Abstract

We have constructed a wave-front sensor to measure the irregular as well as the classical aberrations of the eye, providing a more complete description of the eye's aberrations than has previously been possible. We show that the wave-front sensor provides repeatable and accurate measurements of the eye's wave aberration. The modulation transfer function of the eye computed from the wave-front sensor is in fair, though not complete, agreement with that obtained under similar conditions on the same observers by use of the double-pass and the interferometric techniques. Irregular aberrations, i.e., those beyond defocus, astigmatism, coma, and spherical aberration, do not have a large effect on retinal image quality in normal eyes when the pupil is small (3 mm). However, they play a substantial role when the pupil is large (7.3-mm), reducing visual performance and the resolution of images of the living retina. Although the pattern of aberrations varies from subject to subject, aberrations, including irregular ones, are correlated in left and right eyes of the same subject, indicating that they are not random defects.

© 1997 Optical Society of America

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References

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  1. W. M. Rosenblum, J. L. Christensen, “Objective and subjective spherical aberration measurement of the human eye,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 13, pp. 69–91.
  2. M. C. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
    [CrossRef]
  3. H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrationsof the eye,” J. Opt. Soc. Am. 67, 1508–1518 (1977).
    [CrossRef] [PubMed]
  4. G. Walsh, W. N. Charman, H. C. Howland, “Objective technique for the determination of monochromatic aberrationsof the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
    [CrossRef] [PubMed]
  5. H. von Helmholtz, Physiological Optics, J. P. C. Southall, ed. (Dover, New York, 1896).
  6. F. Berny, S. Slansky, “Wavefront determination resulting from foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. H. Dickenson, ed. (Oriel, Newcastle, UK, 1969), pp. 375–386.
  7. G. Van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
    [CrossRef]
  8. H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations ofbest focus for small artificial pupils,” Vision Res. 29, 979–983 (1989).
    [CrossRef]
  9. J. Liang, B. Grimm, S. Goelz, J. Bille, “Objective measurement of the wave aberrations of the human eye withthe use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
    [CrossRef]
  10. B. Platt, R. V. Shack, “Lenticular Hartmann screen,” Opt. Sci. Center Newsl. (University of Arizona) 5, 15–16 (1971).
  11. D. H. Sliney, M. L. Wolbarsht, “Safety standards and measurement techniques for high intensity lightsources,” Vision Res. 20, 1133–1142 (1980).
    [CrossRef]
  12. D. R. Williams, D. H. Brainard, M. J. McMahon, R. Navarro, “Double-pass and interferometric measures of the optical quality ofthe eye,” J. Opt. Soc. Am. A 11, 3123–3135 (1994).
    [CrossRef]
  13. W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. A 70, 998–1006 (1980).
    [CrossRef]
  14. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983).
  15. W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at differentpoints,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
    [CrossRef]
  16. J. Enoch, V. Lakshminarayanan, “Retinal fibre optics,” in Visual Optics and Instrumentation, W. N. Charman, ed., Vol. 1 of Vision and Visual Dysfunction, J. Cronly-Dillon, ed. (CRC, Boca Raton, Fla., 1991), Chap. 12.
  17. G. Westheimer, “Dependence of the magnitude of the Stiles–Crawford effect onretinal location,” J. Physiol. (London) 192, 309–315 (1967).
  18. J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptiveoptics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
    [CrossRef]
  19. G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
    [CrossRef] [PubMed]
  20. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).
  21. We have also calculated the eye's MTF, incorporating the Stiles–Crawford effect (ρ=0.05). The MTF is increased slightly at lower frequencies but is reduced at higher frequencies; nevertheless, the Stiles–Crawford effect does not substantially change our conclusions.
  22. F. W. Campbell, D. G. Green, “Optical and retinal factors affecting visual resolution,” J. Physiol. (London) 181, 576–593 (1965).
  23. F. W. Campbell, R. W. Gubisch, “Optical quality of the human eye,” J. Physiol. (London) 186, 558–578 (1966).
  24. G. Walsh, W. N. Charman, “Measurement of the axial wavefront aberration of the human eye,” Ophthalmic. Physiol. Opt. 5, 23–31 (1985).
    [CrossRef] [PubMed]
  25. F. Flamant, “Etude de la repartition de lumière dans l'image rétinienned'une fente,” Rev. Opt. Theor. Instrum. 34, 433–459 (1955).
  26. G. Westheimer, F. W. Campbell, “Light distribution in the image formed by the living human eye,” J. Opt. Soc. Am. 52, 1040–1044 (1962).
    [CrossRef] [PubMed]
  27. P. Artal, S. Marcos, R. Navarro, D. R. Williams, “Odd aberrations and double-pass measurements of retinal image quality,” J. Opt. Soc. Am. A 12, 195–201 (1995).
    [CrossRef]
  28. W. N. Charman, G. Walsh, “The optical phase transfer function of the eye and the perception ofspatial phase,” Vision Res. 25, 619–623 (1985).
    [CrossRef]
  29. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 7, 766–795 (1962).
  30. R. H. Webb, C. M. Penney, K. P. Thompson, “Measurement of ocular wave-front distortion with a spatially resolvedrefractometer,” Appl. Opt. 31, 3678–3686 (1992).
    [CrossRef] [PubMed]
  31. W. N. Charman, “Wave aberration of the eye: a review,” Optom. Vis. Sci. 68, 574–583 (1991).
    [CrossRef] [PubMed]
  32. R. A. Applegate, C. A. Johnson, H. C. Howland, R. W. Yee, “Monochromatic wavefront aberrations following radial keratotomy,” in Noninvasive Assessment of Visual System, Vol. 7 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 98–102.
  33. R. A. Applegate, K. A. Gansel, “The importance of pupil size in optical quality measurements following radial keratotomy,” Refract. Corneal Surg. 6, 47–54 (1990).
    [PubMed]
  34. D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of the cone mosaic in the living human eye,” Vision Res. 36, 1067–1079 (1996).
    [CrossRef] [PubMed]

