Illing, "Morphology and mosaic of on-and off-beta cells in the cat retina and some functional considerations," Proc. R. Soc. London Ser. B 212, 177–195 (1981).
    [CrossRef]
  33. G. Osterberg, "Topography of the layer of rods and cones in the human retina," Acta Ophthalmol. Suppl. 6, 1–103 (1935).
  34. W. H. Miller and G. P. Bernard, "Averaging over the foveal receptor aperture curtails aliasing," Vision Res. 23, 1365–1369 (1983).
    [CrossRef] [PubMed]
  35. A. W. Snyder and W. H. Miller, "Photoreceptor diameter and spacing for highest resolving power," J. Opt. Soc. Am. 67, 696–697 (1977).
    [CrossRef] [PubMed]
  36. B. G. Cleland, T. H. Harding, and U. Tulunay-Keesey, "Visual resolution and field size: examination of two kinds of cat retinal ganglion cell," Science 205, 1015–1017 (1979).
    [CrossRef] [PubMed]
  37. S. L. Polyak, The Vertebrate Visual System (U. Chicago Press, Chicago, 1957).
  38. F. M. DeMonasterio and P. Gouras, "Functional properties of ganglion cells of the rhesus monkey retina," J. Physiol. (London) 251, 167–195 (1975).
  39. A. M. Derrington and P. Lennie, "Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus in macaque," J. Physiol. (London) 357, 219–240 (1984).
  40. R. W. Rodieck, K. F. Binmoeller, and J. Dineen, "Parasol and midget ganglion cells of the human retina," J. Comp. Neurol. 233, 115–132 (1985).
    [CrossRef] [PubMed]
  41. L. Peichl and H. Wassle, "Size, scatter and coverage of ganglion cell receptive field centres in the cat retina," J. Physiol. (London) 291, 117–141 (1979).
  42. B. B. Boycott and J. E. Dowling, "Organization of the primate retina: light microscopy," Philos. Trans. R. Soc. London Ser. B 255, 109–184 (1969).
    [CrossRef]
  43. H. Kolb, K. A. Lineberg, and S. Fisher, "A Golgi study of ganglion cells in the human retina," Invest. Ophthalmol. Vis. Sci. Suppl. 27, 203 (1986).
  44. W. R. Levick and L. N. Thibos, "Receptive fields of cat ganglion cells: classification and construction," Prog. Retinal Res. 2, 267–319 (1983).
    [CrossRef]
  45. S. Hochstein and R. M. Shapley, "Linear and nonlinear spatial subunits in Y cat retinal ganglion cells," J. Physiol. (London) 262, 265–284 (1976).
  46. S. Hochstein and R. M. Shapley, "Quantitative analysis of retinal ganglion cell classifications," J. Physiol. (London) 262, 237–264 (1976).
  47. L. N. Thibos and W. R. Levick, "Orientation bias of brisk-transient Y-cells of the cat retina for drifting and alternating gratings," Exp. Brain Res. 58, 1–10 (1985).
    [CrossRef] [PubMed]

1987 (1)

1986 (3)

H. Kolb, K. A. Lineberg, and S. Fisher, "A Golgi study of ganglion cells in the human retina," Invest. Ophthalmol. Vis. Sci. Suppl. 27, 203 (1986).

A. W. Snyder, T. R. J. Bossomaier, and A. Hughes, "Optical image quality and the cone mosaic," Science 231, 499–501 (1986).
[CrossRef] [PubMed]

D. R. Williams, "Seeing through the photoreceptor mosaic," Trends Neurosci. 9, 193–198 (1986).
[CrossRef]

1985 (6)

D. R. Williams, "Visibility of interference fringes near the resolution limit," J. Opt. Soc. Am. A 2, 1087–1093 (1985).
[CrossRef] [PubMed]

