Abstract

Reflectometric techniques estimate the directionality of the retinal cones by measuring the distribution of light at the pupil plane of light reflected off the bleached retina. The waveguide-scattering model of Marcos et al. [J. Opt. Soc. Am. A 15, 2012 (1998)] predicts that the shape of this intensity distribution is determined by both the waveguide properties of the cone photoreceptors and the topography of the cone mosaic (cone spacing). We have performed two types of cone directionality measurement. In the first type, cone directionality estimates are obtained by measuring the spatial distribution of light returning from the retina with a single-entry pupil position (single-entry measurements). In the second type, estimates are obtained by measuring the total amount of light guided back through the pupil as a function of entry pupil position (multiple-entry measurements). As predicted by the model, single-entry measurements provide narrower distributions than the multiple-entry measurements, since the former are affected by both waveguides and scattering and the latter are affected primarily by waveguides. Measurements at different retinal eccentricities and at two different wavelengths are consistent with the model. We show that the broader multiple-entry measurements are not accounted for by cone disarray. Results of multiple-entry measurements are closer to results from measurements of the psychophysical Stiles–Crawford effect (although still narrower), and the variation with retinal eccentricity and wavelength is similar. By combining single- and multiple-entry measurements, we can estimate cone spacing. The estimates at 0- and 2-deg retinal eccentricities are in good agreement with published anatomical data.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London, Ser. B 112, 428–450 (1933).
    [CrossRef]
  2. J. M. Enoch, H. E. Bedell, “The Stiles–Crawford effects,” in Vertebrate Photoreceptor Optics, J. M. Enoch, F. L. Tobey, eds., Springer Series in Optical Sciences (Springer, Heidelberg, 1981).
  3. 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]
  4. J. J. Vos, A. Huigen, “A clinical Stiles–Crawford apparatus,” Am. J. Optom. Arch. Am. Acad. Optom. 39, 68–76 (1962).
    [CrossRef] [PubMed]
  5. F. Fankhauser, J. M. Enoch, P. Cibis, “Receptor orientation in retinal pathology,” Am. J. Optom. Physiol. Opt. 55, 807–812 (1978).
  6. V. C. Smith, J. Pokorny, K. R. Diddie, “Color matching and Stiles–Crawford effect in central serous detachment repair,” Mod. Probl. Ophthalmol. 19, 284–295 (1978).
  7. J. Pokorny, V. C. Smith, P. B. Johnston, “Photoreceptor misalignment accompanying a fibrous scar,” Arch. Ophthalmol. (Chicago) 97, 867–869 (1979).
    [CrossRef]
  8. C. R. Fitzgerald, D. G. Birch, J. M. Enoch, “Functional analysis of vision in patients following retinal detachment repair,” Arch. Ophthalmol. (Chicago) 98, 1237–1244 (1980).
    [CrossRef]
  9. G. J. van Blokland, “Directionality and alignment of the foveal photoreceptors assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
    [CrossRef]
  10. J. M. Gorrand, F. C. Delori, “A reflectometric technique for assessing photoreceptor alignment,” Vision Res. 35, 999–1010 (1995).
    [CrossRef] [PubMed]
  11. S. A. Burns, S. Wu, F. C. Delori, A. E. Elsner, “Direct measurement of human cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1996).
    [CrossRef]
  12. P. J. de Lint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
    [CrossRef]
  13. S. A. Burns, A. E. Elsner, J. M. Gorrand, M. R. Kreitz, F. C. Delori, “Comparison of reflectometric and psychophysical measures of cone orientation,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 160–163.
