Abstract

We have developed a high-resolution imaging technique, based on speckle interferometry, for the objective determination of the cone spacing in the living human fovea. The spatial resolution attained with this technique is theoretically diffraction limited by the pupil size. However, the highest frequency that we measure varies greatly among subjects, especially for fully dilated pupils. We have conducted several experiments (determination of the cutoff frequency of ocular speckle interferometry, the double-pass modulation transfer function, and the Stiles–Crawford effect) that indicate that, as expected, the resolution is not limited by the incoherent modulation transfer function. We found, though, a high correlation between the cutoff frequency and the width of the eye’s Stiles–Crawford function. This implies that the resolution depends on the structural properties of the cone mosaic itself. In addition, we have compared the Nyquist frequency of the cone mosaic, determined objectively by our technique, with the grating visual acuity measured in the same eyes at the same foveal eccentricities. For our subjects, visual resolution nearly matches the Nyquist frequency within the fovea, except at the foveal center, where the optical transfer function of the eye attenuates the contrast of frequencies close to the Nyquist limit to a value below threshold.

© 1997 Optical Society of America

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  1. G. Oersterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. (Suppl.) 6, 11–97 (1935).
  2. C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial asymmetry,” Science 236, 579–582 (1987).
    [Crossref] [PubMed]
  3. C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
    [Crossref]
  4. D. R. Williams, “Topography of the foveal cone mosaic,” Vision Res. 28, 433–454 (1987).
    [Crossref]
  5. P. Artal, R. Navarro, “High-resolution imaging of the living human fovea: measurement of the intercenter cone distance by speckle interferometry,” Opt. Lett. 14, 1098–1100 (1989).
    [Crossref] [PubMed]
  6. J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 253–315.
  7. D. T. Miller, D. R. Williams, G. M. Morris, J. L. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
    [Crossref] [PubMed]
  8. S. Marcos, R. Navarro, P. Artal, “Coherent imaging of the cone mosaic in the living human eye,” J. Opt. Soc. Am. A 13, 897–905 (1996).
    [Crossref]
  9. J. Santamarı́a, P. Artal, J. Bescós, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987).
    [Crossref]
  10. R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
    [Crossref] [PubMed]
  11. T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence: plane-wave illumination,” J. Opt. Soc. Am. A 7, 348–355 (1990).
    [Crossref]
  12. P. Artal, S. Marcos, R. Navarro, D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
    [Crossref]
  13. S. Marcos, R. Navarro, “Imaging the foveal cones in vivo through ocular speckle interferometry: theory and numerical simulations,” J. Opt. Soc. Am. A 13, 2329–2340 (1996).
    [Crossref]
  14. H. Metcalf, “Stiles–Crawford apodization,” J. Opt. Soc. Am. 55, 72–74 (1965).
    [Crossref]
  15. F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
    [Crossref]
  16. G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 4, 851–863 (1987).
    [Crossref] [PubMed]
  17. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  18. W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
    [PubMed]
  19. M. Ye, A. Bradley, L. N. Thibos, X. X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2118 (1992).
    [Crossref] [PubMed]
  20. M. C. Rynders, B. Lidkea, W. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle ψ in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
    [Crossref]
  21. W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new color effect,” Proc. R. Soc. London Ser. B 123, 90–118 (1937).
    [Crossref]
  22. R. A. Applegate, V. Lakshminarayanan, “Parametric representation of Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993).
    [Crossref] [PubMed]
  23. J. M. Gorrand, “Directional effects of the retina appearing in the aerial image,” J. Opt. (Paris) 16, 279–287 (1985).
    [Crossref]
  24. G. J. Van Blockland, “Directionality and alignment of the foveal photoreceptors assessed with light scattered at small angles from the human fovea,” Vision Res. 26, 495–500 (1986).
