Abstract

To determine whether vision with obliquely incident light is degraded by contrast losses originating in the retina, laser interference fringe patterns were produced on the retina for various directions of incidence of the two interfering beams. Contrast-modulation flicker [Vision Res. 38, 985 (1998)] was used as a psychophysical measure of contrast at the level of the photoreceptors. Fringe contrast was shown to be maximal when the interfering beams were equal in perceived brightness, not in physical intensity. The effective fringe contrast was slightly reduced with oblique incidence for high spatial frequencies, but the reduction was too slight to be an important factor in visual resolution. The loss was similar whether the incident beams were displaced from the pupil center in a direction parallel or perpendicular to the grating bars.

© 2001 Optical Society of America

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  1. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  2. D. R. Williams, D. H. Brainard, M. J. McMahon, R. Navarro, “Double-pass and interferometric measures of the optical quality of the eye,” J. Opt. Soc. Am. A 11, 3123–3135 (1994).
    [CrossRef]
  3. F. W. Campbell, “A retinal acuity direction effect,” J. Physiol. (London) 144, 25P–26P (1958).
  4. F. W. Campbell, A. H. Gregory, “The spatial resolving power of the human retina with oblique incidence,” J. Opt. Soc. Am. 50, 831 (1960).
    [CrossRef] [PubMed]
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  6. 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]
  7. W. D. Wright, J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
    [CrossRef]
  8. J. M. Enoch, F. L. Tobey, eds., Vertebrate Photoreceptor Optics (Springer-Verlag, Berlin, 1981).
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  10. L. N. Thibos, A. Bradley, D. L. Still, “Interferometric measurement of visual acuity and the effect of ocular chromatic aberration,” Appl. Opt. 30, 2079–2087 (1991).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  13. G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
    [CrossRef] [PubMed]
  14. B. Chen, W. Makous, “Light capture by human cones,” J. Physiol. (London) 414, 89–109 (1989).
  15. C. Pask, A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vision Res. 38, 953–961 (1998).
    [CrossRef] [PubMed]
  16. W. Makous, J. Schnapf, “Two components of the Stiles–Crawford effect: cone aperture and disarray,” presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Sarasota, Fla., May 3–7, 1973.
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    [CrossRef]
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  27. D. I. MacLeod, D. R. Williams, W. Makous, “A visual nonlinearity fed by single cones,” Vision Res. 32, 347–363 (1992).
    [CrossRef] [PubMed]
  28. J. van de Kraats, T. T. Berendschot, D. van Norren, “The pathways of light measured in funds reflectometry,” Vision Res. 36, 2229–2247 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
  31. P. Artal, “Incorporation of directional effects of the retina into computations of optical transfer functions of human eyes,” J. Opt. Soc. Am. A 6, 1941–1944 (1989).
    [CrossRef] [PubMed]
  32. A. Bradley, L. N. Thibos, “Modeling off-axis vision I: The optical effects of decentering visual targets or the eye’s entrance pupil,” in Vision Models for Target Detection and Recognition: In Memory of Arthur Menendez, A. R. Menendez, E. Peli, eds. (World Scientific, River Edge, N.J., 1995), pp. 313–337.
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2000 (1)

M. J. McMahon, D. I. A. MacLeod, “Visual resolution with obliquely incident light: retinal contrast losses,” Invest. Ophthalmol. Visual Sci. Suppl. 41/4, S100 (2000).

1998 (2)

C. Pask, A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vision Res. 38, 953–961 (1998).
[CrossRef] [PubMed]

S. He, D. I. MacLeod, “Contrast-modulation flicker: dynamics and spatial resolution of the light adaptation process,” Vision Res. 38, 985–1000 (1998).
[CrossRef] [PubMed]

1997 (1)

1996 (3)

S. He, D. I. MacLeod, “Local luminance nonlinearity and receptor aliasing in the detection of high-frequency gratings,” J. Opt. Soc. Am. A 13, 1139–1151 (1996).
[CrossRef]