  14. J. C. He, S. Marcos, S. A. Burns, “Comparison of cone directionality measured using psychophysical and reflectometric techniques,” submitted to J. Opt. Soc. Am. A.
  15. S. Marcos, S. A. Burns, J. C. He, “A model for cone directionality reflectometric measurements based on scattering,” J. Opt. Soc. Am. A 15, 2012–2022 (1998).
    [CrossRef]
  16. P. Beckmann, A. Spizzino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
  17. D. I. A. MacLeod, “Directionally selective light adaptation: a visual consequence of receptor disarray?” Vision Res. 14, 369–378 (1974).
    [CrossRef] [PubMed]
  18. S. A. Burns, S. Wu, J. C. He, A. E. Elsner, “Variations in photoreceptor directionality across the central retina,” J. Opt. Soc. Am. A 14, 2033–2040 (1997).
    [CrossRef]
  19. V. Lakshminarayanan, J. M. Enoch, “Shape of the Stiles–Crawford function for traverses of the entrance pupil not passing through the peak of sensitivity,” Am. J. Optom. Physiol. Opt. 62, 127–128 (1985).
    [CrossRef] [PubMed]
  20. A. Safir, L. J. Hyams, “Distribution of cone orientations as an explanation of the Stiles–Crawford effect,” J. Opt. Soc. Am. 59, 757–765 (1969).
    [CrossRef] [PubMed]
  21. J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
    [CrossRef]
  22. G. Li, H. Zwick, R. Elliott, A. Akers, B. E. Stuck, “Mode structure alterations in normal and laser exposed vertebrate photoreceptors in the small high numerical aperture of the snake,” presented at the OSA Annual Meeting, Baltimore, Md., October 4-9, 1998.
  23. G. Westheimer, “Dependence of the magnitude of the Stiles–Crawford effect on retinal location,” J. Physiol. (London) 192, 309–315 (1967).
  24. J. M. Enoch, G. M. Hope, “Directional sensitivity of the foveal and parafoveal retina,” Invest. Ophthalmol. Visual Sci. 12, 497–503 (1973).
  25. A. W. Snyder, C. L. Pask, “The Stiles–Crawford effect: explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
    [CrossRef] [PubMed]
  26. J. M. Enoch, “Optical properties of the retinal receptors,” J. Opt. Soc. Am. 53, 71–85 (1963).
    [CrossRef]
  27. N. D. Miller, “The changes in the Stiles–Crawford effect with high luminance adapting fields,” Am. J. Optom. Arch. Am. Acad. Optom. 41, 599–608 (1964).
    [CrossRef] [PubMed]
  28. S. J. Starr, “Effect of luminance and wavelength on the Stiles–Crawford effect in dichromats,” Ph.D. dissertation (University of Chicago, Chicago, Ill., 1977).
  29. M. J. Piket-May, A. Taflove, J. B. Troy, “Electrodynamics of visible light interactions with the vertebrate retinal rod,” Opt. Lett. 18, 568–570 (1993).
    [CrossRef]
  30. B. Chen, W. Makous, “Light capture by human cones,” J. Physiol. (London) 190, 583–593 (1989).
  31. C. A. Curcio, K. R. Sloan, R. E. Kalina, A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neurol. 292, 497–523 (1992).
    [CrossRef]
  32. 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]
  33. D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of the cone photoreceptors in the living human eye,” Vision Res. 36, 1067–1079 (1996).
    [CrossRef] [PubMed]
  34. A. R. Wade, F. W. Fitzke, “High-resolution imaging of the human cone photoreceptor mosaic using a laser scanning ophthalmoscope,” Invest. Ophthalmol. Visual Sci. 39, 204 (1998).
  35. In de Lint et al.,12 the sampled retinal area is in fact given by the angular pixel size in the scanning laser ophthalmoscope images. However, their processing includes pixel smoothing (10×10), and final rho values are given after subsequent spatial average across the 2-deg central region.