    [Crossref]
  25. J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
    [Crossref] [PubMed]
  26. S. A. Burns, S. Wu, F. Delori, A. E. Elsner, “Direct measurement of the human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
    [Crossref]
  27. S. A. Burns, S. Wu, A. E. Elsner, “Variations in photoreceptor alignment across the fovea,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 448 (1996).
  28. S. Marcos, R.-P. Tornow, A. E. Elsner, R. Navarro, “Foveal cone spacing and cone photopigment density difference: objective measurements in the same subjects,” Vision Res. (to be published).
  29. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  30. D. R. Williams, “Aliasing in human foveal vision,” Vision Res. 25, 195–206 (1985).
    [Crossref] [PubMed]
  31. D. R. Williams, “Visibility of interference fringes near the resolution limit,” J. Opt. Soc. Am. A 2, 1087–1093 (1985).
    [Crossref] [PubMed]
  32. L. N. Thibos, F. E. Cheney, D. J. Walsh, “Retinal limits and the detection and resolution of gratings,” J. Opt. Soc. Am. A 4, 1524–1529 (1987).
    [Crossref] [PubMed]
  33. M. S. Banks, W. S. Geisler, P. J. Bennet, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
    [Crossref] [PubMed]
  34. D. G. Green, “Regional variations in the visual acuity for interference fringes on the retina,” J. Physiol. (London) 207, 351–356 (1970).
  35. J. Hirsch, C. A. Curcio, “The spatial resolution capacity of human foveal retina,” Vision Res. 29, 1095–1101 (1989).
    [Crossref] [PubMed]
  36. 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).
  37. S. J. Galvin, D. R. Williams, “No aliasing at edges in normal viewing,” Vision Res. 32, 2251–2259 (1992).
    [Crossref] [PubMed]
  38. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1965).
  39. J. Y. Yellot, “Spectral analysis of spatial sampling by photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
    [Crossref]
  40. D. R. Williams, R. Collier, “Consequences of spatial sampling by a human photoreceptor mosaic,” Science 222, 385–387 (1983).
    [Crossref]
  41. E. Ludvigh, “Extrafoveal visual acuity as measured by Snellen test letters,” Am. J. Ophthalmol. 24, 303–310 (1941).
  42. L. Sloan, “The photopic acuity-luminance function with spatial reference to parafoveal vision,” Vision Res. 8, 901–911 (1968).
    [Crossref] [PubMed]
  43. F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).
  44. G. Westheimer, “The spatial grain of the perifoveal visual field,” Vision Res. 12, 157–162 (1972).
  45. J. A. M. Jennings, W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445–455 (1981).
    [Crossref] [PubMed]
  46. C. A. Curcio, K. A. Allen, “Topography of ganglion cells on human retina,” J. Comp. Neurol. 300, 5–25 (1990).
    [Crossref] [PubMed]
  47. L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
    [Crossref] [PubMed]
  48. M. A. Losada, R. Navarro, J. Santamarı́a, “Relative contributions of optical and neural limitations to human contrast sensitivities at different luminance levels,” Vision Res. 33, 2321–2336 (1993).
    [Crossref] [PubMed]
  49. W. Weibull, “A statistical distribution function of wide applicability,” J. Appl. Mech. 18, 292–297 (1974).
  50. 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]
  51. A. W. Snyder, W. H. Miller, “Photoreceptor diameter and spacing for highest resolving power,” J. Opt. Soc. Am. 67, 696–698 (1977).
    [Crossref] [PubMed]

1996 (5)

D. T. Miller, D. R. Williams, G. M. Morris, J. L. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (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]

S. A. Burns, S. Wu, A. E. Elsner, “Variations in photoreceptor alignment across the fovea,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 448 (1996).

S. Marcos, R. Navarro, P. Artal, “Coherent imaging of the cone mosaic in the living human eye,” J. Opt. Soc. Am. A 13, 897–905 (1996).
[Crossref]

S. Marcos, R. Navarro, “Imaging the foveal cones in vivo through ocular speckle interferometry: theory and numerical simulations,” J. Opt. Soc. Am. A 13, 2329–2340 (1996).
[Crossref]

1995 (4)

1993 (3)

1992 (3)

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[Crossref]

M. Ye, A. Bradley, L. N. Thibos, X. X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2118 (1992).
[Crossref] [PubMed]

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

1991 (1)

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 (3)

