Abstract

A method for the determination of the bidimensional optical transfer function (OTF) and the point-spread function of human eyes is presented. Aerial short-term images of a point source are directly recorded with a TV camera and fed into a digital image-processing system that allows one to determine and display such functions. The method has been implemented in such a way that recording and computation can be carried out on a routine basis with minimum discomfort for the observer. A detailed description of the method and typical aerial and retinal images of a point source as well as the OTF’s results are presented in this paper.

© 1987 Optical Society of America

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References

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  1. M. F. Flamant, “Etude de la répartition de lumière dans l’image rétinienne 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 quality of the human eye,”J. Physiol. (London) 186, 558–578 (1966).
  4. R. W. Gubisch, “Optical performance of the human eye,”J. Opt. Soc. Am 57, 407–415 (1967).
    [CrossRef]
  5. R. Röhler, U. Miller, M. Aberl, “Zur Messung der Modulationsübertragungsfunktion des lebenden menschlichen Auges im reflektierten Licht,” Vision. Res. 9, 407–428 (1969).
    [CrossRef]
  6. J. A. M. Jennings, W. N. Charman, “Off-axis image quality in human eye,” Vision. Res. 21, 445–454 (1981).
    [CrossRef]
  7. P. Denieul, “Effects of stimulus vergence on mean accomodation response, microfluctuations of accomodation and optical quality of the human eye,” Vision. Res. 22, 561–569 (1982).
    [CrossRef]
  8. G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
    [CrossRef] [PubMed]
  9. 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]
  10. J. Santamaría, A. Plaza, J. Bescós, “Dynamic recording of the binocular point spread function of the eye optical system,” Opt. Appl. 24, 341–347 (1984).
  11. D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).
  12. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  13. 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]
  14. R. A. Weale, “Polarized light and the human fondus oculi,” J. Physiol. (London) 186, 175–186 (1966).
  15. W. N. Charman, “Reflection of the plane-polarized light by the retina,” Br. J. Physiol. Opt. 34, 34–49 (1980).
  16. J. G. van Blokland, D. van Norren, “Intensity and polarization of light scattered at small angles from the human fovea,” Vision. Res. 26, 485–494 (1986).
    [CrossRef] [PubMed]
  17. D. O’Leary, M. Millodot, “The discrepancy between retinos-copy and subjective refraction: effect of light polarization,” Am. J. Optom. Physiol. Opt. 55, 553–556 (1978).
    [CrossRef]
  18. W. K. Pratt, Digital Image Processing (Wiley, New York, 1978).

1986 (1)

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

1985 (1)

1984 (2)

J. Santamaría, A. Plaza, J. Bescós, “Dynamic recording of the binocular point spread function of the eye optical system,” Opt. Appl. 24, 341–347 (1984).

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

1982 (1)

P. Denieul, “Effects of stimulus vergence on mean accomodation response, microfluctuations of accomodation and optical quality of the human eye,” Vision. Res. 22, 561–569 (1982).
[CrossRef]

1981 (2)

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. A. M. Jennings, W. N. Charman, “Off-axis image quality in human eye,” Vision. Res. 21, 445–454 (1981).
[CrossRef]

1980 (1)

W. N. Charman, “Reflection of the plane-polarized light by the retina,” Br. J. Physiol. Opt. 34, 34–49 (1980).

1978 (1)

D. O’Leary, M. Millodot, “The discrepancy between retinos-copy and subjective refraction: effect of light polarization,” Am. J. Optom. Physiol. Opt. 55, 553–556 (1978).
[CrossRef]

1969 (1)

R. Röhler, U. Miller, M. Aberl, “Zur Messung der Modulationsübertragungsfunktion des lebenden menschlichen Auges im reflektierten Licht,” Vision. Res. 9, 407–428 (1969).
[CrossRef]

1967 (1)

R. W. Gubisch, “Optical performance of the human eye,”J. Opt. Soc. Am 57, 407–415 (1967).
[CrossRef]

1966 (2)

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

R. A. Weale, “Polarized light and the human fondus oculi,” J. Physiol. (London) 186, 175–186 (1966).

1962 (1)

1955 (1)

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

Aberl, M.