1998 (2)

A. R. Wade, F. W. Fitzke, “High-resolution imaging of the human cone photoreceptor mosaic using a laser scanning ophthalmoscope,” Invest. Ophthalmol. Visual Sci. 39, 204 (1998).

S. Marcos, S. A. Burns, J. C. He, “A model for cone directionality reflectometric measurements based on scattering,” J. Opt. Soc. Am. A 15, 2012–2022 (1998).
[CrossRef]

1997 (3)

S. A. Burns, S. Wu, J. C. He, A. E. Elsner, “Variations in photoreceptor directionality across the central retina,” J. Opt. Soc. Am. A 14, 2033–2040 (1997).
[CrossRef]

P. J. de Lint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
[CrossRef]

J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
[CrossRef]

1996 (3)

1995 (1)

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

1993 (2)

1992 (1)

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

1989 (1)

B. Chen, W. Makous, “Light capture by human cones,” J. Physiol. (London) 190, 583–593 (1989).

1986 (1)

G. J. van Blokland, “Directionality and alignment of the foveal photoreceptors assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef]

1985 (1)

V. Lakshminarayanan, J. M. Enoch, “Shape of the Stiles–Crawford function for traverses of the entrance pupil not passing through the peak of sensitivity,” Am. J. Optom. Physiol. Opt. 62, 127–128 (1985).
[CrossRef] [PubMed]

1980 (1)

C. R. Fitzgerald, D. G. Birch, J. M. Enoch, “Functional analysis of vision in patients following retinal detachment repair,” Arch. Ophthalmol. (Chicago) 98, 1237–1244 (1980).
[CrossRef]

1979 (1)

J. Pokorny, V. C. Smith, P. B. Johnston, “Photoreceptor misalignment accompanying a fibrous scar,” Arch. Ophthalmol. (Chicago) 97, 867–869 (1979).
[CrossRef]

1978 (2)

F. Fankhauser, J. M. Enoch, P. Cibis, “Receptor orientation in retinal pathology,” Am. J. Optom. Physiol. Opt. 55, 807–812 (1978).

V. C. Smith, J. Pokorny, K. R. Diddie, “Color matching and Stiles–Crawford effect in central serous detachment repair,” Mod. Probl. Ophthalmol. 19, 284–295 (1978).

1974 (1)

D. I. A. MacLeod, “Directionally selective light adaptation: a visual consequence of receptor disarray?” Vision Res. 14, 369–378 (1974).
[CrossRef] [PubMed]

1973 (2)

J. M. Enoch, G. M. Hope, “Directional sensitivity of the foveal and parafoveal retina,” Invest. Ophthalmol. Visual Sci. 12, 497–503 (1973).

A. W. Snyder, C. L. Pask, “The Stiles–Crawford effect: explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[CrossRef] [PubMed]

1969 (1)

1967 (1)

G. Westheimer, “Dependence of the magnitude of the Stiles–Crawford effect on retinal location,” J. Physiol. (London) 192, 309–315 (1967).

1964 (1)

N. D. Miller, “The changes in the Stiles–Crawford effect with high luminance adapting fields,” Am. J. Optom. Arch. Am. Acad. Optom. 41, 599–608 (1964).
[CrossRef] [PubMed]

1963 (1)

1962 (1)

J. J. Vos, A. Huigen, “A clinical Stiles–Crawford apparatus,” Am. J. Optom. Arch. Am. Acad. Optom. 39, 68–76 (1962).
[CrossRef] [PubMed]

1933 (1)

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London, Ser. B 112, 428–450 (1933).
[CrossRef]

Akers, A.

G. Li, H. Zwick, R. Elliott, A. Akers, B. E. Stuck, “Mode structure alterations in normal and laser exposed vertebrate photoreceptors in the small high numerical aperture of the snake,” presented at the OSA Annual Meeting, Baltimore, Md., October 4-9, 1998.

Applegate, R. A.

Artal, P.

Beckmann, P.

P. Beckmann, A. Spizzino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Bedell, H. E.

J. M. Enoch, H. E. Bedell, “The Stiles–Crawford effects,” in Vertebrate Photoreceptor Optics, J. M. Enoch, F. L. Tobey, eds., Springer Series in Optical Sciences (Springer, Heidelberg, 1981).

Berendschot, T. T. J. M.

P. J. de Lint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
[CrossRef]

Birch, D. G.

C. R. Fitzgerald, D. G. Birch, J. M. Enoch, “Functional analysis of vision in patients following retinal detachment repair,” Arch. Ophthalmol. (Chicago) 98, 1237–1244 (1980).
[CrossRef]

Burns, S. A.