C. A. Curcio, K. A. Allen, “Topography of ganglion cells on human retina,” J. Comp. Neurol. 300, 5–25 (1990).
[Crossref] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[Crossref] [PubMed]

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence: plane-wave illumination,” J. Opt. Soc. Am. A 7, 348–355 (1990).
[Crossref]

1989 (2)

1987 (6)

M. S. Banks, W. S. Geisler, P. J. Bennet, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

D. R. Williams, “Topography of the foveal cone mosaic,” Vision Res. 28, 433–454 (1987).
[Crossref]

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial asymmetry,” Science 236, 579–582 (1987).
[Crossref] [PubMed]

J. Santamarı́a, P. Artal, J. Bescós, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987).
[Crossref]

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 4, 851–863 (1987).
[Crossref] [PubMed]

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

1986 (1)

G. J. Van Blockland, “Directionality and alignment of the foveal photoreceptors assessed with light scattered at small angles from the human fovea,” Vision Res. 26, 495–500 (1986).
[Crossref]

1985 (3)

J. M. Gorrand, “Directional effects of the retina appearing in the aerial image,” J. Opt. (Paris) 16, 279–287 (1985).
[Crossref]

D. R. Williams, “Aliasing in human foveal vision,” Vision Res. 25, 195–206 (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]

1983 (1)

D. R. Williams, R. Collier, “Consequences of spatial sampling by a human photoreceptor mosaic,” Science 222, 385–387 (1983).
[Crossref]

1982 (1)

J. Y. Yellot, “Spectral analysis of spatial sampling by photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
[Crossref]

1981 (1)

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445–455 (1981).
[Crossref] [PubMed]

1979 (1)

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

1977 (1)

1974 (1)

W. Weibull, “A statistical distribution function of wide applicability,” J. Appl. Mech. 18, 292–297 (1974).

1972 (1)

G. Westheimer, “The spatial grain of the perifoveal visual field,” Vision Res. 12, 157–162 (1972).

1970 (1)

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

1968 (1)

L. Sloan, “The photopic acuity-luminance function with spatial reference to parafoveal vision,” Vision Res. 8, 901–911 (1968).
[Crossref] [PubMed]

1965 (3)

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

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

H. Metcalf, “Stiles–Crawford apodization,” J. Opt. Soc. Am. 55, 72–74 (1965).
[Crossref]

1957 (1)

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
[Crossref]

1941 (1)

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

1937 (1)

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new color effect,” Proc. R. Soc. London Ser. B 123, 90–118 (1937).
[Crossref]

1935 (1)

G. Oersterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. (Suppl.) 6, 11–97 (1935).

1928 (1)

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Acres, L. H.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Allen, K. A.

C. A. Curcio, K. A. Allen, “Topography of ganglion cells on human retina,” J. Comp. Neurol. 300, 5–25 (1990).
[Crossref] [PubMed]

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).

Applegate, R. A.

Artal, P.

Banks, M. S.

M. S. Banks, W. S. Geisler, P. J. Bennet, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

Bennet, P. J.

M. S. Banks, W. S. Geisler, P. J. Bennet, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

Bescós, J.

Bradley, A.

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]

M. Ye, A. Bradley, L. N. Thibos, X. X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2118 (1992).
[Crossref] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[Crossref] [PubMed]

Burns, S. A.

S. A. Burns, S. Wu, A. E. Elsner, “Variations in photoreceptor alignment across the fovea,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 448 (1996).

S. A. Burns, S. Wu, F. Delori, A. E. Elsner, “Direct measurement of the human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
[Crossref]

Campbell, F. W.

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 4, 851–863 (1987).
[Crossref] [PubMed]

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

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

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
[Crossref]

Charman, W. N.

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445–455 (1981).
[Crossref] [PubMed]

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

Cheney, F. E.

Chisholm, W.

Collier, R.

D. R. Williams, R. Collier, “Consequences of spatial sampling by a human photoreceptor mosaic,” Science 222, 385–387 (1983).
[Crossref]

Curcio, C. A.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[Crossref]

C. A. Curcio, K. A. Allen, “Topography of ganglion cells on human retina,” J. Comp. Neurol. 300, 5–25 (1990).
[Crossref] [PubMed]

J. Hirsch, C. A. Curcio, “The spatial resolution capacity of human foveal retina,” Vision Res. 29, 1095–1101 (1989).
[Crossref] [PubMed]

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial asymmetry,” Science 236, 579–582 (1987).
[Crossref] [PubMed]

Dainty, J. C.