1997

1996

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of the cone mosaic in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

1995

1994

1992

1991

W. N. Charman, “Wave aberration of the eye: a review,” Optom. Vis. Sci. 68, 574–583 (1991).
[CrossRef] [PubMed]

1990

R. A. Applegate, K. A. Gansel, “The importance of pupil size in optical quality measurements following radial keratotomy,” Refract. Corneal Surg. 6, 47–54 (1990).
[PubMed]

M. C. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

1989

H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations ofbest focus for small artificial pupils,” Vision Res. 29, 979–983 (1989).
[CrossRef]

1988

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

1985

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

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

1984

1980

D. H. Sliney, M. L. Wolbarsht, “Safety standards and measurement techniques for high intensity lightsources,” Vision Res. 20, 1133–1142 (1980).
[CrossRef]

W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. A 70, 998–1006 (1980).
[CrossRef]

1977

1971

B. Platt, R. V. Shack, “Lenticular Hartmann screen,” Opt. Sci. Center Newsl. (University of Arizona) 5, 15–16 (1971).

1967

G. Westheimer, “Dependence of the magnitude of the Stiles–Crawford effect onretinal location,” J. Physiol. (London) 192, 309–315 (1967).

1966

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

1965

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

1962

G. Van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
[CrossRef]

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 7, 766–795 (1962).

G. Westheimer, F. W. Campbell, “Light distribution in the image formed by the living human eye,” J. Opt. Soc. Am. 52, 1040–1044 (1962).
[CrossRef] [PubMed]

1955

F. Flamant, “Etude de la repartition de lumière dans l'image rétinienned'une fente,” Rev. Opt. Theor. Instrum. 34, 433–459 (1955).

1933

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at differentpoints,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Applegate, R. A.

R. A. Applegate, K. A. Gansel, “The importance of pupil size in optical quality measurements following radial keratotomy,” Refract. Corneal Surg. 6, 47–54 (1990).
[PubMed]

R. A. Applegate, C. A. Johnson, H. C. Howland, R. W. Yee, “Monochromatic wavefront aberrations following radial keratotomy,” in Noninvasive Assessment of Visual System, Vol. 7 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 98–102.