S. Marcos, S. A. Burns, J. C. He, “A model for cone directionality reflectometric measurements based on scattering,” J. Opt. Soc. Am. A 15, 2012–2022 (1998).
[CrossRef]

S. A. Burns, S. Wu, J. C. He, A. E. Elsner, “Variations in photoreceptor directionality across the central retina,” J. Opt. Soc. Am. A 14, 2033–2040 (1997).
[CrossRef]

S. A. Burns, S. Wu, F. C. Delori, A. E. Elsner, “Direct measurement of human cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1996).
[CrossRef]

S. A. Burns, A. E. Elsner, J. M. Gorrand, M. R. Kreitz, F. C. Delori, “Comparison of reflectometric and psychophysical measures of cone orientation,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 160–163.

J. C. He, S. Marcos, S. A. Burns, “Comparison of cone directionality measured using psychophysical and reflectometric techniques,” submitted to J. Opt. Soc. Am. A.

Chen, B.

B. Chen, W. Makous, “Light capture by human cones,” J. Physiol. (London) 190, 583–593 (1989).

Cibis, P.

F. Fankhauser, J. M. Enoch, P. Cibis, “Receptor orientation in retinal pathology,” Am. J. Optom. Physiol. Opt. 55, 807–812 (1978).

Crawford, B. H.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London, Ser. B 112, 428–450 (1933).
[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]

de Lint, P. J.

P. J. de Lint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
[CrossRef]

Delori, F. C.

J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
[CrossRef]

S. A. Burns, S. Wu, F. C. Delori, A. E. Elsner, “Direct measurement of human cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1996).
[CrossRef]

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

S. A. Burns, A. E. Elsner, J. M. Gorrand, M. R. Kreitz, F. C. Delori, “Comparison of reflectometric and psychophysical measures of cone orientation,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 160–163.

Diddie, K. R.

V. C. Smith, J. Pokorny, K. R. Diddie, “Color matching and Stiles–Crawford effect in central serous detachment repair,” Mod. Probl. Ophthalmol. 19, 284–295 (1978).

Elliott, R.

G. Li, H. Zwick, R. Elliott, A. Akers, B. E. Stuck, “Mode structure alterations in normal and laser exposed vertebrate photoreceptors in the small high numerical aperture of the snake,” presented at the OSA Annual Meeting, Baltimore, Md., October 4-9, 1998.

Elsner, A. E.

S. A. Burns, S. Wu, J. C. He, A. E. Elsner, “Variations in photoreceptor directionality across the central retina,” J. Opt. Soc. Am. A 14, 2033–2040 (1997).
[CrossRef]

S. A. Burns, S. Wu, F. C. Delori, A. E. Elsner, “Direct measurement of human cone-photoreceptor alignment,” J. Opt. Soc. Am. A 12, 2329–2338 (1996).
[CrossRef]

S. A. Burns, A. E. Elsner, J. M. Gorrand, M. R. Kreitz, F. C. Delori, “Comparison of reflectometric and psychophysical measures of cone orientation,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 160–163.

Enoch, J. M.

V. Lakshminarayanan, J. M. Enoch, “Shape of the Stiles–Crawford function for traverses of the entrance pupil not passing through the peak of sensitivity,” Am. J. Optom. Physiol. Opt. 62, 127–128 (1985).
[CrossRef] [PubMed]

C. R. Fitzgerald, D. G. Birch, J. M. Enoch, “Functional analysis of vision in patients following retinal detachment repair,” Arch. Ophthalmol. (Chicago) 98, 1237–1244 (1980).
[CrossRef]

F. Fankhauser, J. M. Enoch, P. Cibis, “Receptor orientation in retinal pathology,” Am. J. Optom. Physiol. Opt. 55, 807–812 (1978).

J. M. Enoch, G. M. Hope, “Directional sensitivity of the foveal and parafoveal retina,” Invest. Ophthalmol. Visual Sci. 12, 497–503 (1973).

J. M. Enoch, “Optical properties of the retinal receptors,” J. Opt. Soc. Am. 53, 71–85 (1963).
[CrossRef]

J. M. Enoch, H. E. Bedell, “The Stiles–Crawford effects,” in Vertebrate Photoreceptor Optics, J. M. Enoch, F. L. Tobey, eds., Springer Series in Optical Sciences (Springer, Heidelberg, 1981).

Fankhauser, F.