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

L. N. Thibos and D. J. Walsh, "Detection of high frequency gratings in the periphery," J. Opt. Soc. Am. A 2, P64 (1985).

A. Hughes, "New perspectives in retinal organisation," Prog. Retinal Res. 4, 243–313 (1985).
[CrossRef]

R. W. Rodieck, K. F. Binmoeller, and J. Dineen, "Parasol and midget ganglion cells of the human retina," J. Comp. Neurol. 233, 115–132 (1985).
[CrossRef] [PubMed]

L. N. Thibos and W. R. Levick, "Orientation bias of brisk-transient Y-cells of the cat retina for drifting and alternating gratings," Exp. Brain Res. 58, 1–10 (1985).
[CrossRef] [PubMed]

1984 (2)

V. H. Perry, R. Oehler, and A. Cowey, "Retinal ganglion cells that project to the dorsal lateral geniculate nucleus in the macaque monkey," Neuroscience 12, 111–1123 (1984).
[CrossRef] [PubMed]

A. M. Derrington and P. Lennie, "Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus in macaque," J. Physiol. (London) 357, 219–240 (1984).

1983 (2)

W. R. Levick and L. N. Thibos, "Receptive fields of cat ganglion cells: classification and construction," Prog. Retinal Res. 2, 267–319 (1983).
[CrossRef]

W. H. Miller and G. P. Bernard, "Averaging over the foveal receptor aperture curtails aliasing," Vision Res. 23, 1365–1369 (1983).
[CrossRef] [PubMed]

1982 (1)

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

1981 (1)

H. Wassle, B. B. Boycott, and R. B. Illing, "Morphology and mosaic of on-and off-beta cells in the cat retina and some functional considerations," Proc. R. Soc. London Ser. B 212, 177–195 (1981).
[CrossRef]

1980 (1)

W. Lotmar, "Apparatus for the measurement of retinal visual acuity by moiré fringes," Invest. Ophthalmol. Vis. Sci. 19, 393–400 (1980).
[PubMed]

1979 (3)

V. Virsu and J. Rovamo, "Visual resolution, contrast sensitivity and the cortical magnification factor," Exp. Brain Res. 37, 475–494 (1979).
[CrossRef]

B. G. Cleland, T. H. Harding, and U. Tulunay-Keesey, "Visual resolution and field size: examination of two kinds of cat retinal ganglion cell," Science 205, 1015–1017 (1979).
[CrossRef] [PubMed]

L. Peichl and H. Wassle, "Size, scatter and coverage of ganglion cell receptive field centres in the cat retina," J. Physiol. (London) 291, 117–141 (1979).

1977 (2)

1976 (2)

S. Hochstein and R. M. Shapley, "Linear and nonlinear spatial subunits in Y cat retinal ganglion cells," J. Physiol. (London) 262, 265–284 (1976).

S. Hochstein and R. M. Shapley, "Quantitative analysis of retinal ganglion cell classifications," J. Physiol. (London) 262, 237–264 (1976).

1975 (3)

F. M. DeMonasterio and P. Gouras, "Functional properties of ganglion cells of the rhesus monkey retina," J. Physiol. (London) 251, 167–195 (1975).

M. Millodot, A. L. Johnson, A. Lamont, and H. W. Leibowitz, "Effect of dioptrics on peripheral visual acuity," Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

L. Frisen and A. Glansholm, "Optical and neural resolution in peripheral vision," Invest. Ophthalmol. 14, 528–536 (1975).
[PubMed]

1974 (1)

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

1973 (1)

J. M. Enoch and G. M. Hope, "Interferometric resolution determinations in the fovea and parafovea," Doc. Ophthalmol. 34, 143–156 (1973).
[CrossRef] [PubMed]

1971 (1)

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

1970 (2)

D. G. Green, "Regional variations in the visual acuity for interference fringes on the retina," J. Physiol. (London) 207, 351–356 (1970).

