Abstract

Point-spread functions (PSF’s) of human eyes at medium pupil size (3.5 mm) were derived from double-pass measurements. It was demonstrated that reliable information on PSF shape in the central 7-arcmin radius can be obtained in spite of uncertainty about the height and extent of the tail of the double-pass image. Measurements from some healthy young eyes (of subjects 21–31 years old) and several older eyes (of subjects 63–75 years old) with good acuity revealed little difference in the half-width at half-height of the PSF, but, owing to the higher tail in their PSF’s, the Strehl ratio of the older eyes is much lower. Computation of the modulation transfer functions of the older eyes revealed a more prominent loss at low spatial frequencies.

© 1995 Optical Society of America

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References

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  1. F. Flamant, “Etude de la repartition de lumière dans l’image rétinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).
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    [Crossref] [PubMed]
  3. F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 559–579 (1966).
  4. 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]
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    [Crossref]
  6. W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
    [Crossref] [PubMed]
  7. G. Westheimer, J. Liang, “Evaluating diffusion of light in the eye by objective means,” Invest. Ophthalmol. Vis. Sci. 35, 2652–2657 (1994).
    [PubMed]
  8. J. W. Goodmann, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 90–96.
  9. J. F. Simon, P. M. Denieul, “Influence of the size of the test field employed in measurements of the modulation transfer function of the eye,” J. Opt. Soc. Am. 63, 894–896 (1973).
    [Crossref] [PubMed]
  10. W. N. Charman, J. A. M. Jennings, “Merits of the Gaussian moment in judging optical line-spread widths,” Vision Res. 19, 851–852 (1979).
    [Crossref]
  11. 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]
  12. R. W. Gubisch, “Optical performance of the human eye,” J. Opt. Soc. Am. 57, 408–415 (1967).
    [Crossref]
  13. R. Navarro, P. Artal, D. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
    [Crossref] [PubMed]
  14. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 311.

1995 (1)

1994 (2)

G. Westheimer, J. Liang, “Evaluating diffusion of light in the eye by objective means,” Invest. Ophthalmol. Vis. Sci. 35, 2652–2657 (1994).
[PubMed]

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]

1993 (1)

1987 (1)

1985 (1)

W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
[Crossref] [PubMed]

1979 (1)

W. N. Charman, J. A. M. Jennings, “Merits of the Gaussian moment in judging optical line-spread widths,” Vision Res. 19, 851–852 (1979).
[Crossref]

1973 (1)

1967 (1)

R. W. Gubisch, “Optical performance of the human eye,” J. Opt. Soc. Am. 57, 408–415 (1967).
[Crossref]

1966 (1)

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 559–579 (1966).

1962 (1)

1955 (1)

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

Artal, P.

Bescós, J.

Brainard, D. H.

Campbell, F. W.

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 559–579 (1966).

G. Westheimer, F. W. Campbell, “Light distribution in the image formed by the living human eye,” J. Opt. Soc. Am. 52, 1040–1045 (1962).
[Crossref] [PubMed]

Charman, W. N.

W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
[Crossref] [PubMed]

W. N. Charman, J. A. M. Jennings, “Merits of the Gaussian moment in judging optical line-spread widths,” Vision Res. 19, 851–852 (1979).
[Crossref]

Denieul, P. M.

Flamant, F.

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

Goodmann, J. W.

J. W. Goodmann, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 90–96.

Gubisch, R. W.

R. W. Gubisch, “Optical performance of the human eye,” J. Opt. Soc. Am. 57, 408–415 (1967).
[Crossref]

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 559–579 (1966).

Jennings, J. A. M.

W. N. Charman, J. A. M. Jennings, “Merits of the Gaussian moment in judging optical line-spread widths,” Vision Res. 19, 851–852 (1979).
[Crossref]

Liang, J.

G. Westheimer, J. Liang, “Evaluating diffusion of light in the eye by objective means,” Invest. Ophthalmol. Vis. Sci. 35, 2652–2657 (1994).
[PubMed]

Marcos, S.

McMahon, M. J.

Navarro, R.

Santamaría, J.

Simon, J. F.