F. Fankhauser, J. M. Enoch, P. Cibis, “Receptor orientation in retinal pathology,” Am. J. Optom. Physiol. Opt. 55, 807–812 (1978).

Fitzgerald, C. R.

C. R. Fitzgerald, D. G. Birch, J. M. Enoch, “Functional analysis of vision in patients following retinal detachment repair,” Arch. Ophthalmol. (Chicago) 98, 1237–1244 (1980).
[CrossRef]

Fitzke, F. W.

A. R. Wade, F. W. Fitzke, “High-resolution imaging of the human cone photoreceptor mosaic using a laser scanning ophthalmoscope,” Invest. Ophthalmol. Visual Sci. 39, 204 (1998).

Gorrand, J. M.

J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
[CrossRef]

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

S. A. Burns, A. E. Elsner, J. M. Gorrand, M. R. Kreitz, F. C. Delori, “Comparison of reflectometric and psychophysical measures of cone orientation,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 160–163.

He, J. C.

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]

Hope, G. M.

J. M. Enoch, G. M. Hope, “Directional sensitivity of the foveal and parafoveal retina,” Invest. Ophthalmol. Visual Sci. 12, 497–503 (1973).

Huigen, A.

J. J. Vos, A. Huigen, “A clinical Stiles–Crawford apparatus,” Am. J. Optom. Arch. Am. Acad. Optom. 39, 68–76 (1962).
[CrossRef] [PubMed]

Hyams, L. J.

Johnston, P. B.

J. Pokorny, V. C. Smith, P. B. Johnston, “Photoreceptor misalignment accompanying a fibrous scar,” Arch. Ophthalmol. (Chicago) 97, 867–869 (1979).
[CrossRef]

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]

Kreitz, M. R.

S. A. Burns, A. E. Elsner, J. M. Gorrand, M. R. Kreitz, F. C. Delori, “Comparison of reflectometric and psychophysical measures of cone orientation,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 160–163.

Lakshminarayanan, V.

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]

V. Lakshminarayanan, J. M. Enoch, “Shape of the Stiles–Crawford function for traverses of the entrance pupil not passing through the peak of sensitivity,” Am. J. Optom. Physiol. Opt. 62, 127–128 (1985).
[CrossRef] [PubMed]

Li, G.

G. Li, H. Zwick, R. Elliott, A. Akers, B. E. Stuck, “Mode structure alterations in normal and laser exposed vertebrate photoreceptors in the small high numerical aperture of the snake,” presented at the OSA Annual Meeting, Baltimore, Md., October 4-9, 1998.

Liang, J.

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

MacLeod, D. I. A.

D. I. A. MacLeod, “Directionally selective light adaptation: a visual consequence of receptor disarray?” Vision Res. 14, 369–378 (1974).
[CrossRef] [PubMed]

Makous, W.

B. Chen, W. Makous, “Light capture by human cones,” J. Physiol. (London) 190, 583–593 (1989).

Marcos, S.

Miller, D. T.

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

Miller, N. D.

N. D. Miller, “The changes in the Stiles–Crawford effect with high luminance adapting fields,” Am. J. Optom. Arch. Am. Acad. Optom. 41, 599–608 (1964).
[CrossRef] [PubMed]

Morris, G. M.

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

Navarro, R.

Pask, C. L.

A. W. Snyder, C. L. Pask, “The Stiles–Crawford effect: explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[CrossRef] [PubMed]

Piket-May, M. J.

Pokorny, J.

J. Pokorny, V. C. Smith, P. B. Johnston, “Photoreceptor misalignment accompanying a fibrous scar,” Arch. Ophthalmol. (Chicago) 97, 867–869 (1979).
[CrossRef]

V. C. Smith, J. Pokorny, K. R. Diddie, “Color matching and Stiles–Crawford effect in central serous detachment repair,” Mod. Probl. Ophthalmol. 19, 284–295 (1978).

Safir, A.

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]

Smith, V. C.