J. van de Kraats, T. T. Berendschot, D. van Norren, “The pathways of light measured in funds reflectometry,” Vision Res. 36, 2229–2247 (1996).
[CrossRef] [PubMed]

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

1994 (1)

1992 (1)

D. I. MacLeod, D. R. Williams, W. Makous, “A visual nonlinearity fed by single cones,” Vision Res. 32, 347–363 (1992).
[CrossRef] [PubMed]

1991 (1)

1989 (2)

1988 (1)

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

1985 (1)

1983 (2)

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupils,” Vision Res. 23, 573–579 (1983).
[CrossRef] [PubMed]

M. Alpern, K. Kitahara, R. Tamaki, “The dependence of the colour and brightness of a monochromatic light upon its angle of incidence on the retina,” J. Physiol. (London) 338, 651–668 (1983).

1981 (1)

L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
[CrossRef] [PubMed]

1974 (1)

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

1967 (1)

D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,” J. Physiol. (London) 190, 583–593 (1967).

1965 (2)

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]

1961 (1)

J. M. Enoch, W. S. Stiles, “The colour change of monochromatic light with retinal angle of incidence,” Opt. Acta (London) 8, 329–358 (1961).
[CrossRef]

1960 (1)

1958 (1)

F. W. Campbell, “A retinal acuity direction effect,” J. Physiol. (London) 144, 25P–26P (1958).

1936 (1)

W. D. Wright, J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
[CrossRef]

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]

Alpern, M.

M. Alpern, K. Kitahara, R. Tamaki, “The dependence of the colour and brightness of a monochromatic light upon its angle of incidence on the retina,” J. Physiol. (London) 338, 651–668 (1983).

Artal, P.

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

P. Artal, “Incorporation of directional effects of the retina into computations of optical transfer functions of human eyes,” J. Opt. Soc. Am. A 6, 1941–1944 (1989).
[CrossRef] [PubMed]

Berendschot, T. T.

J. van de Kraats, T. T. Berendschot, D. van Norren, “The pathways of light measured in funds reflectometry,” Vision Res. 36, 2229–2247 (1996).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Bour, L. J.

L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
[CrossRef] [PubMed]

Bradley, A.

L. N. Thibos, A. Bradley, D. L. Still, “Interferometric measurement of visual acuity and the effect of ocular chromatic aberration,” Appl. Opt. 30, 2079–2087 (1991).
[CrossRef] [PubMed]

A. Bradley, L. N. Thibos, “Modeling off-axis vision I: The optical effects of decentering visual targets or the eye’s entrance pupil,” in Vision Models for Target Detection and Recognition: In Memory of Arthur Menendez, A. R. Menendez, E. Peli, eds. (World Scientific, River Edge, N.J., 1995), pp. 313–337.

Brainard, D. H.

Campbell, F. W.

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

F. W. Campbell, A. H. Gregory, “The spatial resolving power of the human retina with oblique incidence,” J. Opt. Soc. Am. 50, 831 (1960).
[CrossRef] [PubMed]

F. W. Campbell, “A retinal acuity direction effect,” J. Physiol. (London) 144, 25P–26P (1958).

Charman, W. N.

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

Chen, B.

B. Chen, W. Makous, “Light capture by human cones,” J. Physiol. (London) 414, 89–109 (1989).

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]

Dunnewold, C. J. W.

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupils,” Vision Res. 23, 573–579 (1983).
[CrossRef] [PubMed]

Enoch, J. M.

J. M. Enoch, W. S. Stiles, “The colour change of monochromatic light with retinal angle of incidence,” Opt. Acta (London) 8, 329–358 (1961).
[CrossRef]

J. M. Enoch, “Retinal directional resolution,” in Visual Science: Proceedings of the 1968 International Symposium, J. R. Pierce, J. R. Levene, eds. (Indiana U. Press, Bloomington, Ind., 1971).

Green, D. G.

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,” J. Physiol. (London) 190, 583–593 (1967).

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

Gregory, A. H.

He, S.