Smith, W. J.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 311.

Walsh, G.

W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
[Crossref] [PubMed]

Westheimer, G.

G. Westheimer, J. Liang, “Evaluating diffusion of light in the eye by objective means,” Invest. Ophthalmol. Vis. Sci. 35, 2652–2657 (1994).
[PubMed]

G. Westheimer, F. W. Campbell, “Light distribution in the image formed by the living human eye,” J. Opt. Soc. Am. 52, 1040–1045 (1962).
[Crossref] [PubMed]

Williams, D.

Williams, D. R.

Invest. Ophthalmol. Vis. Sci. (1)

G. Westheimer, J. Liang, “Evaluating diffusion of light in the eye by objective means,” Invest. Ophthalmol. Vis. Sci. 35, 2652–2657 (1994).
[PubMed]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (4)

J. Physiol. (London) (1)

F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 559–579 (1966).

Rev. Opt. (1)

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

Vision Res. (2)

W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception of spatial phase,” Vision Res. 25, 619–623 (1985).
[Crossref] [PubMed]

W. N. Charman, J. A. M. Jennings, “Merits of the Gaussian moment in judging optical line-spread widths,” Vision Res. 19, 851–852 (1979).
[Crossref]

Other (2)

J. W. Goodmann, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), pp. 90–96.

W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 311.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of double-pass procedure. The point source of monochromatic light P, the retina R, and the CCD camera plane D, are all conjugate with respect to the eye’s optics. The light distribution in D is the autocorrelation of the PSF of the eye. PB, pellicle beam splitter.

Fig. 2
Fig. 2

Analysis of the double-pass PSF for subject JL. Triangles, x direction; squares, y direction; circles, radial distribution averaged over all meridians. The subject’s aerial image is somewhat elliptical, with principal meridian 25°. (a) Original aerial image [g(x, 0), g(0, y), g(r)]; (b) constructed PSF’s [h(x, 0), h(0, y), h(r)]; (c) MTF’s [H(u, 0), H(0, v), H(r)]; (d) comparison of the original double-pass aerial image and the constructed PSF’s in terms of radial distribution averaged over all meridians for subject JL. The extent of the aerial image in this case is a square of 48 arcmin in the eye’s space.

Fig. 3
Fig. 3

Reconstruction of the radially averaged PSF for subject JL under three regimes of truncation of the double-pass data: 24′ × 24′, 40′ × 40′, and 48′ × 48′. Logarithmic scale on the ordinate axis.

Fig. 4
Fig. 4

Reconstruction of the radially averaged PSF for subject JL for the full 48′ × 48′ extent of the original aerial image, under three regimes of pedestal treatments: full pedestal as in the original data, pedestal reduced to 40%, and pedestal fully removed. Logarithmic scale on the ordinate axis.

Fig. 5
Fig. 5

(a) Averaged PSF’s of the young subjects and of the older subjects plotted with linear coordinates; (b) PSF’s of the young subjects and of the older subjects. Logarithmic scale on the ordinate axis. The error bars indicate the intersubject standard deviation within the age group.

Fig. 6
Fig. 6

Comparison of the averaged MTF of the young subjects with that of the older subjects.

Tables (3)

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Table 1 Parameters Characterizing Optical Performance of the Tested Eyesa

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Table 2 Strehl Ratios of the Tested Eyesa

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Table 3 Comparison of the MTF’s of Older Eyes with Those of Young Eyesa

Equations (7)

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

g ( x , y ) = h 0 ( x , y ) h 0 ( - x , - y ) + n ( x , y ) ,
G ( u , v ) = H 0 ( u , v ) H 0 * ( u , v ) + N ( u , v ) ,
H ( u , v ) = H 0 ( u , v ) + N ( u , v ) ,
H ( u , v ) = H 0 ( u , v ) + N ( u , v ) .
h ( x , y ) = h 0 ( x , y ) + n ( x , y ) ,
h 0 ( x , y ) = Re { h ( x , y ) } trunc ( x , y ) ,
trunc ( x , y ) = rect ( 2 x / L ) rect ( 2 y / L ) ,

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