J. Pokorny, V. C. Smith, P. B. Johnston, “Photoreceptor misalignment accompanying a fibrous scar,” Arch. Ophthalmol. (Chicago) 97, 867–869 (1979).
[CrossRef]

V. C. Smith, J. Pokorny, K. R. Diddie, “Color matching and Stiles–Crawford effect in central serous detachment repair,” Mod. Probl. Ophthalmol. 19, 284–295 (1978).

Snyder, A. W.

A. W. Snyder, C. L. Pask, “The Stiles–Crawford effect: explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[CrossRef] [PubMed]

Spizzino, A.

P. Beckmann, A. Spizzino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Starr, S. J.

S. J. Starr, “Effect of luminance and wavelength on the Stiles–Crawford effect in dichromats,” Ph.D. dissertation (University of Chicago, Chicago, Ill., 1977).

Stiles, W. S.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London, Ser. B 112, 428–450 (1933).
[CrossRef]

Stuck, B. E.

G. Li, H. Zwick, R. Elliott, A. Akers, B. E. Stuck, “Mode structure alterations in normal and laser exposed vertebrate photoreceptors in the small high numerical aperture of the snake,” presented at the OSA Annual Meeting, Baltimore, Md., October 4-9, 1998.

Taflove, A.

Troy, J. B.

van Blokland, G. J.

G. J. van Blokland, “Directionality and alignment of the foveal photoreceptors assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 495–500 (1986).
[CrossRef]

van Norren, D.

P. J. de Lint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
[CrossRef]

Vos, J. J.

J. J. Vos, A. Huigen, “A clinical Stiles–Crawford apparatus,” Am. J. Optom. Arch. Am. Acad. Optom. 39, 68–76 (1962).
[CrossRef] [PubMed]

Wade, A. R.

A. R. Wade, F. W. Fitzke, “High-resolution imaging of the human cone photoreceptor mosaic using a laser scanning ophthalmoscope,” Invest. Ophthalmol. Visual Sci. 39, 204 (1998).

Westheimer, G.

G. Westheimer, “Dependence of the magnitude of the Stiles–Crawford effect on retinal location,” J. Physiol. (London) 192, 309–315 (1967).

Williams, D. R.

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

Wu, S.

Zwick, H.

G. Li, H. Zwick, R. Elliott, A. Akers, B. E. Stuck, “Mode structure alterations in normal and laser exposed vertebrate photoreceptors in the small high numerical aperture of the snake,” presented at the OSA Annual Meeting, Baltimore, Md., October 4-9, 1998.

Am. J. Optom. Arch. Am. Acad. Optom. (2)

J. J. Vos, A. Huigen, “A clinical Stiles–Crawford apparatus,” Am. J. Optom. Arch. Am. Acad. Optom. 39, 68–76 (1962).
[CrossRef] [PubMed]

N. D. Miller, “The changes in the Stiles–Crawford effect with high luminance adapting fields,” Am. J. Optom. Arch. Am. Acad. Optom. 41, 599–608 (1964).
[CrossRef] [PubMed]

Am. J. Optom. Physiol. Opt. (2)

F. Fankhauser, J. M. Enoch, P. Cibis, “Receptor orientation in retinal pathology,” Am. J. Optom. Physiol. Opt. 55, 807–812 (1978).

V. Lakshminarayanan, J. M. Enoch, “Shape of the Stiles–Crawford function for traverses of the entrance pupil not passing through the peak of sensitivity,” Am. J. Optom. Physiol. Opt. 62, 127–128 (1985).
[CrossRef] [PubMed]

Arch. Ophthalmol. (Chicago) (2)

J. Pokorny, V. C. Smith, P. B. Johnston, “Photoreceptor misalignment accompanying a fibrous scar,” Arch. Ophthalmol. (Chicago) 97, 867–869 (1979).
[CrossRef]

C. R. Fitzgerald, D. G. Birch, J. M. Enoch, “Functional analysis of vision in patients following retinal detachment repair,” Arch. Ophthalmol. (Chicago) 98, 1237–1244 (1980).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (2)

J. M. Enoch, G. M. Hope, “Directional sensitivity of the foveal and parafoveal retina,” Invest. Ophthalmol. Visual Sci. 12, 497–503 (1973).