S. He, D. I. MacLeod, “Contrast-modulation flicker: dynamics and spatial resolution of the light adaptation process,” Vision Res. 38, 985–1000 (1998).
[CrossRef] [PubMed]

S. He, D. I. MacLeod, “Local luminance nonlinearity and receptor aliasing in the detection of high-frequency gratings,” J. Opt. Soc. Am. A 13, 1139–1151 (1996).
[CrossRef]

Iglesias, I.

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

Kitahara, K.

M. Alpern, K. Kitahara, R. Tamaki, “The dependence of the colour and brightness of a monochromatic light upon its angle of incidence on the retina,” J. Physiol. (London) 338, 651–668 (1983).

Klein, S. A.

S. A. Klein, “Photoreceptor waveguides—a simple approach,” in Basic and Clinical Applications of Vision Science: The Professor Jay M. Enoch Festschrift Volume, V. Lakshminarayanan, ed. (Kluwer Academic, Boston, Mass., 1997), pp. 37–41.

Liang, J.

Lopes Cardozo, N. J.

L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
[CrossRef] [PubMed]

MacLeod, D. I.

S. He, D. I. MacLeod, “Contrast-modulation flicker: dynamics and spatial resolution of the light adaptation process,” Vision Res. 38, 985–1000 (1998).
[CrossRef] [PubMed]

S. He, D. I. MacLeod, “Local luminance nonlinearity and receptor aliasing in the detection of high-frequency gratings,” J. Opt. Soc. Am. A 13, 1139–1151 (1996).
[CrossRef]

D. I. MacLeod, D. R. Williams, W. Makous, “A visual nonlinearity fed by single cones,” Vision Res. 32, 347–363 (1992).
[CrossRef] [PubMed]

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

MacLeod, D. I. A.

M. J. McMahon, D. I. A. MacLeod, “Visual resolution with obliquely incident light: retinal contrast losses,” Invest. Ophthalmol. Visual Sci. Suppl. 41/4, S100 (2000).

Makous, W.

D. I. MacLeod, D. R. Williams, W. Makous, “A visual nonlinearity fed by single cones,” Vision Res. 32, 347–363 (1992).
[CrossRef] [PubMed]

B. Chen, W. Makous, “Light capture by human cones,” J. Physiol. (London) 414, 89–109 (1989).

W. Makous, J. Schnapf, “Two components of the Stiles–Crawford effect: cone aperture and disarray,” presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Sarasota, Fla., May 3–7, 1973.

J. Schnapf, W. Makous, “Individually adaptable optical channels in human retina,” presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Sarasota, Fla., April 25–29, 1974.

Marcos, S.

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

McMahon, M. J.

M. J. McMahon, D. I. A. MacLeod, “Visual resolution with obliquely incident light: retinal contrast losses,” Invest. Ophthalmol. Visual Sci. Suppl. 41/4, S100 (2000).

D. R. Williams, D. H. Brainard, M. J. McMahon, R. Navarro, “Double-pass and interferometric measures of the optical quality of the eye,” J. Opt. Soc. Am. A 11, 3123–3135 (1994).
[CrossRef]

Metcalf, H.

Navarro, R.

Nelson, J. H.

W. D. Wright, J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
[CrossRef]

Pask, C.

C. Pask, A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vision Res. 38, 953–961 (1998).
[CrossRef] [PubMed]

Schnapf, J.

W. Makous, J. Schnapf, “Two components of the Stiles–Crawford effect: cone aperture and disarray,” presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Sarasota, Fla., May 3–7, 1973.

J. Schnapf, W. Makous, “Individually adaptable optical channels in human retina,” presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Sarasota, Fla., April 25–29, 1974.

Stacey, A.

C. Pask, A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vision Res. 38, 953–961 (1998).
[CrossRef] [PubMed]

Stiles, W. S.

J. M. Enoch, W. S. Stiles, “The colour change of monochromatic light with retinal angle of incidence,” Opt. Acta (London) 8, 329–358 (1961).
[CrossRef]

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]

Still, D. L.

Tamaki, R.

M. Alpern, K. Kitahara, R. Tamaki, “The dependence of the colour and brightness of a monochromatic light upon its angle of incidence on the retina,” J. Physiol. (London) 338, 651–668 (1983).