E. T. Rolls and A. Cowey, "Topography of the retina and striate cortex and its relationship to visual acuity in rhesus monkeys and squirrel monkeys," Exp. Brain Res. 10, 298–310 (1970),
[CrossRef] [PubMed]

1969 (1)

B. B. Boycott and J. E. Dowling, "Organization of the primate retina: light microscopy," Philos. Trans. R. Soc. London Ser. B 255, 109–184 (1969).
[CrossRef]

1966 (1)

F. W. Campbell and R. W. Gubish, "Optical quality of the human eye," J. Physiol. (London) 186, 558–578 (1966).

1960 (1)

G. Westheimer, "Modulation thresholds for sinusoidal light distributions on the retina," J. Physiol. (London) 152, 67–74 (1960).

1958 (1)

F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).
[PubMed]

1935 (1)

G. Osterberg, "Topography of the layer of rods and cones in the human retina," Acta Ophthalmol. Suppl. 6, 1–103 (1935).

Bernard, G. P.

W. H. Miller and G. P. Bernard, "Averaging over the foveal receptor aperture curtails aliasing," Vision Res. 23, 1365–1369 (1983).
[CrossRef] [PubMed]

Binmoeller, K. F.

R. W. Rodieck, K. F. Binmoeller, and J. Dineen, "Parasol and midget ganglion cells of the human retina," J. Comp. Neurol. 233, 115–132 (1985).
[CrossRef] [PubMed]

Bossomaier, T. R. J.

A. W. Snyder, T. R. J. Bossomaier, and A. Hughes, "Optical image quality and the cone mosaic," Science 231, 499–501 (1986).
[CrossRef] [PubMed]

Boycott, B. B.

H. Wassle, B. B. Boycott, and R. B. Illing, "Morphology and mosaic of on-and off-beta cells in the cat retina and some functional considerations," Proc. R. Soc. London Ser. B 212, 177–195 (1981).
[CrossRef]

B. B. Boycott and J. E. Dowling, "Organization of the primate retina: light microscopy," Philos. Trans. R. Soc. London Ser. B 255, 109–184 (1969).
[CrossRef]

Bradley, A.

L. N. Thibos, A. Bradley, D. Still, and P. Henderson, "Do white-light interferometers bypass the eye's optics? Clinical implications of decentering the optical beam in the pupil," in Digest of the Conference on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1987), pp. 80–82.

Campbell, F. W.

F. W. Campbell and R. W. Gubish, "Optical quality of the human eye," J. Physiol. (London) 186, 558–578 (1966).

Cavonius, C. R.

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

Cheney, F. E.

L. N. Thibos, D. J. Walsh, and F. E. Cheney, "Vision beyond the resolution limit: aliasing in the periphery," submitted to Vision Res.

F. E. Cheney, "The effect of lateral chromatic aberration on the detection of gratings in peripheral vision," M.S. thesis (Indiana University, Bloomington, Ind., 1987).

Cleland, B. G.

B. G. Cleland, T. H. Harding, and U. Tulunay-Keesey, "Visual resolution and field size: examination of two kinds of cat retinal ganglion cell," Science 205, 1015–1017 (1979).
[CrossRef] [PubMed]

Cowey, A.

V. H. Perry, R. Oehler, and A. Cowey, "Retinal ganglion cells that project to the dorsal lateral geniculate nucleus in the macaque monkey," Neuroscience 12, 111–1123 (1984).
[CrossRef] [PubMed]

E. T. Rolls and A. Cowey, "Topography of the retina and striate cortex and its relationship to visual acuity in rhesus monkeys and squirrel monkeys," Exp. Brain Res. 10, 298–310 (1970),
[CrossRef] [PubMed]

DeMonasterio, F. M.

F. M. DeMonasterio and P. Gouras, "Functional properties of ganglion cells of the rhesus monkey retina," J. Physiol. (London) 251, 167–195 (1975).

Derrington, A. M.

A. M. Derrington and P. Lennie, "Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus in macaque," J. Physiol. (London) 357, 219–240 (1984).

Dineen, J.