A. R. Wade, F. W. Fitzke, “High-resolution imaging of the human cone photoreceptor mosaic using a laser scanning ophthalmoscope,” Invest. Ophthalmol. Visual Sci. 39, 204 (1998).

J. Comp. Neurol. (1)

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

J. Mod. Opt. (1)

J. M. Gorrand, F. C. Delori, “A model for assessment of cone directionality,” J. Mod. Opt. 44, 473–491 (1997).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

J. Physiol. (London) (2)

B. Chen, W. Makous, “Light capture by human cones,” J. Physiol. (London) 190, 583–593 (1989).

G. Westheimer, “Dependence of the magnitude of the Stiles–Crawford effect on retinal location,” J. Physiol. (London) 192, 309–315 (1967).

Mod. Probl. Ophthalmol. (1)

V. C. Smith, J. Pokorny, K. R. Diddie, “Color matching and Stiles–Crawford effect in central serous detachment repair,” Mod. Probl. Ophthalmol. 19, 284–295 (1978).

Opt. Lett. (1)

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

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at different points,” Proc. R. Soc. London, Ser. B 112, 428–450 (1933).
[CrossRef]

Vision Res. (6)

G. J. van Blokland, “Directionality and alignment of the foveal photoreceptors assessed with light scattered from the human fundus in vivo,” 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]

P. J. de Lint, T. T. J. M. Berendschot, D. van Norren, “Local photoreceptor alignment measured with a scanning laser ophthalmoscope,” Vision Res. 37, 243–248 (1997).
[CrossRef]

D. I. A. MacLeod, “Directionally selective light adaptation: a visual consequence of receptor disarray?” Vision Res. 14, 369–378 (1974).
[CrossRef] [PubMed]

A. W. Snyder, C. L. Pask, “The Stiles–Crawford effect: explanation and consequences,” Vision Res. 13, 1115–1137 (1973).
[CrossRef] [PubMed]

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

Other (7)

In de Lint et al.,12 the sampled retinal area is in fact given by the angular pixel size in the scanning laser ophthalmoscope images. However, their processing includes pixel smoothing (10×10), and final rho values are given after subsequent spatial average across the 2-deg central region.

S. J. Starr, “Effect of luminance and wavelength on the Stiles–Crawford effect in dichromats,” Ph.D. dissertation (University of Chicago, Chicago, Ill., 1977).

G. Li, H. Zwick, R. Elliott, A. Akers, B. E. Stuck, “Mode structure alterations in normal and laser exposed vertebrate photoreceptors in the small high numerical aperture of the snake,” presented at the OSA Annual Meeting, Baltimore, Md., October 4-9, 1998.

S. A. Burns, A. E. Elsner, J. M. Gorrand, M. R. Kreitz, F. C. Delori, “Comparison of reflectometric and psychophysical measures of cone orientation,” in Noninvasive Assessment of the Visual System, Vol. 1 of 1992 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1992), pp. 160–163.

J. C. He, S. Marcos, S. A. Burns, “Comparison of cone directionality measured using psychophysical and reflectometric techniques,” submitted to J. Opt. Soc. Am. A.

J. M. Enoch, H. E. Bedell, “The Stiles–Crawford effects,” in Vertebrate Photoreceptor Optics, J. M. Enoch, F. L. Tobey, eds., Springer Series in Optical Sciences (Springer, Heidelberg, 1981).

P. Beckmann, A. Spizzino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Theory of single- and multiple-entry reflectometric measurements. The intensity distribution at the pupil plane of light returning from a small area of bleached retina is imaged on a CCD camera for a series of entry pupil locations [(a), data from subject SM, 0 deg, 543 nm, horizontal axis]. The total amount of guided light is maximum for the location in the pupil toward which the photoreceptors are pointing. The circled image corresponds to the optimal entry pupil location and is the image used for single-entry reflectometric measurements. Since these measurements are based on a single image, we refer to them as single-entry measurements [(b)]. The intensity distribution for the optimal image is fitted to a constant added to a two-dimensional Gaussian function, from which we obtain the rho value: ρs. As the entry position of the illuminating beam moves away from the optimal entry pupil, less light is captured by the cones and guided back. The measurements based on a series of images across the pupil are referred to as multiple-entry measurements [(c)]. The total amount of guided light as a function of entry pupil position is fitted with a Gaussian function, with the rho value ρmx. The final rho, ρm, is computed as the mean of the estimates for the horizontal and vertical axes (ρmx and ρmy).