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence: plane-wave illumination,” J. Opt. Soc. Am. A 7, 348–355 (1990).
[Crossref]

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 253–315.

Delori, F.

Delori, F. C.

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[Crossref] [PubMed]

Elsner, A. E.

S. A. Burns, S. Wu, A. E. Elsner, “Variations in photoreceptor alignment across the fovea,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 448 (1996).

S. A. Burns, S. Wu, F. Delori, A. E. Elsner, “Direct measurement of the human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
[Crossref]

S. Marcos, R.-P. Tornow, A. E. Elsner, R. Navarro, “Foveal cone spacing and cone photopigment density difference: objective measurements in the same subjects,” Vision Res. (to be published).

Galvin, S. J.

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

Geisler, W. S.

M. S. Banks, W. S. Geisler, P. J. Bennet, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1965).

Gorrand, J. M.

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[Crossref] [PubMed]

J. M. Gorrand, “Directional effects of the retina appearing in the aerial image,” J. Opt. (Paris) 16, 279–287 (1985).
[Crossref]

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).

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

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

Hendrickson, A. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[Crossref]

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial asymmetry,” Science 236, 579–582 (1987).
[Crossref] [PubMed]

Hess, R. F.

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).

Hines, D. C.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Hirsch, J.

J. Hirsch, C. A. Curcio, “The spatial resolution capacity of human foveal retina,” Vision Res. 29, 1095–1101 (1989).
[Crossref] [PubMed]

Howarth, P. A.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[Crossref] [PubMed]

Jennings, J. A. M.

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445–455 (1981).
[Crossref] [PubMed]

Kalina, R. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[Crossref]

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial asymmetry,” Science 236, 579–582 (1987).
[Crossref] [PubMed]

Lakshminarayanan, V.

Legge, G. E.

Liang, J. L.

D. T. Miller, D. R. Williams, G. M. Morris, J. L. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[Crossref] [PubMed]

Lidkea, B.

Losada, M. A.

M. A. Losada, R. Navarro, J. Santamarı́a, “Relative contributions of optical and neural limitations to human contrast sensitivities at different luminance levels,” Vision Res. 33, 2321–2336 (1993).
[Crossref] [PubMed]

Ludvigh, E.

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

Marcos, S.

Mavroidis, T.

Metcalf, H.

Miller, D. T.

D. T. Miller, D. R. Williams, G. M. Morris, J. L. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[Crossref] [PubMed]

Miller, W. H.

Morris, G. M.

D. T. Miller, D. R. Williams, G. M. Morris, J. L. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[Crossref] [PubMed]

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).

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 4, 851–863 (1987).
[Crossref] [PubMed]

Navarro, R.

Northcott, M. J.

Oersterberg, G.

G. Oersterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. (Suppl.) 6, 11–97 (1935).

Packer, O.

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial asymmetry,” Science 236, 579–582 (1987).
[Crossref] [PubMed]

Raaf, J. E.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Rynders, M. C.

Santamari´a, J.

M. A. Losada, R. Navarro, J. Santamarı́a, “Relative contributions of optical and neural limitations to human contrast sensitivities at different luminance levels,” Vision Res. 33, 2321–2336 (1993).
[Crossref] [PubMed]

J. Santamarı́a, P. Artal, J. Bescós, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987).
[Crossref]

Sloan, K. R.

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[Crossref]

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial asymmetry,” Science 236, 579–582 (1987).
[Crossref] [PubMed]

Sloan, L.

L. Sloan, “The photopic acuity-luminance function with spatial reference to parafoveal vision,” Vision Res. 8, 901–911 (1968).
[Crossref] [PubMed]

Snyder, A. W.

Stiles, W. S.

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new color effect,” Proc. R. Soc. London Ser. B 123, 90–118 (1937).
[Crossref]

Still, D. L.