R. W. Rodieck, K. F. Binmoeller, and J. Dineen, "Parasol and midget ganglion cells of the human retina," J. Comp. Neurol. 233, 115–132 (1985).
[CrossRef] [PubMed]

Dowling, J. E.

B. B. Boycott and J. E. Dowling, "Organization of the primate retina: light microscopy," Philos. Trans. R. Soc. London Ser. B 255, 109–184 (1969).
[CrossRef]

Drasdo, N.

N. Drasdo, "The neural representation of visual space," Nature 266, 54–556 (1977).
[CrossRef] [PubMed]

Enoch, J. M.

J. M. Enoch and G. M. Hope, "Interferometric resolution determinations in the fovea and parafovea," Doc. Ophthalmol. 34, 143–156 (1973).
[CrossRef] [PubMed]

Fisher, S.

H. Kolb, K. A. Lineberg, and S. Fisher, "A Golgi study of ganglion cells in the human retina," Invest. Ophthalmol. Vis. Sci. Suppl. 27, 203 (1986).

Frisen, L.

L. Frisen and A. Glansholm, "Optical and neural resolution in peripheral vision," Invest. Ophthalmol. 14, 528–536 (1975).
[PubMed]

Glansholm, A.

L. Frisen and A. Glansholm, "Optical and neural resolution in peripheral vision," Invest. Ophthalmol. 14, 528–536 (1975).
[PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gouras, P.

F. M. DeMonasterio and P. Gouras, "Functional properties of ganglion cells of the rhesus monkey retina," J. Physiol. (London) 251, 167–195 (1975).

Grand, Y. Le

Y. Le Grand, "La formation des images retiniennes. Sur un mode de vision eliminant les defauts optiques de l'oeil," presented at the 2e Reunion de l'lnstitut d'Optique, Paris, 1937.

Green, D. G.

D. G. Green, "Regional variations in the visual acuity for interference fringes on the retina," J. Physiol. (London) 207, 351–356 (1970).

Gubish, R. W.

F. W. Campbell and R. W. Gubish, "Optical quality of the human eye," J. Physiol. (London) 186, 558–578 (1966).

Harding, T. H.

B. G. Cleland, T. H. Harding, and U. Tulunay-Keesey, "Visual resolution and field size: examination of two kinds of cat retinal ganglion cell," Science 205, 1015–1017 (1979).
[CrossRef] [PubMed]

Henderson, P.

L. N. Thibos, A. Bradley, D. Still, and P. Henderson, "Do white-light interferometers bypass the eye's optics? Clinical implications of decentering the optical beam in the pupil," in Digest of the Conference on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1987), pp. 80–82.

Hiltz, R.

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

Hochstein, S.

S. Hochstein and R. M. Shapley, "Linear and nonlinear spatial subunits in Y cat retinal ganglion cells," J. Physiol. (London) 262, 265–284 (1976).

S. Hochstein and R. M. Shapley, "Quantitative analysis of retinal ganglion cell classifications," J. Physiol. (London) 262, 237–264 (1976).

Hope, G. M.

J. M. Enoch and G. M. Hope, "Interferometric resolution determinations in the fovea and parafovea," Doc. Ophthalmol. 34, 143–156 (1973).
[CrossRef] [PubMed]

Hughes, A.

A. W. Snyder, T. R. J. Bossomaier, and A. Hughes, "Optical image quality and the cone mosaic," Science 231, 499–501 (1986).
[CrossRef] [PubMed]

A. Hughes, "New perspectives in retinal organisation," Prog. Retinal Res. 4, 243–313 (1985).
[CrossRef]

A. Hughes, "Cat retina and the sampling theorem; the relation of transient and sustained brisk-unit cut-off frequency to alpha-and beta-mode cell density," Exp. Brain Res. 42, 196–202 (1981).
[CrossRef]

Hyvarinen, L.

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

Illing, R. B.

H. Wassle, B. B. Boycott, and R. B. Illing, "Morphology and mosaic of on-and off-beta cells in the cat retina and some functional considerations," Proc. R. Soc. London Ser. B 212, 177–195 (1981).
[CrossRef]

Johnson, A. L.