Thibos, L. N.

L. N. Thibos, A. Bradley, D. L. Still, “Interferometric measurement of visual acuity and the effect of ocular chromatic aberration,” Appl. Opt. 30, 2079–2087 (1991).
[CrossRef] [PubMed]

A. Bradley, L. N. Thibos, “Modeling off-axis vision I: The optical effects of decentering visual targets or the eye’s entrance pupil,” in Vision Models for Target Detection and Recognition: In Memory of Arthur Menendez, A. R. Menendez, E. Peli, eds. (World Scientific, River Edge, N.J., 1995), pp. 313–337.

van de Kraats, J.

J. van de Kraats, T. T. Berendschot, D. van Norren, “The pathways of light measured in funds reflectometry,” Vision Res. 36, 2229–2247 (1996).
[CrossRef] [PubMed]

van Meeteren, A.

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupils,” Vision Res. 23, 573–579 (1983).
[CrossRef] [PubMed]

van Norren, D.

J. van de Kraats, T. T. Berendschot, D. van Norren, “The pathways of light measured in funds reflectometry,” Vision Res. 36, 2229–2247 (1996).
[CrossRef] [PubMed]

Walsh, G.

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

Wijngaard, W.

W. Wijngaard, “Theoretical consideration of optical interactions in an array of retinal receptors,” in Vertebrate Photoreceptor Optics, J. M. Enoch, F. L. Tobey, eds. (Springer-Verlag, Berlin, 1981), pp. 301–323.

Williams, D. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

Wright, W. D.

W. D. Wright, J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
[CrossRef]

Appl. Opt. (1)

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

M. J. McMahon, D. I. A. MacLeod, “Visual resolution with obliquely incident light: retinal contrast losses,” Invest. Ophthalmol. Visual Sci. Suppl. 41/4, S100 (2000).

J. Opt. Soc. Am. (2)

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

J. Physiol. (London) (5)

M. Alpern, K. Kitahara, R. Tamaki, “The dependence of the colour and brightness of a monochromatic light upon its angle of incidence on the retina,” J. Physiol. (London) 338, 651–668 (1983).

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

F. W. Campbell, “A retinal acuity direction effect,” J. Physiol. (London) 144, 25P–26P (1958).

D. G. Green, “Visual resolution when light enters the eye through different parts of the pupil,” J. Physiol. (London) 190, 583–593 (1967).

B. Chen, W. Makous, “Light capture by human cones,” J. Physiol. (London) 414, 89–109 (1989).

Opt. Acta (London) (1)

J. M. Enoch, W. S. Stiles, “The colour change of monochromatic light with retinal angle of incidence,” Opt. Acta (London) 8, 329–358 (1961).
[CrossRef]

Proc. Phys. Soc. London (1)

W. D. Wright, J. H. Nelson, “The relation between the apparent intensity of a beam of light and the angle at which the beam strikes the retina,” Proc. Phys. Soc. London 48, 401–405 (1936).
[CrossRef]

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. (9)

S. He, D. I. MacLeod, “Contrast-modulation flicker: dynamics and spatial resolution of the light adaptation process,” Vision Res. 38, 985–1000 (1998).
[CrossRef] [PubMed]

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

L. J. Bour, N. J. Lopes Cardozo, “On the birefringence of the living human eye,” Vision Res. 21, 1413–1421 (1981).
[CrossRef] [PubMed]

C. Pask, A. Stacey, “Optical properties of retinal photoreceptors and the Campbell effect,” Vision Res. 38, 953–961 (1998).
[CrossRef] [PubMed]

A. van Meeteren, C. J. W. Dunnewold, “Image quality of the human eye for eccentric entrance pupils,” Vision Res. 23, 573–579 (1983).
[CrossRef] [PubMed]

P. Artal, S. Marcos, I. Iglesias, D. G. Green, “Optical modulation transfer and contrast sensitivity with decentered small pupils in the human eye,” Vision Res. 36, 3575–3586 (1996).
[CrossRef] [PubMed]