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

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[Crossref] [PubMed]

Thibos, L. N.

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]

M. C. Rynders, B. Lidkea, W. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle ψ in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
[Crossref]

M. Ye, A. Bradley, L. N. Thibos, X. X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2118 (1992).
[Crossref] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[Crossref] [PubMed]

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

Tornow, R.-P.

S. Marcos, R.-P. Tornow, A. E. Elsner, R. Navarro, “Foveal cone spacing and cone photopigment density difference: objective measurements in the same subjects,” Vision Res. (to be published).

Van Blockland, G. J.

G. J. Van Blockland, “Directionality and alignment of the foveal photoreceptors assessed with light scattered at small angles from the human fovea,” Vision Res. 26, 495–500 (1986).
[Crossref]

Walsh, D. J.

Weibull, W.

W. Weibull, “A statistical distribution function of wide applicability,” J. Appl. Mech. 18, 292–297 (1974).

Westheimer, G.

G. Westheimer, “The spatial grain of the perifoveal visual field,” Vision Res. 12, 157–162 (1972).

Weymouth, F. W.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Wheeler, C.

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Williams, D. R.

D. T. Miller, D. R. Williams, G. M. Morris, J. L. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[Crossref] [PubMed]

P. Artal, S. Marcos, R. Navarro, D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
[Crossref]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[Crossref] [PubMed]

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

D. R. Williams, “Topography of the foveal cone mosaic,” Vision Res. 28, 433–454 (1987).
[Crossref]

D. R. Williams, “Aliasing in human foveal vision,” Vision Res. 25, 195–206 (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]

D. R. Williams, R. Collier, “Consequences of spatial sampling by a human photoreceptor mosaic,” Science 222, 385–387 (1983).
[Crossref]

Woo, G. C.

Wu, S.

S. A. Burns, S. Wu, A. E. Elsner, “Variations in photoreceptor alignment across the fovea,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 448 (1996).

S. A. Burns, S. Wu, F. Delori, A. E. Elsner, “Direct measurement of the human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
[Crossref]

Ye, M.

M. Ye, A. Bradley, L. N. Thibos, X. X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2118 (1992).
[Crossref] [PubMed]

Yellot, J. Y.

J. Y. Yellot, “Spectral analysis of spatial sampling by photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
[Crossref]

Zhang, X.

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[Crossref] [PubMed]

Zhang, X. X.

M. Ye, A. Bradley, L. N. Thibos, X. X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2118 (1992).
[Crossref] [PubMed]

Acta Ophthalmol. (Suppl.) (1)

G. Oersterberg, “Topography of the layer of rods and cones in the human retina,” Acta Ophthalmol. (Suppl.) 6, 11–97 (1935).

Am. J. Ophthalmol. (2)

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

F. W. Weymouth, D. C. Hines, L. H. Acres, J. E. Raaf, C. Wheeler, “Visual acuity within the area centralis and its relation to eye movements and fixation,” Am. J. Ophthalmol. 11, 947–960 (1928).

Br. J. Physiol. Opt. (1)

W. N. Charman, “Effect of refractive error in visual tests with sinusoidal gratings,” Br. J. Physiol. Opt. 33, 10–20 (1979).
[PubMed]

Invest. Ophthalmol. Visual Sci. Suppl. (1)

S. A. Burns, S. Wu, A. E. Elsner, “Variations in photoreceptor alignment across the fovea,” Invest. Ophthalmol. Visual Sci. Suppl. 37, 448 (1996).

J. Appl. Mech. (1)

W. Weibull, “A statistical distribution function of wide applicability,” J. Appl. Mech. 18, 292–297 (1974).

J. Comp. Neurol. (2)

C. A. Curcio, K. A. Allen, “Topography of ganglion cells on human retina,” J. Comp. Neurol. 300, 5–25 (1990).
[Crossref] [PubMed]

C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
[Crossref]

J. Opt. (Paris) (1)

J. M. Gorrand, “Directional effects of the retina appearing in the aerial image,” J. Opt. (Paris) 16, 279–287 (1985).
[Crossref]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (12)

