Abstract

Foveal point-spread functions are computed from experimental wave-aberration data for individual emmetropic subjects. The effects of pupil size and image focus are considered in the calculations. Foveal images of extended test objects are generated from the point-spread functions corresponding to different image-quality situations. Wiener-filtered test objects are also computed to obtain a partial compensation of the spatial degradation introduced by the eye’s optical system in the visual process.

© 1990 Optical Society of America

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References

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  1. 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] [PubMed]
  2. P. Artal, J. Santamaría, J. Bescós, “Retrieval of the wave aberration of the human eyes from actual point-spread function data,” J. Opt. Soc. Am. A 5, 1201–1206 (1988).
    [CrossRef] [PubMed]
  3. 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]
  4. P. Artal, J. Santamaría, J. Bescós, “Optical-digital procedure for the determination of the retinal image of a point test in white light,” Opt. Eng. 28, 687–690 (1989).
    [CrossRef]
  5. P. Artal, “Incorporation of directional effects of the retina into the computations of the optical transfer function of human eyes,” J. Opt. Soc. Am. A 6, 1941–1944 (1989).
    [CrossRef] [PubMed]
  6. W. K. Pratt, Digital Image Processing (Wiley-Interscience, New York, 1978).
  7. F. W. Campbell, R. W. Gubisch, “Optical image quality of the human eye,” J. Physiol. (London) 186, 558–578 (1966).
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).
  9. G. Westheimer, “Pupil size and visual resolution,” Vision Res. 4, 39–45 (1964).
    [CrossRef] [PubMed]
  10. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  11. H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–102 (1955).
    [CrossRef]
  12. J. M. Otero, A. Duran, “Rendimiento fotometrico de sistemas opticos a bajas luminosidades,” Anal. Fis. Quim. 37, 459–477 (1941).
  13. M. Koomen, R. Skolnik, R. Tousey, “A study of night myopia,” J. Opt. Soc. Am. 41, 80–90 (1951).
    [CrossRef]
  14. G. 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]
  15. E. Peli, T. Peli, “Image enhancement for visually impaired,” Opt. Eng. 23, 47–51 (1984).
    [CrossRef]
  16. D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
    [CrossRef] [PubMed]
  17. 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]

1989 (3)

1988 (3)

1987 (2)

1984 (1)

E. Peli, T. Peli, “Image enhancement for visually impaired,” Opt. Eng. 23, 47–51 (1984).
[CrossRef]

1966 (1)

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

1965 (1)

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

1964 (1)

G. Westheimer, “Pupil size and visual resolution,” Vision Res. 4, 39–45 (1964).
[CrossRef] [PubMed]

1955 (1)

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–102 (1955).
[CrossRef]

1951 (1)

1941 (1)

J. M. Otero, A. Duran, “Rendimiento fotometrico de sistemas opticos a bajas luminosidades,” Anal. Fis. Quim. 37, 459–477 (1941).

Artal, P.

Bescós, J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Campbell, F. W.

G. 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, R. W. Gubisch, “Optical image quality of the human eye,” J. Physiol. (London) 186, 558–578 (1966).

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

Duran, A.

J. M. Otero, A. Duran, “Rendimiento fotometrico de sistemas opticos a bajas luminosidades,” Anal. Fis. Quim. 37, 459–477 (1941).

Green, D. G.

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

Gubisch, R. W.

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

Hopkins, H. H.

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–102 (1955).
[CrossRef]

Koomen, M.

Legge, G.

Mullen, K. T.

Navarro, R.

Otero, J. M.

J. M. Otero, A. Duran, “Rendimiento fotometrico de sistemas opticos a bajas luminosidades,” Anal. Fis. Quim. 37, 459–477 (1941).

Peli, E.

E. Peli, T. Peli, “Image enhancement for visually impaired,” Opt. Eng. 23, 47–51 (1984).
[CrossRef]

Peli, T.

E. Peli, T. Peli, “Image enhancement for visually impaired,” Opt. Eng. 23, 47–51 (1984).
[CrossRef]

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley-Interscience, New York, 1978).

Santamaría, J.

Skolnik, R.

Tousey, R.

Westheimer, G.

G. Westheimer, “Pupil size and visual resolution,” Vision Res. 4, 39–45 (1964).
[CrossRef] [PubMed]

Williams, D. R.

D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
[CrossRef] [PubMed]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

Woo, G. C.

Anal. Fis. Quim. (1)

J. M. Otero, A. Duran, “Rendimiento fotometrico de sistemas opticos a bajas luminosidades,” Anal. Fis. Quim. 37, 459–477 (1941).