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

D. I. MacLeod, D. R. Williams, W. Makous, “A visual nonlinearity fed by single cones,” Vision Res. 32, 347–363 (1992).
[CrossRef] [PubMed]

J. van de Kraats, T. T. Berendschot, D. van Norren, “The pathways of light measured in funds reflectometry,” Vision Res. 36, 2229–2247 (1996).
[CrossRef] [PubMed]

Other (8)

A. Bradley, L. N. Thibos, “Modeling off-axis vision I: The optical effects of decentering visual targets or the eye’s entrance pupil,” in Vision Models for Target Detection and Recognition: In Memory of Arthur Menendez, A. R. Menendez, E. Peli, eds. (World Scientific, River Edge, N.J., 1995), pp. 313–337.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999).

S. A. Klein, “Photoreceptor waveguides—a simple approach,” in Basic and Clinical Applications of Vision Science: The Professor Jay M. Enoch Festschrift Volume, V. Lakshminarayanan, ed. (Kluwer Academic, Boston, Mass., 1997), pp. 37–41.

W. Wijngaard, “Theoretical consideration of optical interactions in an array of retinal receptors,” in Vertebrate Photoreceptor Optics, J. M. Enoch, F. L. Tobey, eds. (Springer-Verlag, Berlin, 1981), pp. 301–323.

J. M. Enoch, F. L. Tobey, eds., Vertebrate Photoreceptor Optics (Springer-Verlag, Berlin, 1981).

J. M. Enoch, “Retinal directional resolution,” in Visual Science: Proceedings of the 1968 International Symposium, J. R. Pierce, J. R. Levene, eds. (Indiana U. Press, Bloomington, Ind., 1971).

W. Makous, J. Schnapf, “Two components of the Stiles–Crawford effect: cone aperture and disarray,” presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Sarasota, Fla., May 3–7, 1973.

J. Schnapf, W. Makous, “Individually adaptable optical channels in human retina,” presented at the annual meeting of the Association for Research in Vision and Ophthalmology, Sarasota, Fla., April 25–29, 1974.

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Figures (6)

Fig. 1
Fig. 1

Effective fringe contrast as a function of point source intensity ratio. Measurements of fringe contrast were made over a 2-log-unit range of point source intensity ratios to determine the optimal intensity ratio for maximizing fringe contrast. The 0 log (point source intensity ratio) denotes the x axis position that equates the beams for brightness, with a deviation from physical equality to compensate for the Stiles–Crawford effect. The black arrows pointing to the x axis mark the point source intensity ratio for physical equality. The smooth curves are theoretical fits to the measured contrast values (see Appendix A). Solid diamonds above the curves show the fitted optimal point source intensity ratio for maximum fringe contrast, with horizontal error bars enclosing the 95% confidence interval. All three conditions yielded maximum fringe contrast at a point source intensity value that was not statistically different from Stiles–Crawford equality.

Fig. 2
Fig. 2

Effect of oblique incidence on grating contrast. Each panel shows the measured fringe contrast for a 51-c/deg spatial-frequency grating (68 c/deg for panel (d)). White bars, point sources centered on the Stiles-Crawford peak. Light-gray bars, point sources displaced parallel to the bars of the grating. Dark-gray bars, point sources displaced perpendicular to the grating bars. The results demonstrate a small decrease in fringe contrast with oblique incidence. Unlike the original Campbell result,3 the decrease in contrast was no greater for displacements perpendicular to the bars of the grating than for displacements parallel to the bars of the grating. A 2.5-mm displacement of the point sources [(b)] produced a larger decrease in fringe contrast than a 1.5-mm displacement [(a)]. Error bars represent ±SEM.