S. A. Burns, S. Wu, F. Delori, A. E. Elsner, “Direct measurement of the human-cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1995).
[Crossref]

G. E. Legge, K. T. Mullen, G. C. Woo, F. W. Campbell, “Tolerance to visual defocus,” J. Opt. Soc. Am. A 4, 851–863 (1987).
[Crossref] [PubMed]

S. Marcos, R. Navarro, P. Artal, “Coherent imaging of the cone mosaic in the living human eye,” J. Opt. Soc. Am. A 13, 897–905 (1996).
[Crossref]

J. Santamarı́a, P. Artal, J. Bescós, “Determination of the point-spread function of human eyes using a hybrid optical–digital method,” J. Opt. Soc. Am. A 4, 1109–1114 (1987).
[Crossref]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[Crossref] [PubMed]

T. Mavroidis, J. C. Dainty, M. J. Northcott, “Imaging of coherently illuminated objects through turbulence: plane-wave illumination,” J. Opt. Soc. Am. A 7, 348–355 (1990).
[Crossref]

P. Artal, S. Marcos, R. Navarro, D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
[Crossref]

S. Marcos, R. Navarro, “Imaging the foveal cones in vivo through ocular speckle interferometry: theory and numerical simulations,” J. Opt. Soc. Am. A 13, 2329–2340 (1996).
[Crossref]

M. C. Rynders, B. Lidkea, W. Chisholm, L. N. Thibos, “Statistical distribution of foveal transverse chromatic aberration, pupil centration, and angle ψ in a population of young adult eyes,” J. Opt. Soc. Am. A 12, 2348–2357 (1995).
[Crossref]

R. A. Applegate, V. Lakshminarayanan, “Parametric representation of Stiles–Crawford functions: normal variation of peak location and directionality,” J. Opt. Soc. Am. A 10, 1611–1623 (1993).
[Crossref] [PubMed]

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

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

J. Physiol. (London) (4)

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

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

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

Opt. Acta (1)

F. W. Campbell, “The depth of field of the human eye,” Opt. Acta 4, 157–164 (1957).
[Crossref]

Opt. Lett. (1)

Proc. R. Soc. London Ser. B (1)

W. S. Stiles, “The luminous efficiency of monochromatic rays entering the eye pupil at different points and a new color effect,” Proc. R. Soc. London Ser. B 123, 90–118 (1937).
[Crossref]

Science (2)

C. A. Curcio, K. R. Sloan, O. Packer, A. E. Hendrickson, R. E. Kalina, “Distribution of cones in human and monkey retina: individual variability and radial asymmetry,” Science 236, 579–582 (1987).
[Crossref] [PubMed]

D. R. Williams, R. Collier, “Consequences of spatial sampling by a human photoreceptor mosaic,” Science 222, 385–387 (1983).
[Crossref]

Vision Res. (16)

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]

J. Y. Yellot, “Spectral analysis of spatial sampling by photoreceptors: topological disorder prevents aliasing,” Vision Res. 22, 1205–1210 (1982).
[Crossref]

L. Sloan, “The photopic acuity-luminance function with spatial reference to parafoveal vision,” Vision Res. 8, 901–911 (1968).
[Crossref] [PubMed]

L. N. Thibos, A. Bradley, D. L. Still, X. Zhang, P. A. Howarth, “Theory and measurement of ocular chromatic aberration,” Vision Res. 30, 33–49 (1990).
[Crossref] [PubMed]

M. A. Losada, R. Navarro, J. Santamarı́a, “Relative contributions of optical and neural limitations to human contrast sensitivities at different luminance levels,” Vision Res. 33, 2321–2336 (1993).
[Crossref] [PubMed]

G. Westheimer, “The spatial grain of the perifoveal visual field,” Vision Res. 12, 157–162 (1972).

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in the human eye,” Vision Res. 21, 445–455 (1981).
[Crossref] [PubMed]

D. R. Williams, “Topography of the foveal cone mosaic,” Vision Res. 28, 433–454 (1987).
[Crossref]

M. Ye, A. Bradley, L. N. Thibos, X. X. Zhang, “The effect of pupil size on chromostereopsis and chromatic diplopia: interaction between the Stiles–Crawford effect and chromatic aberrations,” Vision Res. 32, 2121–2118 (1992).
[Crossref] [PubMed]