M. Millodot, A. L. Johnson, A. Lamont, and H. W. Leibowitz, "Effect of dioptrics on peripheral visual acuity," Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Kerr, J. L.

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

Kolb, H.

H. Kolb, K. A. Lineberg, and S. Fisher, "A Golgi study of ganglion cells in the human retina," Invest. Ophthalmol. Vis. Sci. Suppl. 27, 203 (1986).

Lamont, A.

M. Millodot, A. L. Johnson, A. Lamont, and H. W. Leibowitz, "Effect of dioptrics on peripheral visual acuity," Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Laurinen, P.

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

Leibowitz, H. W.

M. Millodot, A. L. Johnson, A. Lamont, and H. W. Leibowitz, "Effect of dioptrics on peripheral visual acuity," Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Lennie, P.

A. M. Derrington and P. Lennie, "Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus in macaque," J. Physiol. (London) 357, 219–240 (1984).

Levick, W. R.

L. N. Thibos and W. R. Levick, "Orientation bias of brisk-transient Y-cells of the cat retina for drifting and alternating gratings," Exp. Brain Res. 58, 1–10 (1985).
[CrossRef] [PubMed]

W. R. Levick and L. N. Thibos, "Receptive fields of cat ganglion cells: classification and construction," Prog. Retinal Res. 2, 267–319 (1983).
[CrossRef]

Lineberg, K. A.

H. Kolb, K. A. Lineberg, and S. Fisher, "A Golgi study of ganglion cells in the human retina," Invest. Ophthalmol. Vis. Sci. Suppl. 27, 203 (1986).

Lotmar, W.

W. Lotmar, "Apparatus for the measurement of retinal visual acuity by moiré fringes," Invest. Ophthalmol. Vis. Sci. 19, 393–400 (1980).
[PubMed]

Miller, W. H.

W. H. Miller and G. P. Bernard, "Averaging over the foveal receptor aperture curtails aliasing," Vision Res. 23, 1365–1369 (1983).
[CrossRef] [PubMed]

A. W. Snyder and W. H. Miller, "Photoreceptor diameter and spacing for highest resolving power," J. Opt. Soc. Am. 67, 696–697 (1977).
[CrossRef] [PubMed]

Millodot, M.

M. Millodot, A. L. Johnson, A. Lamont, and H. W. Leibowitz, "Effect of dioptrics on peripheral visual acuity," Vision Res. 15, 1357–1362 (1975).
[CrossRef] [PubMed]

Oehler, R.

V. H. Perry, R. Oehler, and A. Cowey, "Retinal ganglion cells that project to the dorsal lateral geniculate nucleus in the macaque monkey," Neuroscience 12, 111–1123 (1984).
[CrossRef] [PubMed]

Osterberg, G.

G. Osterberg, "Topography of the layer of rods and cones in the human retina," Acta Ophthalmol. Suppl. 6, 1–103 (1935).

Pdlyak, S. L.

S. L. Pdlyak, The Retina (U. Chicago Press, Chicago, 1941).

Peichl, L.

L. Peichl and H. Wassle, "Size, scatter and coverage of ganglion cell receptive field centres in the cat retina," J. Physiol. (London) 291, 117–141 (1979).

Perry, V. H.

V. H. Perry, R. Oehler, and A. Cowey, "Retinal ganglion cells that project to the dorsal lateral geniculate nucleus in the macaque monkey," Neuroscience 12, 111–1123 (1984).
[CrossRef] [PubMed]

Polyak, S. L.

S. L. Polyak, The Vertebrate Visual System (U. Chicago Press, Chicago, 1957).

Rodieck, R. W.

R. W. Rodieck, K. F. Binmoeller, and J. Dineen, "Parasol and midget ganglion cells of the human retina," J. Comp. Neurol. 233, 115–132 (1985).
[CrossRef] [PubMed]

Rolls, E. T.