Artal, P.

Berny, F.

F. Berny, S. Slansky, “Wavefront determination resulting from foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. H. Dickenson, ed. (Oriel, Newcastle, UK, 1969), pp. 375–386.

Bille, J.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983).

Brainard, D. H.

Buettner, J.

H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations ofbest focus for small artificial pupils,” Vision Res. 29, 979–983 (1989).
[CrossRef]

Campbell, F. W.

F. W. Campbell, R. W. Gubisch, “Optical 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).

G. Westheimer, F. W. Campbell, “Light distribution in the image formed by the living human eye,” J. Opt. Soc. Am. 52, 1040–1044 (1962).
[CrossRef] [PubMed]

Campbell, M. C.

M. C. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Charman, W. N.

W. N. Charman, “Wave aberration of the eye: a review,” Optom. Vis. Sci. 68, 574–583 (1991).
[CrossRef] [PubMed]

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

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

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

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

Christensen, J. L.

W. M. Rosenblum, J. L. Christensen, “Objective and subjective spherical aberration measurement of the human eye,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 13, pp. 69–91.

Crawford, B. H.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at differentpoints,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Enoch, J.

J. Enoch, V. Lakshminarayanan, “Retinal fibre optics,” in Visual Optics and Instrumentation, W. N. Charman, ed., Vol. 1 of Vision and Visual Dysfunction, J. Cronly-Dillon, ed. (CRC, Boca Raton, Fla., 1991), Chap. 12.

Flamant, F.

F. Flamant, “Etude de la repartition de lumière dans l'image rétinienned'une fente,” Rev. Opt. Theor. Instrum. 34, 433–459 (1955).

Gansel, K. A.

R. A. Applegate, K. A. Gansel, “The importance of pupil size in optical quality measurements following radial keratotomy,” Refract. Corneal Surg. 6, 47–54 (1990).
[PubMed]

Goelz, S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

Green, D. G.

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

Grimm, B.

Gubisch, R. W.

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

Harrison, E. M.

M. C. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Howland, B.

Howland, H. C.

H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations ofbest focus for small artificial pupils,” Vision Res. 29, 979–983 (1989).
[CrossRef]

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

H. C. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrationsof the eye,” J. Opt. Soc. Am. 67, 1508–1518 (1977).
[CrossRef] [PubMed]

R. A. Applegate, C. A. Johnson, H. C. Howland, R. W. Yee, “Monochromatic wavefront aberrations following radial keratotomy,” in Noninvasive Assessment of Visual System, Vol. 7 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 98–102.

Johnson, C. A.

R. A. Applegate, C. A. Johnson, H. C. Howland, R. W. Yee, “Monochromatic wavefront aberrations following radial keratotomy,” in Noninvasive Assessment of Visual System, Vol. 7 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 98–102.

Lakshminarayanan, V.

J. Enoch, V. Lakshminarayanan, “Retinal fibre optics,” in Visual Optics and Instrumentation, W. N. Charman, ed., Vol. 1 of Vision and Visual Dysfunction, J. Cronly-Dillon, ed. (CRC, Boca Raton, Fla., 1991), Chap. 12.

Liang, J.

Marcos, S.

McMahon, M. J.

Miller, D. T.

J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptiveoptics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
[CrossRef]

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of the cone mosaic in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

Morris, G. M.

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of the cone mosaic in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

Navarro, R.

Penney, C. M.

Platt, B.

B. Platt, R. V. Shack, “Lenticular Hartmann screen,” Opt. Sci. Center Newsl. (University of Arizona) 5, 15–16 (1971).

Rosenblum, W. M.

W. M. Rosenblum, J. L. Christensen, “Objective and subjective spherical aberration measurement of the human eye,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 13, pp. 69–91.

Shack, R. V.

B. Platt, R. V. Shack, “Lenticular Hartmann screen,” Opt. Sci. Center Newsl. (University of Arizona) 5, 15–16 (1971).

Simonet, P.

M. C. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

Slansky, S.

F. Berny, S. Slansky, “Wavefront determination resulting from foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. H. Dickenson, ed. (Oriel, Newcastle, UK, 1969), pp. 375–386.