Fig. 2
Fig. 2

Example of multiple-entry reflectometric functions (total guided intensity as a function of entry pupil position) for different subjects (SM, SB, and JH), retinal eccentricities (0 and 2 deg temporal), and wavelengths (543 and 632 nm). Each panel represents results from a single session. Circles are averaged across five consecutive measurements at the same pupil location. Filled circles stand for measurements across the horizontal axis, and open circles stand for measurements across the vertical axis. (Error bars stand for ±1 standard error of the mean.) Positive entry pupil positions stand for temporal and superior locations, and negative positions stand for nasal and inferior locations. Dashed and dotted curves represent the best fit to the measurements across the horizontal and vertical axes, respectively.

Fig. 3
Fig. 3

Rho value as a function of retinal eccentricity for single-entry measurements ρs and multiple-entry measurements ρm. (a) Results for the three subjects. Symbols with the same shape correspond to the same subject. Single-entry measurements (filled symbols) are in all cases narrower than multiple-entry measurements (open symbols). (b) Results for subject JH for two wavelengths: 543 nm (filled symbols) and 632 nm (open symbols). Circles represent single-entry measurements, and squares represent multiple-entry measurements. Single-entry measurements are narrower in green light than in red light; however, there is no significant difference across wavelengths for multiple-entry measurements. Standard errors are smaller than 0.0166 mm-2 for single-entry measurements and smaller than 0.0108 mm-2 for multiple-entry measurements.

Fig. 4
Fig. 4

Scheme of computer simulations showing the effect of cone disarray. Gdis stands for the cone disarray distribution (a Gaussian distribution in the simulation, represented as three delta functions for graphical purposes), and Gwg represents the angular tuning of a cone [(b)]. Part (a) represents the convolution process to compute the intensity distribution at the pupil plane for different entry pupil positions (shown for entry pupil positions coincident with the location of the delta functions). Cone disarray has two consequences: displacement of the peak of the intensity distribution and broadening of the function calculated as the total guided intensity versus pupil position with respect to the distribution computed from a single image.

Fig. 5
Fig. 5

Rho value as a function of retinal eccentricity for single-entry measurements ρs (filled circles), multiple-entry measurements ρm (filled squares), and Stiles–Crawford effect (SCE) measurements ρSCE from He et al.,14 (filled triangles): (a) subject JH, (b) subject SM, and (c) subject SB. The variation of ρm and ρSCE with retinal eccentricity is similar; both increase more slowly with increasing retinal eccentricity than ρs. However, SCE measurements are still broader than multiple-entry measurements. (d) Rho value as a function of wavelength for subject JH: ρs (open circles), multiple-entry measurements ρm (open squares), and SCE measurements ρSCE (open triangles). ρs decreases markedly with wavelength, whereas ρSCE and ρm do not change significantly. Error bars represent ±1 standard error of the mean.

Fig. 6
Fig. 6

Derived cone spacing as a function of retinal eccentricity for the three observers. Filled symbols are results using green light, and open symbols are results using red light. Solid line, average across the three subjects; dashed curve, average of anatomical data of Curcio et al.31

Fig. 7
Fig. 7

Entry and exit pupil configurations in different cone directionality reflectometric techniques: (a) Gorrand and Delori,10 (b) de Lint et al.,12 (c) van Blokland,9 (d) Burns et al.13 and present paper.

Tables (2)

Tables Icon

Table 1 ρs and ρm for 0- and 2-deg Retinal Eccentricity (Three Subjects and Average) for the Experiments in the Present Study

Tables Icon

Table 2 Values for Configurations of ρGorrandDelori, ρde Lint etal., and ρvan Blokland (0 and 2 deg): Simulations Based on Results from Our Experiments and Experimental Values Reported in the Literature

Equations (1)

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

[Gwg(x-xi)Gdis] * Gwg,

Metrics