Abstract

A recent study has shown that the double-pass method provides a good estimate of the ocular modulation transfer function (MTF) but that it does not yield the phase transfer function (PTF) [ J. Opt. Soc. Am. A 12, 195 ( 1995)]. Therefore, one cannot recover the true retinal point-spread function (PSF). We present a modification of the double-pass method to overcome this problem. The key is to break the symmetry between the two passes. By using an unexpanded Gaussian input beam, we produce a diffraction-limited PSF for the first pass. Then, by using a large exit pupil, we get an aberrated PSF for the second pass. The double-pass aerial image is the cross correlation of both PSF’s, so that the Fourier transform of such an aerial image directly provides the true retinal PTF, up to the cutoff frequency of the effective (small), diffraction-limited entrance pupil. The resulting double-pass aerial image is a blurred version of the true retinal PSF. Thus it shows the effect not only of even symmetric aberrations but also of odd and irregular aberrations such as coma. We have explored two different ways to retrieve the true retinal PSF: (a) deblurring of the aerial image and (b) PSF reconstruction combining PTF data with conventional double-pass MTF. We present promising initial results with both artificial and real eyes.

© 1995 Optical Society of America

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References

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  1. M. F. Flamant, “Etude de la repartition de la lumiére dans l’image rétinienne d’une fente,” Rev. Opt. 34, 433–459 (1955).
  2. R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
    [Crossref] [PubMed]
  3. P. Artal, R. Navarro, “Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression,” J. Opt. Soc. Am. A 11, 246–249 (1994).
    [Crossref]
  4. R. Navarro, M. Ferro, P. Artal, I. Miranda, “Modulation transfer functions of eyes implanted with intraocular lenses,” Appl. Opt. 32, 6359–6367 (1993).
    [Crossref] [PubMed]
  5. D. R. Williams, D. Brainard, M. 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]
  6. J. Liang, D. R. Williams, “Effect of higher order aberrations on image quality in the human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 70–73.
  7. J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
    [Crossref]
  8. P. Artal, S. Marcos, R. Navarro, D. Williams, “Odd aberrations and double pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
    [Crossref]
  9. H. C. Howland, B. Howland, “A subjective method for the measurement of the monochromatic abberations of the eye,”J. Opt. Soc. Am. 67, 1508–1518 (1977).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  11. J. R. Fienup, “Reconstruction of an object from the modulus of its Fourier transform,” Opt. Lett. 3, 27–29 (1978).
    [Crossref] [PubMed]
  12. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  13. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
    [Crossref]
  14. W. J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966).
  15. D. C. Ghiglia, G. A. Masting, L. A. Romero, “Cellular-automata method for phase unwrapping,” J. Opt. Soc. Am. A 4, 267–280 (1987).
    [Crossref]

1995 (1)

1994 (3)

1993 (2)

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]

1978 (1)

1977 (1)

1955 (1)

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

Artal, P.

Bille, J. F.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Brainard, D.

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]

Ferro, M.

Fienup, J. R.

Flamant, M. F.

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

Ghiglia, D. C.

Goelz, S.

Grimm, B.

Howland, B.

Howland, H. C.

Liang, J.

J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
[Crossref]

J. Liang, D. R. Williams, “Effect of higher order aberrations on image quality in the human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 70–73.

Marcos, S.

Masting, G. A.

McMahon, M.

Miranda, I.

Navarro, R.

Romero, L. A.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[Crossref]

Smith, W. J.

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

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[Crossref]

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]

Williams, D.

Williams, D. R.

D. R. Williams, D. Brainard, M. 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]

R. Navarro, P. Artal, D. R. Williams, “Modulation transfer of the human eye as a function of retinal eccentricity,” J. Opt. Soc. Am. A 10, 201–212 (1993).
[Crossref] [PubMed]

J. Liang, D. R. Williams, “Effect of higher order aberrations on image quality in the human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 70–73.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

Opt. Lett. (1)

Rev. Opt. (1)

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

Vision Res. (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]

Other (4)

J. Liang, D. R. Williams, “Effect of higher order aberrations on image quality in the human eye,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 70–73.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
[Crossref]

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

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Figures (9)

Fig. 1
Fig. 1

Principle of the method. In the first pass (upper) the light from a point source (traveling from left to right) passes through a small pupil so that the image is a diffraction-limited Airy disk. Then, with a large pupil (lower) in the second pass (the light travels from right to left), the resulting image is the cross correlation between an aberrated second-pass image and the inverted image of the Airy disk.

Fig. 2
Fig. 2

Experimental setup. An unexpanded Gaussian beam (ω0 = 0.4 mm) filtered with a spatial filter SF enters the eye after reflection off a pellicle and forms diffraction-limited image O′. Optional trial lenses compensate for sphere and cylinder refraction. After reflection off the retina, the beam passes through the full pupil and a 500-mm lens forms an aerial image on a CCD array.

Fig. 3
Fig. 3

Results obtained with an artificial eye. The images in the upper row were obtained with an unexpanded Gaussian beam; those in the lower row were obtained with an expanded beam and a 4-mm pupil. The two panels in the left column show the resulting single-pass images. The two panels in the center column were recorded after reflection off a diffuser and a second passage through the lens. The two panels in the right column are the computed cross correlation between the images of two left panels (upper row) and the autocorrelation of the image of the lower-left panel (lower row), respectively.

Fig. 4
Fig. 4

Comparison of the single-pass PTF (left) with the one-and-a-half-pass estimate (right). Changes in gray level correspond to phase increments of π; middle gray signifies zero phase, and darker and lighter levels denote negative and positive phase, respectively. The agreement is good up to the diffraction limit of the first-pass Gaussian PSF, except for remaining linear offsets. In this and subsequent figures, cpd stands for c/deg.

Fig. 5
Fig. 5

Radial profiles of the MTF’s obtained from the aerial images of Fig. 3 (artificial eye). The match between the singlepass and double-pass MTF’s is very good. With this novel technique, decorrelation is possible up to the effective cutoff frequency of the first-pass, diffraction-limited image.

Fig. 6
Fig. 6

Reconstruction of the first-pass PSF (right) from the double-pass MTF and one-and-a-half-pass PTF data. The left panel shows the directly recorded single-pass PSF for comparison.

Fig. 7
Fig. 7

Aerial images for three observers (ON, MA, and RN), for 0°, fovea (upper row), and 25°, peripheral retina (lower row). They show different amounts of astigmatism (even symmetric), coma (odd symmetric), and irregular aberration.

Fig. 8
Fig. 8

Phase transfer functions for observer MA, for 0° (left), and 25° (right) eccentricity. Changes in gray level correspond to phase increments of π; middle gray stands for zero phase, and darker and lighter levels mean negative and positive phases, respectively. They differ both in the effective cutoff frequency and the steepness owing to the larger aberrations in the off-axis case.

Fig. 9
Fig. 9

Decorrelated version (right) of the one-and-a-half-pass aerial image (left) of observer MA, for 25° of eccentricity. Image features, including noise, are sharper after decorrelation.

Equations (1)

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I ( x , y ) = P 1 ( x , y ) P 2 ( x , y ) ,

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