Sliney, D. H.

D. H. Sliney, M. L. Wolbarsht, “Safety standards and measurement techniques for high intensity lightsources,” Vision Res. 20, 1133–1142 (1980).
[CrossRef]

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 7, 766–795 (1962).

Southwell, W. H.

W. H. Southwell, “Wave-front estimation from wave-front slope measurements,” J. Opt. Soc. Am. A 70, 998–1006 (1980).
[CrossRef]

Stiles, W. S.

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at differentpoints,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Thompson, K. P.

Van den Brink, G.

G. Van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
[CrossRef]

von Helmholtz, H.

H. von Helmholtz, Physiological Optics, J. P. C. Southall, ed. (Dover, New York, 1896).

Walsh, G.

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

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

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

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

Webb, R. H.

Westheimer, G.

G. Westheimer, “Dependence of the magnitude of the Stiles–Crawford effect onretinal location,” J. Physiol. (London) 192, 309–315 (1967).

G. Westheimer, F. W. Campbell, “Light distribution in the image formed by the living human eye,” J. Opt. Soc. Am. 52, 1040–1044 (1962).
[CrossRef] [PubMed]

Williams, D. R.

Wolbarsht, M. L.

D. H. Sliney, M. L. Wolbarsht, “Safety standards and measurement techniques for high intensity lightsources,” Vision Res. 20, 1133–1142 (1980).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983).

Yee, R. W.

R. A. Applegate, C. A. Johnson, H. C. Howland, R. W. Yee, “Monochromatic wavefront aberrations following radial keratotomy,” in Noninvasive Assessment of Visual System, Vol. 7 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 98–102.

Appl. Opt.

Biophys. J.

M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. J. 7, 766–795 (1962).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Physiol. (London)

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

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

G. Westheimer, “Dependence of the magnitude of the Stiles–Crawford effect onretinal location,” J. Physiol. (London) 192, 309–315 (1967).

Ophthalmic. Physiol. Opt.

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

Opt. Sci. Center Newsl. (University of Arizona)

B. Platt, R. V. Shack, “Lenticular Hartmann screen,” Opt. Sci. Center Newsl. (University of Arizona) 5, 15–16 (1971).

Optom. Vis. Sci.

W. N. Charman, “Wave aberration of the eye: a review,” Optom. Vis. Sci. 68, 574–583 (1991).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. B

W. S. Stiles, B. H. Crawford, “The luminous efficiency of rays entering the eye pupil at differentpoints,” Proc. R. Soc. London Ser. B 112, 428–450 (1933).
[CrossRef]

Refract. Corneal Surg.

R. A. Applegate, K. A. Gansel, “The importance of pupil size in optical quality measurements following radial keratotomy,” Refract. Corneal Surg. 6, 47–54 (1990).
[PubMed]

Rev. Opt. Theor. Instrum.

F. Flamant, “Etude de la repartition de lumière dans l'image rétinienned'une fente,” Rev. Opt. Theor. Instrum. 34, 433–459 (1955).

Vision Res.

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

D. T. Miller, D. R. Williams, G. M. Morris, J. Liang, “Images of the cone mosaic in the living human eye,” Vision Res. 36, 1067–1079 (1996).
[CrossRef] [PubMed]

D. H. Sliney, M. L. Wolbarsht, “Safety standards and measurement techniques for high intensity lightsources,” Vision Res. 20, 1133–1142 (1980).
[CrossRef]

G. Walsh, W. N. Charman, “The effect of pupil centration and diameter on ocular performance,” Vision Res. 28, 659–665 (1988).
[CrossRef] [PubMed]

M. C. Campbell, E. M. Harrison, P. Simonet, “Psychophysical measurement of the blur on the retina due to opticalaberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
[CrossRef]

G. Van den Brink, “Measurements of the geometrical aberrations of the eye,” Vision Res. 2, 233–244 (1962).
[CrossRef]

H. C. Howland, J. Buettner, “Computing high order wave aberration coefficients from variations ofbest focus for small artificial pupils,” Vision Res. 29, 979–983 (1989).
[CrossRef]

Other

W. M. Rosenblum, J. L. Christensen, “Objective and subjective spherical aberration measurement of the human eye,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 13, pp. 69–91.

