Abstract

Two-dimensional optical transfer functions (OTF’s) of individual human eyes are computed from the retinal images of a point test object, using a phase-retrieval method. The retinal reflection directionality effect is included in the computations by means of an apodization pupil, and subsequently the Stiles–Crawford effect is also considered. The modulation transfer functions obtained when the retinal reflection directionality effect is considered show lower values of the modulation; on the other hand, their two-dimensional form and the corresponding phase transfer functions remain practically unchanged. The importance of the Stiles–Crawford apodization depends on the wave aberration of the individual subject, but in general it produces an improvement in image quality, and the modulation transfer function becomes more symmetrical.

© 1989 Optical Society of America

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References

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  1. M. F. Flamant, “Etude de la repartition de lumiere dans l’image retinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).
  2. J. Krauskopf, “Light distribution in human retinal images,”J. Opt. Soc. Am. 52, 1046–1050 (1962).
    [CrossRef]
  3. F. W. Campbell, R. W. Gubisch, “Optical performance of the human eye,”J. Physiol. (London) 186, 558–578 (1966).
  4. A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic-method for the dynamic study of the image formation by the human eye. Microfluctuations of the accommodation,” J. Opt. 12, 123–128 (1981).
    [CrossRef]
  5. J. Santamaría, 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]
  6. P. Artal, J. Santamaría, J. Bescós, “Retrieval of wave aberration of human eyes from actual point-spread-function data,” J. Opt. Soc. Am. A 5, 1201–1206 (1988).
    [CrossRef] [PubMed]
  7. F. Berny, “Correlation de phase entre deux sources formees sur un surface diffusante. Application a la retine humaine,” Vision Res. 12, 1631–1645 (1972).
    [CrossRef] [PubMed]
  8. J. M. Gorrand, “Diffusion of the human retina and quality of the optics of the eye on the fovea and peripheral retina,” Vision Res. 19, 907–912 (1979).
    [CrossRef]
  9. J. M. Gorrand, R. Alfieri, J. Y. Boire, “Diffusion of the retinal layers of the living human eyes,” Vision Res. 24, 1097–1106 (1984).
    [CrossRef]
  10. J. M. Gorrand, “Reflection characteristics of the human fovea assessed by reflecto-modulometry,” Ophthalmol. Physiol. Opt. 9, 53–60 (1989).
    [CrossRef]
  11. G. L. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
    [CrossRef]
  12. R. J. Deeley, N. Drasdo, “The effect of optical degradation on the contrast sensitivity function measured at the fovea and in the periphery,” Vision Res. 27, 1179–1186 (1987).
    [CrossRef] [PubMed]
  13. A. van Meeteren, “Calculations on the optical modulation function of the human eye for white light,” Opt. Acta 21, 395–412 (1972).
    [CrossRef]
  14. R. Navarro, J. Santamaría, J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273–1281 (1985).
    [CrossRef] [PubMed]
  15. G. L. van Blockland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 1791–1795 (1988).
  16. P. Artal, J. Santamaría, J. Bescós, “Phase transfer function of human eyes and its influence on the point-spread function and wave aberration,” J. Opt. Soc. Am. A 5, 1791–1795 (1988).
    [CrossRef] [PubMed]
  17. G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberration of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
    [CrossRef] [PubMed]
  18. G. Walsh, W. N. Charman, “Measure of the axial wavefront aberration of the human eye,” Ophthalmol. Physiol. Opt. 5, 23–31 (1985).
    [CrossRef]
  19. H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberration of the human eye,”J. Opt. Soc. Am. 67, 1508–1518 (1977).
    [CrossRef] [PubMed]

1989 (1)

J. M. Gorrand, “Reflection characteristics of the human fovea assessed by reflecto-modulometry,” Ophthalmol. Physiol. Opt. 9, 53–60 (1989).
[CrossRef]

1988 (3)

1987 (2)

R. J. Deeley, N. Drasdo, “The effect of optical degradation on the contrast sensitivity function measured at the fovea and in the periphery,” Vision Res. 27, 1179–1186 (1987).
[CrossRef] [PubMed]

J. Santamaría, 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]

1986 (1)

G. L. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef]

1985 (2)

R. Navarro, J. Santamaría, J. Bescós, “Accommodation-dependent model of the human eye with aspherics,” J. Opt. Soc. Am. A 2, 1273–1281 (1985).
[CrossRef] [PubMed]