E. T. Rolls and A. Cowey, "Topography of the retina and striate cortex and its relationship to visual acuity in rhesus monkeys and squirrel monkeys," Exp. Brain Res. 10, 298–310 (1970),
[CrossRef] [PubMed]

Rovamo, J.

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[CrossRef]

Shapley, R. M.

S. Hochstein and R. M. Shapley, "Quantitative analysis of retinal ganglion cell classifications," J. Physiol. (London) 262, 237–264 (1976).

S. Hochstein and R. M. Shapley, "Linear and nonlinear spatial subunits in Y cat retinal ganglion cells," J. Physiol. (London) 262, 265–284 (1976).

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A. W. Snyder, T. R. J. Bossomaier, and A. Hughes, "Optical image quality and the cone mosaic," Science 231, 499–501 (1986).
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Still, D.

L. N. Thibos, A. Bradley, D. Still, and P. Henderson, "Do white-light interferometers bypass the eye's optics? Clinical implications of decentering the optical beam in the pupil," in Digest of the Conference on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1987), pp. 80–82.

Thibos, L. N.

L. N. Thibos, "Calculation of the influence of lateral chromaticaberration on image quality across the visual field," J. Opt. Soc. Am. A 4, 1673–1680 (1987).
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L. N. Thibos and W. R. Levick, "Orientation bias of brisk-transient Y-cells of the cat retina for drifting and alternating gratings," Exp. Brain Res. 58, 1–10 (1985).
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L. N. Thibos and D. J. Walsh, "Detection of high frequency gratings in the periphery," J. Opt. Soc. Am. A 2, P64 (1985).

W. R. Levick and L. N. Thibos, "Receptive fields of cat ganglion cells: classification and construction," Prog. Retinal Res. 2, 267–319 (1983).
[CrossRef]

L. N. Thibos, D. J. Walsh, and F. E. Cheney, "Vision beyond the resolution limit: aliasing in the periphery," submitted to Vision Res.

L. N. Thibos, A. Bradley, D. Still, and P. Henderson, "Do white-light interferometers bypass the eye's optics? Clinical implications of decentering the optical beam in the pupil," in Digest of the Conference on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1987), pp. 80–82.

Tulunay-Keesey, U.

B. G. Cleland, T. H. Harding, and U. Tulunay-Keesey, "Visual resolution and field size: examination of two kinds of cat retinal ganglion cell," Science 205, 1015–1017 (1979).
[CrossRef] [PubMed]

Virsu, V.

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

V. Virsu and J. Rovamo, "Visual resolution, contrast sensitivity and the cortical magnification factor," Exp. Brain Res. 37, 475–494 (1979).
[CrossRef]

Walsh, D. J.

L. N. Thibos and D. J. Walsh, "Detection of high frequency gratings in the periphery," J. Opt. Soc. Am. A 2, P64 (1985).

L. N. Thibos, D. J. Walsh, and F. E. Cheney, "Vision beyond the resolution limit: aliasing in the periphery," submitted to Vision Res.

Wassle, H.

H. Wassle, B. B. Boycott, and R. B. Illing, "Morphology and mosaic of on-and off-beta cells in the cat retina and some functional considerations," Proc. R. Soc. London Ser. B 212, 177–195 (1981).
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L. Peichl and H. Wassle, "Size, scatter and coverage of ganglion cell receptive field centres in the cat retina," J. Physiol. (London) 291, 117–141 (1979).

Wertheim, Th.

Th. Wertheim, "Peripheral visual acuity" (1894) [translated by I. L. Dunsky, Am. J. Optom. Physiol. Opt. 57, 919–924 (1980)]. Wertheim's normalized eccentricity curves (Table 2) were put on an absolute scale by using the data from a second experiment (Table 1).

Westheimer, G.

G. Westheimer, "Modulation thresholds for sinusoidal light distributions on the retina," J. Physiol. (London) 152, 67–74 (1960).