H. von Helmholtz, Physiological Optics, J. P. C. Southall, ed. (Dover, New York, 1896).

F. Berny, S. Slansky, “Wavefront determination resulting from foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques, J. H. Dickenson, ed. (Oriel, Newcastle, UK, 1969), pp. 375–386.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968).

We have also calculated the eye's MTF, incorporating the Stiles–Crawford effect (ρ=0.05). The MTF is increased slightly at lower frequencies but is reduced at higher frequencies; nevertheless, the Stiles–Crawford effect does not substantially change our conclusions.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983).

R. A. Applegate, C. A. Johnson, H. C. Howland, R. W. Yee, “Monochromatic wavefront aberrations following radial keratotomy,” in Noninvasive Assessment of Visual System, Vol. 7 of 1989 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1989), pp. 98–102.

J. Enoch, V. Lakshminarayanan, “Retinal fibre optics,” in Visual Optics and Instrumentation, W. N. Charman, ed., Vol. 1 of Vision and Visual Dysfunction, J. Cronly-Dillon, ed. (CRC, Boca Raton, Fla., 1991), Chap. 12.

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Figures (12)

Fig. 1
Fig. 1

Hartmann–Shack wave-front sensor for the eye. Light from a He–Ne laser produces a compact point source on the retina. If the eye has aberrations, the wave front of the light returning from the retina forms a distorted wave front at the pupil plane. This wave front is recreated by lenses L 3 , L 2 , L 4 and L 5 at the plane of lenslet array. The two-dimensional lenslet array samples this warped wave front and forms an array of focused spots on a CCD array. Each of the spots from the lenslets is displaced on the CCD array in proportion to the slope of the wave front; the wave aberration itself can be calculated from this displacement.

Fig. 2
Fig. 2

Wave-front-sensor images and wave aberration of eyes for a small 3-mm pupil. a. The image from the wave-front sensor for an ideal eye on the left, which corresponds to no phase error across the pupil, as shown in the wave aberration on the right. b. and c. show the wave-front-sensor images for two real eyes along with the calculated wave aberration. The contour interval in the wave-aberration plots (d.–f.) is 0.15 μm. The pupil was sampled with a center-to-center spacing of 0.2 mm.

Fig. 3
Fig. 3

Wave-front-sensor images and wave aberration of eyes for a 7.3-mm pupil. a.–c. are the wave-front-sensor images for three observers. The center-to-center spacing of lenslets in the pupil was 0.42 mm. d.–f. are the corresponding wave aberrations of the three eyes from measurements of the wave-front slopes. The contour interval in the wave-aberration plots is 0.15 μm for OP and 0.3 μm for JL and ML. Defocus and astigmatism have been removed from the wave aberrations, thus showing the presence of substantial irregular aberrations. The peak-to-valley wave-front error for the 7.3-mm pupil is approximately 7 μm, 4 μm, and 5 μm for JL, OP, and ML, respectively.

Fig. 4
Fig. 4

Repeatability of measurements with the wave-front sensor. a. Measurements of the wave aberration along one cross section of a 3-mm pupil for a real eye (RNB) and an artificial eye. b. Measurement of the wave aberration along one cross section of a 7.3-mm pupil for observer JL. The error bars are ± 1 standard deviation.    

Fig. 5
Fig. 5

Measurement of trial lenses with the wave-front sensor. The curve shows the power in diopters derived from the wave-front sensor as a function of the nominal power of trial lenses inserted into the system.

Fig. 6
Fig. 6

Comparison of MTF's obtained with wave-front sensing, the double-pass method, and the interferometric technique. a.–c. compare the MTF's for each of the three observers, and d. shows the mean for the three observers. The interferometric and the double-pass data are from Williams et al.,12 who studied the same observers measured here. The curves show the eye's MTF for horizontal gratings. The error bars for the interferometric MTF's are ± 1 standard error of the measurements.