D. T. Miller, D. R. Williams, G. M. Morris, J. L. Liang, “Images of cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[Crossref] [PubMed]

G. J. Van Blockland, “Directionality and alignment of the foveal photoreceptors assessed with light scattered at small angles from the human fovea,” Vision Res. 26, 495–500 (1986).
[Crossref]

J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
[Crossref] [PubMed]

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

J. Hirsch, C. A. Curcio, “The spatial resolution capacity of human foveal retina,” Vision Res. 29, 1095–1101 (1989).
[Crossref] [PubMed]

D. R. Williams, “Aliasing in human foveal vision,” Vision Res. 25, 195–206 (1985).
[Crossref] [PubMed]

M. S. Banks, W. S. Geisler, P. J. Bennet, “The physical limits of grating visibility,” Vision Res. 27, 1915–1924 (1987).
[Crossref] [PubMed]

Other (3)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1965).

S. Marcos, R.-P. Tornow, A. E. Elsner, R. Navarro, “Foveal cone spacing and cone photopigment density difference: objective measurements in the same subjects,” Vision Res. (to be published).

J. C. Dainty, “Stellar speckle interferometry,” in Laser Speckle and Related Phenomena, 2nd ed., J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984), pp. 253–315.

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Figures (8)

Fig. 1
Fig. 1

One-dimensional (radial profiles) double-pass MTF’s for 5-mm and 8-mm pupils, for subjects (a) MA and (b) RN.

Fig. 2
Fig. 2

Diagram of the two-channel Maxwellian-view system used to measure the SCE. BS, beam-splitter; P1 and P1, 1.5-mm pinholes backilluminated by halogen lamps; L1 and L1, condenser lenses; L2 and L2, collimators: L3 and L3 project a 3-deg bipartite field stop (HF and HF) onto the subject’s fovea; GF, green filter; M, movable mirror; IR CCD, pupil monitoring system.

Fig. 3
Fig. 3

Relative luminous efficiency curves (log units) for the four subjects. Symbols represent the experimental data from three different sets of measurements; the solid curve represents parabolic fits. For presentation the curves have been displaced in the vertical direction. Spacing between major ticks in the y axis is 0.2 unit.

Fig. 4
Fig. 4

Width of the SC relative luminous efficiency curves (FWHM) for two physical pupil diameters versus OSI cutoff spatial frequencies (normalized to the diffraction limit cutoff). The dashed line represents a linear fit to the 8-mm data. Error bars represent the standard error of the mean.

Fig. 5
Fig. 5

Psychometric functions for detection of sinusoidal vertical gratings at four foveal eccentricities for subject MA. Each point is the result of at least 100 trials in a two-alternative, forced-choice procedure. Smooth curves are fits to Weibull functions.

Fig. 6
Fig. 6

Psychometric functions for orientation discrimination (circles) compared with detection of vertical (squares) and horizontal (triangles) gratings for foveal eccentricities 0° and 1° for subject SM. Thresholds are similar for the three tasks.

Fig. 7
Fig. 7

Comparison of Nyquist frequency of the cone mosaic and visual acuity, for the four subjects, as a function of foveal eccentricity.

Fig. 8
Fig. 8

Possible explanation for the disagreement between Nyquist frequency and visual acuity at the foveal center. The shaded area represents the range of interferometric contrast-sensitivity data for six subjects from Williams’s study.31 Solid and dashed curves represent the inverted double-pass MTF’s for 5-mm pupils for subjects RN and MA, respectively, in log scale (displayed on the left y axis). Open vertical bars indicate visual acuity and solid bars the Nyquist frequency for subjects RN and MA.

Tables (1)

Tables Icon

Table 1 Cutoff Spatial Frequencies of the Average Power Spectra (c/deg) for Four Subjects and Two Pupil Diameters

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

η=ηmax10ρ(x-xmax)2;
FWHM=20.30/ρ.
fc=257.1(0.43w-1.62).
P(f)=100-50 exp[-(f/a)b],

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