R. Röhler, U. Miller, M. Aberl, “Zur Messung der Modulationsübertragungsfunktion des lebenden menschlichen Auges im reflektierten Licht,” Vision. Res. 9, 407–428 (1969).
[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]

Bescós, J.

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]

J. Santamaría, A. Plaza, J. Bescós, “Dynamic recording of the binocular point spread function of the eye optical system,” Opt. Appl. 24, 341–347 (1984).

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]

Campbell, F. W.

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

Charman, W. N.

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

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in human eye,” Vision. Res. 21, 445–454 (1981).
[CrossRef]

W. N. Charman, “Reflection of the plane-polarized light by the retina,” Br. J. Physiol. Opt. 34, 34–49 (1980).

Denieul, P.

P. Denieul, “Effects of stimulus vergence on mean accomodation response, microfluctuations of accomodation and optical quality of the human eye,” Vision. Res. 22, 561–569 (1982).
[CrossRef]

Flamant, M. F.

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gubisch, R. W.

R. W. Gubisch, “Optical performance of the human eye,”J. Opt. Soc. Am 57, 407–415 (1967).
[CrossRef]

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

Howland, H. C.

Jennings, J. A. M.

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in human eye,” Vision. Res. 21, 445–454 (1981).
[CrossRef]

Krauskopf, J.

Miller, U.

R. Röhler, U. Miller, M. Aberl, “Zur Messung der Modulationsübertragungsfunktion des lebenden menschlichen Auges im reflektierten Licht,” Vision. Res. 9, 407–428 (1969).
[CrossRef]

Millodot, M.

D. O’Leary, M. Millodot, “The discrepancy between retinos-copy and subjective refraction: effect of light polarization,” Am. J. Optom. Physiol. Opt. 55, 553–556 (1978).
[CrossRef]

Navarro, R.

O’Leary, D.

D. O’Leary, M. Millodot, “The discrepancy between retinos-copy and subjective refraction: effect of light polarization,” Am. J. Optom. Physiol. Opt. 55, 553–556 (1978).
[CrossRef]

Plaza, A.

J. Santamaría, A. Plaza, J. Bescós, “Dynamic recording of the binocular point spread function of the eye optical system,” Opt. Appl. 24, 341–347 (1984).

Pratt, W. K.

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

Röhler, R.

R. Röhler, U. Miller, M. Aberl, “Zur Messung der Modulationsübertragungsfunktion des lebenden menschlichen Auges im reflektierten Licht,” Vision. Res. 9, 407–428 (1969).
[CrossRef]

Santamaría, J.

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]

J. Santamaría, A. Plaza, J. Bescós, “Dynamic recording of the binocular point spread function of the eye optical system,” Opt. Appl. 24, 341–347 (1984).

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]

Sliney, D.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).

van Blokland, J. G.

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

van Norren, D.

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

Walsh, G.

Weale, R. A.

R. A. Weale, “Polarized light and the human fondus oculi,” J. Physiol. (London) 186, 175–186 (1966).

Wolbarsht, M.

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).

Am. J. Optom. Physiol. Opt. (1)

D. O’Leary, M. Millodot, “The discrepancy between retinos-copy and subjective refraction: effect of light polarization,” Am. J. Optom. Physiol. Opt. 55, 553–556 (1978).
[CrossRef]

Br. J. Physiol. Opt. (1)

W. N. Charman, “Reflection of the plane-polarized light by the retina,” Br. J. Physiol. Opt. 34, 34–49 (1980).

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 (1)

R. W. Gubisch, “Optical performance of the human eye,”J. Opt. Soc. Am 57, 407–415 (1967).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J. Physiol. (London) (2)

R. A. Weale, “Polarized light and the human fondus oculi,” J. Physiol. (London) 186, 175–186 (1966).

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

Opt. Appl. (1)

J. Santamaría, A. Plaza, J. Bescós, “Dynamic recording of the binocular point spread function of the eye optical system,” Opt. Appl. 24, 341–347 (1984).