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F. W. Weymouth, "Visual sensory units and the minimal angle of resolution," Am. J. Ophthalmol. 46, 102–113 (1958).
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V. Virsu and J. Rovamo, "Visual resolution, contrast sensitivity and the cortical magnification factor," Exp. Brain Res. 37, 475–494 (1979).
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L. N. Thibos and W. R. Levick, "Orientation bias of brisk-transient Y-cells of the cat retina for drifting and alternating gratings," Exp. Brain Res. 58, 1–10 (1985).
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H. Kolb, K. A. Lineberg, and S. Fisher, "A Golgi study of ganglion cells in the human retina," Invest. Ophthalmol. Vis. Sci. Suppl. 27, 203 (1986).

Invest. Opthalmol. Vis. Sci. (1)

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

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R. W. Rodieck, K. F. Binmoeller, and J. Dineen, "Parasol and midget ganglion cells of the human retina," J. Comp. Neurol. 233, 115–132 (1985).
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G. Westheimer, "Modulation thresholds for sinusoidal light distributions on the retina," J. Physiol. (London) 152, 67–74 (1960).

D. G. Green, "Regional variations in the visual acuity for interference fringes on the retina," J. Physiol. (London) 207, 351–356 (1970).

F. M. DeMonasterio and P. Gouras, "Functional properties of ganglion cells of the rhesus monkey retina," J. Physiol. (London) 251, 167–195 (1975).

A. M. Derrington and P. Lennie, "Spatial and temporal contrast sensitivities of neurones in lateral geniculate nucleus in macaque," J. Physiol. (London) 357, 219–240 (1984).

L. Peichl and H. Wassle, "Size, scatter and coverage of ganglion cell receptive field centres in the cat retina," J. Physiol. (London) 291, 117–141 (1979).

S. Hochstein and R. M. Shapley, "Linear and nonlinear spatial subunits in Y cat retinal ganglion cells," J. Physiol. (London) 262, 265–284 (1976).

S. Hochstein and R. M. Shapley, "Quantitative analysis of retinal ganglion cell classifications," J. Physiol. (London) 262, 237–264 (1976).

Nature (1)

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Percept. Psychophys. (1)

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

Philos. Trans. R. Soc. London Ser. B (1)

B. B. Boycott and J. E. Dowling, "Organization of the primate retina: light microscopy," Philos. Trans. R. Soc. London Ser. B 255, 109–184 (1969).
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Proc. R. Soc. London Ser. B (1)

H. Wassle, B. B. Boycott, and R. B. Illing, "Morphology and mosaic of on-and off-beta cells in the cat retina and some functional considerations," Proc. R. Soc. London Ser. B 212, 177–195 (1981).
[CrossRef]

Prog. Retinal Res. (2)

W. R. Levick and L. N. Thibos, "Receptive fields of cat ganglion cells: classification and construction," Prog. Retinal Res. 2, 267–319 (1983).
[CrossRef]

A. Hughes, "New perspectives in retinal organisation," Prog. Retinal Res. 4, 243–313 (1985).
[CrossRef]

Science (2)

B. G. Cleland, T. H. Harding, and U. Tulunay-Keesey, "Visual resolution and field size: examination of two kinds of cat retinal ganglion cell," Science 205, 1015–1017 (1979).
[CrossRef] [PubMed]

A. W. Snyder, T. R. J. Bossomaier, and A. Hughes, "Optical image quality and the cone mosaic," Science 231, 499–501 (1986).
[CrossRef] [PubMed]

Trends Neurosci. (1)

D. R. Williams, "Seeing through the photoreceptor mosaic," Trends Neurosci. 9, 193–198 (1986).
[CrossRef]

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M. Millodot, A. L. Johnson, A. Lamont, and H. W. Leibowitz, "Effect of dioptrics on peripheral visual acuity," Vision Res. 15, 1357–1362 (1975).
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R. Hiltz and C. R. Cavonius, "Functional organization of the peripheral retina: sensitivity to periodic stimuli," Vision Res. 14, 1333–1338 (1974).
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W. H. Miller and G. P. Bernard, "Averaging over the foveal receptor aperture curtails aliasing," Vision Res. 23, 1365–1369 (1983).
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Other (10)

S. L. Polyak, The Vertebrate Visual System (U. Chicago Press, Chicago, 1957).

The center-to-center spacing of an hexagonal array of density D is given by the formula S2 = 2/(D√3). The MAR of such an array is MAR = 0.5S√3 Combining these formulas leads to the result MAR = 0.93/√D, which is not much different from Eq. (1).