G. Walsh, W. N. Charman, “Measure of the axial wavefront aberration of the human eye,” Ophthalmol. Physiol. Opt. 5, 23–31 (1985).
[CrossRef]

1984 (2)

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberration of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

J. M. Gorrand, R. Alfieri, J. Y. Boire, “Diffusion of the retinal layers of the living human eyes,” Vision Res. 24, 1097–1106 (1984).
[CrossRef]

1981 (1)

A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic-method for the dynamic study of the image formation by the human eye. Microfluctuations of the accommodation,” J. Opt. 12, 123–128 (1981).
[CrossRef]

1979 (1)

J. M. Gorrand, “Diffusion of the human retina and quality of the optics of the eye on the fovea and peripheral retina,” Vision Res. 19, 907–912 (1979).
[CrossRef]

1977 (1)

1972 (2)

F. Berny, “Correlation de phase entre deux sources formees sur un surface diffusante. Application a la retine humaine,” Vision Res. 12, 1631–1645 (1972).
[CrossRef] [PubMed]

A. van Meeteren, “Calculations on the optical modulation function of the human eye for white light,” Opt. Acta 21, 395–412 (1972).
[CrossRef]

1966 (1)

F. W. Campbell, R. W. Gubisch, “Optical performance of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

1962 (1)

1955 (1)

M. F. Flamant, “Etude de la repartition de lumiere dans l’image retinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).

Alfieri, R.

J. M. Gorrand, R. Alfieri, J. Y. Boire, “Diffusion of the retinal layers of the living human eyes,” Vision Res. 24, 1097–1106 (1984).
[CrossRef]

Arnulf, A.

A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic-method for the dynamic study of the image formation by the human eye. Microfluctuations of the accommodation,” J. Opt. 12, 123–128 (1981).
[CrossRef]

Artal, P.

Berny, F.

F. Berny, “Correlation de phase entre deux sources formees sur un surface diffusante. Application a la retine humaine,” Vision Res. 12, 1631–1645 (1972).
[CrossRef] [PubMed]

Bescós, J.

Boire, J. Y.

J. M. Gorrand, R. Alfieri, J. Y. Boire, “Diffusion of the retinal layers of the living human eyes,” Vision Res. 24, 1097–1106 (1984).
[CrossRef]

Campbell, F. W.

F. W. Campbell, R. W. Gubisch, “Optical performance of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

Charman, W. N.

G. Walsh, W. N. Charman, “Measure of the axial wavefront aberration of the human eye,” Ophthalmol. Physiol. Opt. 5, 23–31 (1985).
[CrossRef]

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberration of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

Deeley, R. J.

R. J. Deeley, N. Drasdo, “The effect of optical degradation on the contrast sensitivity function measured at the fovea and in the periphery,” Vision Res. 27, 1179–1186 (1987).
[CrossRef] [PubMed]

Drasdo, N.

R. J. Deeley, N. Drasdo, “The effect of optical degradation on the contrast sensitivity function measured at the fovea and in the periphery,” Vision Res. 27, 1179–1186 (1987).
[CrossRef] [PubMed]

Flamant, M. F.

M. F. Flamant, “Etude de la repartition de lumiere dans l’image retinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).

Gorrand, J. M.

J. M. Gorrand, “Reflection characteristics of the human fovea assessed by reflecto-modulometry,” Ophthalmol. Physiol. Opt. 9, 53–60 (1989).
[CrossRef]

J. M. Gorrand, R. Alfieri, J. Y. Boire, “Diffusion of the retinal layers of the living human eyes,” Vision Res. 24, 1097–1106 (1984).
[CrossRef]

J. M. Gorrand, “Diffusion of the human retina and quality of the optics of the eye on the fovea and peripheral retina,” Vision Res. 19, 907–912 (1979).
[CrossRef]

Gubisch, R. W.

F. W. Campbell, R. W. Gubisch, “Optical performance of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

Howland, B.

Howland, H. C.

Krauskopf, J.

Navarro, R.

Santamaría, J.

van Blockland, G. L.

G. L. van Blockland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 1791–1795 (1988).

G. L. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef]

van Meeteren, A.

A. van Meeteren, “Calculations on the optical modulation function of the human eye for white light,” Opt. Acta 21, 395–412 (1972).
[CrossRef]

van Norren, D.

G. L. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef]

Walsh, G.