Fig. 7
Fig. 7

Comparison of MTF's obtained with the wave-front sensor and with the aberroscope for a 3-mm pupil. Circles show the MTF of the eye from the objective aberroscope.19 Squares show, for three observers, the mean MTF's with both defocus and astigmatism removed. Triangles show, for the same observers, the mean MTF's derived from wave aberrations that included only third- and fourth-order Zernike aberrations, with higher and lower orders removed. The shaded area shows the range of the MTF's for 12 eyes for a 3-mm pupil measured with our wave-front sensor.

Fig. 8
Fig. 8

Zernike description of the eye's aberrations. a. The wave aberration in YL's eye for a 7.3-mm pupil, shown at the top, is decomposed into Zernike polynomials up to tenth order. Contour line spacing is 0.15 μm. Modes shown include classical aberrations such as defocus (0.1 D), astigmatism (0.8 D at 15 deg), coma, and spherical aberration. The decomposition reveals higher-order, irregular aberrations in addition to classical aberrations. b. The upper curve (squares) shows the RMS wave-front error of each Zernike order for a 7.3-mm pupil averaged across 14 human eyes. Error bars indicate the standard deviation among eyes. For the second-order Zernike modes, only astigmatism is shown. The average amount of astigmatism in these observers was 0.6 D, corresponding to a mean RMS value of 0.77 μm. The middle curve (triangles) shows the data for a 3.4-mm pupil averaged across 12 tested eyes. The lower curve (circles) is for an artificial eye. The error bars show the standard deviation of ten repeated measurements.  

Fig. 9
Fig. 9

Similarity of the eye's aberrations in the left and right eyes. a. Three-dimensional surface plots of the wave aberration of the left and right eyes of two observers, showing the mirror symmetry of left and right eyes. Defocus and astigmatism have been removed from the wave aberration. b. Coefficients of individual Zernike modes in the right eye plotted against the corresponding coefficients of the left eye, showing the correlation between left and right eyes. Data of four subjects are combined.

Fig. 10
Fig. 10

Mean of the radially averaged MTF's of the eye for different pupil sizes. The numbers on the curves indicate the pupil size of the eye. The mean MTF's for a 2- and a 3-mm pupil are derived from the wave aberration of 12 eyes measured across a 3.4-mm pupil, and the mean MTF's for 4-, 5-, 6-, and 7.3-mm pupils are derived from the wave aberration of 14 eyes measured across a 7.3-mm pupil. Defocus and astigmatism were removed for each eye and each pupil size. Plots a. (linear) and b. (semilog) are from the same data.

Fig. 11
Fig. 11

Mean of the radially averaged MTF's for two pupil sizes: a. 3 mm and b. 7.3 mm. The top curve in the lower part of the figure is the MTF for an aberration-free eye, in which diffraction is the sole source of image blur. The lowest curve is for eyes corrected to remove defocus and astigmatism entirely. The middle curve is for eyes with second-, third-, and fourth-order Zernike aberrations corrected but with the higher-order, irregular aberrations (orders 5–10) uncorrected. The error bars are the standard deviation of 12 tested eyes for the small (3-mm) pupil and of 14 tested eyes for the large (7.3-mm) pupil. The upper part of the figure plots the ratio of the diffraction MTF to the mean MTF of real eyes if only defocus and astigmatism are corrected (squares) and the ratio of the diffraction MTF to the mean MTF of real eyes if the higher-order (fifth to tenth) irregular aberrations remain uncorrected (triangles).

Fig. 12
Fig. 12

Strehl ratio of the eye's PSF for a 3-mm pupil (squares) and for a 7.3-mm pupil (triangles). Error bars show the standard deviation of 12 tested eyes for the 3-mm pupil and of 14 tested eyes for the 7.3-mm pupil. Each data point shows the Strehl ratio that would have been obtained with lower Zernike orders removed to provide a measure of optical quality were lower orders corrected. The abscissa indicates the highest lower order removed in each case. For example, a value of 2 on the abscissa means that only second-order aberrations, corresponding to defocus and astigmatism, have been removed. A value of 3 indicates that both second- and third-order aberrations have been removed.

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