L. N. Thibos, A. Bradley, D. Still, and P. Henderson, "Do white-light interferometers bypass the eye's optics? Clinical implications of decentering the optical beam in the pupil," in Digest of the Conference on Noninvasive Assessment of the Visual System (Optical Society of America, Washington, D.C., 1987), pp. 80–82.

F. E. Cheney, "The effect of lateral chromatic aberration on the detection of gratings in peripheral vision," M.S. thesis (Indiana University, Bloomington, Ind., 1987).

S. L. Pdlyak, The Retina (U. Chicago Press, Chicago, 1941).

A. Hughes, "Cat retina and the sampling theorem; the relation of transient and sustained brisk-unit cut-off frequency to alpha-and beta-mode cell density," Exp. Brain Res. 42, 196–202 (1981).
[CrossRef]

Th. Wertheim, "Peripheral visual acuity" (1894) [translated by I. L. Dunsky, Am. J. Optom. Physiol. Opt. 57, 919–924 (1980)]. Wertheim's normalized eccentricity curves (Table 2) were put on an absolute scale by using the data from a second experiment (Table 1).

L. N. Thibos, D. J. Walsh, and F. E. Cheney, "Vision beyond the resolution limit: aliasing in the periphery," submitted to Vision Res.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Y. Le Grand, "La formation des images retiniennes. Sur un mode de vision eliminant les defauts optiques de l'oeil," presented at the 2e Reunion de l'lnstitut d'Optique, Paris, 1937.

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Figures (3)

Fig. 1
Fig. 1

Variation of maximum-resolvable (open symbols) and maximum-detectable (filled symbols) spatial frequency across the visual field. Each symbol represents the mean of five determinations for horizontal gratings located on the horizontal meridian. Subject LT was tested with white gratings located in either the nasal (squares) or temporal (inverted triangles) visual fields, while subjects FC (circles) and AB (triangles) were tested only in the nasal visual field. As a control against the possible effects of chromatic aberration, subjects LT (diamonds) and AB (asterisk) were also tested using monochromatic (550-nm) gratings. Smooth curves were drawn by eye through the means of the results for the three subjects viewing white-light gratings. Published data of Kerr6 (K) and of Wertheim3 (W) obtained with conventional visual stimuli are also shown.

Fig. 2
Fig. 2

Comparison of the MAR with spacing of retinal cells. Psychophysical data (filled squares; left ordinate) represent the mean results from Fig. 1 for three subjects viewing white gratings. Spacing of beta ganglion cells in monkey retina measured by Perry et al.29 (circles; right ordinate) and cone spacing measured by Osterberg33 (inverted triangles; right ordinate) were calculated from published data by assuming that spacing = 1 / density.

Fig. 3
Fig. 3

Comparison of the MAD with the radius of retinal fields. Psychophysical data (filled squares; left ordinate) represent the mean results from Fig. 1 for three subjects viewing white gratings. Anatomical measurements of dendritic fields40 (diamonds; right ordinate) and cones37 (inverted triangles; right ordinate) are for human. Physiological measurements of the size of the center component of receptive fields of the smallest retinal ganglion cells38 (circles; right ordinate) and LGN neurons39 (triangles; right ordinate) are for rhesus monkey. Dashed curve is the predicted limit to detection if cone size is the limiting factor.

Equations (2)

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MAR = S = 1 / D .
MAD = R .

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