Fig. 3
Fig. 3

Spatial-frequency dependence of the decreased contrast with oblique incidence. Data points represent the difference in log fringe contrast between centered point entry and a 2.5-mm temporal displacement parallel to the bars of the grating for that spatial frequency. This decrease in log fringe contrast with oblique incidence is measured as a function of spatial frequency for two observers, MM and DM. Error bars=±SEM. Also shown are Gaussian fits to the data from Chen and Makous.14

Fig. 4
Fig. 4

Cone light-capture scenarios. Three simple cone light-capture models. In (a) light is perfectly waveguided by the cones. This model predicts no loss in resolution or sensitivity with oblique incidence. Model (b) proposes that obliquely incident light escapes from the cone and produces no visual effect. This type of model is often suggested to explain the large decrease in perceived brightness with obliquely incident light (the Stiles–Crawford effect). Model (c) proposes that some of the light that leaks from a cone is recaptured by a neighboring cone. This scenario results in a decrease in fringe contrast with oblique incidence. The simple case of this model, where light travels straight through a receptor, predicts a loss in resolution for grating oriented perpendicular to the pupil displacement, but not for parallel displacements.

Fig. 5
Fig. 5

Spatial extent of the retinal blurring produced by oblique incidence. The point-spread function for obliquely incident light was assumed to be the convolution of the spread function for a centered point source with a Gaussian blur function. The calculated Gaussian spatial blurring profile for oblique incidence is shown and is compared graphically with the cone outer segment length, width, and spacing (1 µm width, 40 µm length, and 2.3 µm spacing). The straight line across the outer segments illustrates the angle of incidence associated with a 2.5-mm shift from Stiles–Crawford peak in the plane of the pupil (approximately 7°). The spatial blur function derived from our measurements demonstrates that the blurring with oblique incidence is small in comparison with the size and spacing of foveal cones.

Fig. 6
Fig. 6

Retinal contribution to loss of resolution with oblique incidence. The smooth curve shows CRT grating contrast sensitivity measured by Green9 through a displaced, 2-mm artificial pupil. The inset shows an expanded view of the spatial-frequency range near the resolution limit, which is 19.4 c/deg for Green’s measurements. The inset also shows the resolution limit calculated after removal of the retinal contribution: 19.5 c/deg. The loss in resolution based on the simple geometrical model in which light tracks straight through the cone outer segments [Figs. 4(c) and 5] is also shown. This loss in resolution is calculated by estimating the sampling aperture for obliquely incident light as the convolution of the sampling aperture for central entry with a rectangular function given by the lateral distance across the cone outer segments subtended by the obliquely incident ray. This simple model, which simulates a complete lack of waveguiding, would lower the resolution limit to 18.9 c/deg.

Equations (19)

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NA(CE)2.
C=2I1I2I1+I2.
C=2xx+1.
NA4x(x+1)2.
log(CE)=km1+log4 * 10(x-m2)(10(x-m2)+1)22,
f(x)=1σ2π exp-x22σ2,
I1(x)=I1 exp-(x1-x)22s2,
ΔI(x)=2I1(x)I2(x)=2I1I2 exp-(x1-x)2+(x2-x)24s2.
C=f(x)ΔI(x)dxf(x)I1(x)dx+f(x)I2(x)dx.
f(x)I1(x)dx=I1S(x1)=I1 exp-x122(s2+σ2).
C=kI1I2I1S(x1)+I2S(x2).
I1=expx122(s2+σ2),I2=expx222(s2+σ2).
ΔI(x)=2 expx12+x224(s2+σ2)×exp-x22s2+x (x1+x2)2s2-(x12+x22)4s2,
2/πσ exp-x2 (s2+σ2)2s2σ2+x (x1+x2)2s2-(x12+x22) σ24s2(s2+σ2).
2/πσ exp-xs2+σ22s2σ2-(x1+x2)σ28s2(s2+σ2)2+(x1+x2)2 σ28s2(s2+σ2)×exp-(x12+x22) σ24s2(s2+σ2),
f(x)ΔI(x)dx=2ss2+σ2×exp-(x1-x2)2 σ28s2(s2+σ2).
f(x)I1(x)=1σ2π exp-x22σ2×expx122(s2+σ2)-(x1-x)22s2,
f(x)I1(x)=1σ2π exp-xs2+σ22s2σ2-x1σ2s2(s2+σ2)2.
C=exp-(x1-x2)2 σ28s2(s2+σ2).

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