J. Opt. Soc. Am. (1)

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

J. Physiol. (London) (2)

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

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

Opt. Eng. (2)

E. Peli, T. Peli, “Image enhancement for visually impaired,” Opt. Eng. 23, 47–51 (1984).
[CrossRef]

P. Artal, J. Santamaría, J. Bescós, “Optical-digital procedure for the determination of the retinal image of a point test in white light,” Opt. Eng. 28, 687–690 (1989).
[CrossRef]

Opt. Lett. (1)

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

H. H. Hopkins, “The frequency response of a defocused optical system,” Proc. R. Soc. London Ser. A 231, 91–102 (1955).
[CrossRef]

Vision Res. (2)

G. Westheimer, “Pupil size and visual resolution,” Vision Res. 4, 39–45 (1964).
[CrossRef] [PubMed]

D. R. Williams, “Topography of the foveal cone mosaic in the living human eye,” Vision Res. 28, 433–454 (1988).
[CrossRef] [PubMed]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1970).

W. K. Pratt, Digital Image Processing (Wiley-Interscience, New York, 1978).

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Figures (10)

Fig. 1
Fig. 1

Contour plot at Imax/10 intervals of the two-dimensional PSF of the eye of a normal and emmetropic subject (PA) with a slight residual astigmatism. It has been computed from the wave-aberration function with values of the pupil diameters from 2 to 6 mm.

Fig. 2
Fig. 2

Sections of two-dimensional modulation transfer functions (MTF’s) at 0 deg for pupil diameters (millimeters). (Numbers on curves indicate diameter in millimeters; C/DG is cycles per degree.)

Fig. 3
Fig. 3

The inverse of the Strehl ratio as a function of the pupil size for two emmetropic subjects, PA ( * * ) and JS , and a diffraction-limited system (- - - -).

Fig. 4
Fig. 4

Variations of an asymmetry parameter computed for two individual eyes and for an aberration-free system (- - - -).

Fig. 5
Fig. 5

(a) Original test object used in the computations. It corresponds to a section of the painting Guernica by Picasso (Prado Museum, Madrid). The geometrical image is 345 μm × 345 μm (1.2 deg × 1.2 deg) on the central fovea. (b) Foveal retinal image of the original object presented in (a) when it is illuminated in red light (632 nm) and viewed by an emmetropic subject with a 3-mm-diameter pupil. (c) Foveal retinal image of the original object in (a) viewed by the same subject as in (b) but with a 6-mm-diameter pupil.

Fig. 6
Fig. 6

Contour plots of the bidimensional PSF of the eye of an emmetropic subject (PA) with a slight residual astigmatism with 3-mm pupil diameter under different states of focus from −1 to 1 D.

Fig. 7
Fig. 7

Comparison of the Strehl ratio for two different subjects with different states of focus and for the following pupil sizes: 2-mm pupil diameter (– –), 3-mm pupil diameter (—), 4-mm pupil diameter (– - –), and 5-mm pupil diameter (– - - –). The figures on curves indicate the optimal focus (diopters) for each pupil diameter.

Fig. 8
Fig. 8

Depth of focus as a function of pupil size. The mean results for five emmetropic subjects computed from their wave-aberration results.

Fig. 9
Fig. 9

(a) Retinal image of the original test object of Fig. 5(a) for an emmetropic subject (PA) with −0.25 D of defocus. (b) Retinal image of the original object of Fig. 5(a) for an emmetropic subject (PA) with −1 D of defocus.

Fig. 10
Fig. 10

(a) Prefiltered image computed from the original Fig. 5(a) by means of a Wiener filter adapted to the OTF of the subject PA for a 6-mm pupil with a value of the filter’s parameter of 0.001. (b) Foveal retinal image of the prefiltered test (a) obtained under the same conditions of image quality (6-mm pupil diameter) as that presented in Fig. 5(c).

Equations (5)

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P s ( x , y ) = | 1 R 2 x 2 + y 2 R 2 exp [ ( i 2 π λ ) W ( x / R , y / R ) ] × exp [ i 2 π λ f R ( x x + y y ) ] d x d y | 2 ,
g ( x , y ) = f ( x 0 , y 0 ) P s ( x x 0 , y y 0 ) d x 0 d y 0 ,
W a ( x / R , y / R ) = W ( x / R , y / R ) + W 20 ( x 2 + y 2 ) / R 2 .
F w ( u , υ ) = H * ( u , υ ) | H ( u , υ ) | 2 + ϕ n ( u , υ ) ϕ f ( u , υ ) ,
f w ( x 0 , y 0 ) = f ( x 0 , y 0 ) FT 1 [ F w ( u , υ ) ] ,

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