G. Walsh, W. N. Charman, “Measure of the axial wavefront aberration of the human eye,” Ophthalmol. Physiol. Opt. 5, 23–31 (1985).
[CrossRef]

G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberration of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
[CrossRef] [PubMed]

J. Opt. (1)

A. Arnulf, J. Santamaría, J. Bescós, “A cinematographic-method for the dynamic study of the image formation by the human eye. Microfluctuations of the accommodation,” J. Opt. 12, 123–128 (1981).
[CrossRef]

J. Opt. Soc. Am. (2)

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

J. Physiol. (London) (1)

F. W. Campbell, R. W. Gubisch, “Optical performance of the human eye,”J. Physiol. (London) 186, 558–578 (1966).

Ophthalmol. Physiol. Opt. (2)

J. M. Gorrand, “Reflection characteristics of the human fovea assessed by reflecto-modulometry,” Ophthalmol. Physiol. Opt. 9, 53–60 (1989).
[CrossRef]

G. Walsh, W. N. Charman, “Measure of the axial wavefront aberration of the human eye,” Ophthalmol. Physiol. Opt. 5, 23–31 (1985).
[CrossRef]

Opt. Acta (1)

A. van Meeteren, “Calculations on the optical modulation function of the human eye for white light,” Opt. Acta 21, 395–412 (1972).
[CrossRef]

Rev. Opt. (1)

M. F. Flamant, “Etude de la repartition de lumiere dans l’image retinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).

Vision Res. (6)

G. L. van Blockland, “Directionality and alignment of the foveal receptors, assessed with light scattered from the human fundus in vivo,” Vision Res. 26, 1791–1795 (1988).

G. L. van Blockland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision Res. 26, 485–494 (1986).
[CrossRef]

R. J. Deeley, N. Drasdo, “The effect of optical degradation on the contrast sensitivity function measured at the fovea and in the periphery,” Vision Res. 27, 1179–1186 (1987).
[CrossRef] [PubMed]

F. Berny, “Correlation de phase entre deux sources formees sur un surface diffusante. Application a la retine humaine,” Vision Res. 12, 1631–1645 (1972).
[CrossRef] [PubMed]

J. M. Gorrand, “Diffusion of the human retina and quality of the optics of the eye on the fovea and peripheral retina,” Vision Res. 19, 907–912 (1979).
[CrossRef]

J. M. Gorrand, R. Alfieri, J. Y. Boire, “Diffusion of the retinal layers of the living human eyes,” Vision Res. 24, 1097–1106 (1984).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Contour plot at 0.1 intervals, of the two-dimensional MTF, M(u, v), of an emmetropized subject with a 5-mm pupil diameter. Results were obtained in foveal vision, with monochromatic incident light (632 nm) without consideration of retinal directionalities in the calculations. (b) Contour plot at 10-deg intervals of the two-dimensional phase transfer function (PTF), O(u, v), for the same subject and conditions as in Fig. 1(a). c/dg, Cycles per degree.

Fig. 2
Fig. 2

(a) Contour plot at 0.1 intervals of the two-dimensional MTF, Md(u, v), obtained when the directionality of the retinal reflection is included in the computations, for the same subject as in Fig. 1. (b) Contour plot at 10-deg intervals of the two-dimensional PTF with consideration of retinal reflection directionality, Qd(u, v), for the same subject and conditions as in (a). c/dg, Cycles per degree.

Fig. 3
Fig. 3

Contour plot at 0.1 intervals of the two-dimensional MTF, Ms(u, v), with the incorporation of the Stiles–Crawford effect after the consideration of retinal reflection directionality. c/dg, Cycles per degree.

Fig. 4
Fig. 4

Comparison of sections of the MTF’s at 0 deg: ×, M(u, v) with no consideration of directional effects [Fig. 1(a)]; ○, Md(u, v) with the retinal reflection directionality incorporated into the computations [Fig. 2(a)]; •, Ms(u, v) also with incorporation of the Stiles–Crawford effect (Fig. 3). c/dg, Cycles per degree.

Equations (3)

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p d ( α , β ) = exp ( - 0.108 R 2 r 2 ) if α 2 + β 2 < 1 = 0 if α 2 + β 2 1 ,
H d ( u , v ) = { p ( α , β ) exp [ i W d ( α , β ) ] } * { p ( α , β ) exp [ i W d ( α , β ) ] } ,
H s ( u , v ) = { p d ( α , β ) exp [ i W d ( α , β ) ] } * { p d ( α , β ) exp [ i W d ( α , β ) ] } .

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