Rev. Opt. (1)

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

Vision. Res. (4)

R. Röhler, U. Miller, M. Aberl, “Zur Messung der Modulationsübertragungsfunktion des lebenden menschlichen Auges im reflektierten Licht,” Vision. Res. 9, 407–428 (1969).
[CrossRef]

J. A. M. Jennings, W. N. Charman, “Off-axis image quality in human eye,” Vision. Res. 21, 445–454 (1981).
[CrossRef]

P. Denieul, “Effects of stimulus vergence on mean accomodation response, microfluctuations of accomodation and optical quality of the human eye,” Vision. Res. 22, 561–569 (1982).
[CrossRef]

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

Other (3)

D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for recording the aerial image of a point test. M, microscope objective; O, pinhole; ND, density filter; BS, beam splitter; A, analyzer; T, timer; C, TV camera; α, angle of incidence.

Fig. 2
Fig. 2

Typical aerial short-term images for observer PA.

Fig. 3
Fig. 3

Isometric plots of simulated images. (a) Typical short-term image. (b) Aerial image computed by autoconvolution of the PSF.

Fig. 4
Fig. 4

Isometric plots of simulated images. (a) Averaged image of 16 short-term images. (b) Averaged image of 128 short-term images.

Fig. 5
Fig. 5

Averaged aerial images for subject PA: (a) with reflected light-maintaining polarization and (b) with all reflected light.

Fig. 6
Fig. 6

(a) Averaged aerial image, (b) PSF, and (c) MTF, and their corresponding isometric plots for observer PA; c/dg, cycles per degree.

Fig. 7
Fig. 7

(a) Averaged aerial image, (b) PSF, and (c) MTF, and their corresponding isometric plots for observer JS.

Fig. 8
Fig. 8

Comparison of the mean MTF of Campbell and Gubisch3 (short-dashed line) and two different sections of the MTF for subject JS at 45 deg (long-dashed line) and −45 deg (solid line).

Equations (10)

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O i ( x , y ) = { [ O ( x , y ) A ( x , y ) ] × R i ( x , y ) } A ( x , y ) = [ O ( x , y ) × R i ( x , y ) ] A ( x , y ) ,
I i ( x , y ) = O i ( x , y ) 2 = [ A ( x , y ) × R i ( x , y ) ] A ( x , y ) 2 .
I ( x , y ) = ( 1 / N ) × I i ( x , y ) = A ( x , y ) 2 A ( x , y ) 2 ,
P ( α , β ) = exp { i k [ W 20 ( α 2 + β 2 ) + W 40 ( α 2 + β 2 ) 2 + W 22 α 2 ] } if α 2 + β 2 < 1 , P ( α , β ) = 0 if α 2 + β 2 1 ,
= [ I a ( x , y ) - I ( x , y ) ] 2 / [ I ( x , y ) ] 2 ,
I ( x , y ) = P s ( x , y ) P s ( x , y ) ,
I ( x , y ) = ( 1 / N ) [ I i ( x , y ) - N i ( x , y ) ] .
H ( u , v ) = { FT [ I ( x , y ) ] } 1 / 2 = M ( u , v ) exp [ i O ( u , v ) ] .
Q ( u , v ) = 1 - [ ( M m × f ) / M ( u , v ) ] if M ( u , v ) > ( M m × f ) , Q ( u , v ) = 0 if M ( u , v ) < ( M m × f ) ,
H ( u , v ) = H ( u , v ) Q ( u , v ) = M ( u , v ) exp [ i O ( u , v ) ] ,

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