Abstract

A Hartmann–Shack wave-front sensor is used to measure the wave aberrations of the human eye by sensing the wave front emerging from the eye produced by the retinal reflection of a focused light spot on the fovea. Since the test involves the measurements of the local slopes of the wave front, the actual wave front is reconstructed by the use of wave-front estimation with Zernike polynomials. From the estimated Zernike coefficients of the tested wave front the aberrations of the eye are evaluated. It is shown that with this method, using a Hartmann–Shack wave-front sensor, one can obtain a fast, precise, and objective measurement of the aberrations of the eye.

© 1994 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.
    [CrossRef]
  2. A. Ivanoff, Les Aberrations de l’oeil (Éditions de la Revue d’Optique, Theorie et Instrumentale, Paris, 1953).
  3. M. S. Smirnov, “Measurement of the wave aberrations of the eye,” Biophysics (USSR) 6, 776–794 (1961).
  4. M. Campbell, E. Harrison, P. Simonet, “Psychophysical measurement of blur on the retina due to optical aberrations of the eye,” Vision Res. 30, 1587–1602 (1990).
    [CrossRef]
  5. F. Berny, S. Slansky, “Wavefront determination resulting from Foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques,H. Dickson, ed. (Oriel, London, 1970), pp. 375–386.
  6. B. Howland, H. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1976).
    [CrossRef] [PubMed]
  7. H. Howland, B. Howland, “A subjective method for the measurement of monochromatic aberrations of the eye,” J. Opt. Soc. Am. 67, 1508–1518 (1977).
    [CrossRef] [PubMed]
  8. G. Walsh, W. N. Charman, H. Howland, “Objective technology for the determination of monochromatic aberrations of the human eye,” J. Opt. Soc. Am. A 1, 987–992 (1984).
    [CrossRef] [PubMed]
  9. A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 28, 804–808 (1989).
    [CrossRef] [PubMed]
  10. A. W. Dreher, “Aufbau eines konfokalen Laser-Augentomographen mit aktiv-optischer Fokuskontrolle zur Topographie des Meschlichen Augenhintergrundes,” Ph.D. dissertation (University of Heidelberg, Heidelberg, Germany, 1988).
  11. J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Hartmann– Shack sensor as a component in an active optical system to improve the depth resolution of the laser tomographic scanner,” in Active and Adaptive Optical Systems,M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 543–554 (1991).
    [CrossRef]
  12. B. Platt, R. V. Shack, “Lenticular Hartmann–screen,” Opt. Sci. Center Newsl. 5 (1), 15–16 (1971).
  13. F. Merkle, “Adaptive optics,” in International Trends in Optics,J. Goodman, ed. (Academic, Boston, Mass., 1991), pp. 379–390.
  14. J. E. Pearson, R. H. Freeman, H. C. Reynolds, “Adaptive optical techniques for wave front correction,” in Applied Optics and Optical Engineering,R. Shannon, J. Wyant, eds. (Academic, New York, 1979), Vol. 7, pp. 245–340.
    [CrossRef]
  15. M. Rimmer, J. Wyant, “Evaluation of large aberrations using a lateral shear interferometer having variable shear,” Appl. Opt. 14, 142–150 (1975).
    [PubMed]
  16. R. Cubalchini, “Modal wavefront estimation from phase derivative measurements,” J. Opt. Soc. Am. 69, 972–977 (1979).
    [CrossRef]
  17. W. H. Southwell, “Wavefront estimation from wavefront slope measurements,” J. Opt. Soc. Am. 70, 998–1006 (1980).
    [CrossRef]
  18. D. Malacara, Optical Shop Testing (Wiley, New York, 1991), pp. 472–484.
  19. D. Malacara, Optical Shop Testing (Wiley, New York, 1991), p. 465.
  20. J. Liang, “A new method to precisely measure the wave aberrations of the human eye with a Hartmann–Shack wavefront sensor,” Ph.D. dissertation (University of Heidelberg, Heidelberg, Germany, 1991).
  21. P. Salomon, “Charge-coupled device (CCD) trackers for highaccuracy guidance applications,” Opt. Eng. 20, 135–142 (1981).
    [CrossRef]
  22. J. Cox, “Evaluation of peak location algorithms with subpixel accuracy for mosaic focal planes,” in Processing of Images and Data from Optical Sensors,W. H. Carter, ed., Proc. Soc. Photo-Opt. Instrum. Eng.292, 288–299 (1981).
    [CrossRef]
  23. F. W. Campbell, R. W. Gubish, “Optical quality of the human eye,” J. Physiol. (London) 186, 558–578 (1966).
  24. D. Malacara, Optical Shop Testing (Wiley, New York, 1991), p. 67.
  25. D. Sliney, M. Wolbarsht, Safety with Lasers and Other Optical Sources (Plenum, New York, 1980).

1990 (1)

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

1989 (1)

1984 (1)

1981 (1)

P. Salomon, “Charge-coupled device (CCD) trackers for highaccuracy guidance applications,” Opt. Eng. 20, 135–142 (1981).
[CrossRef]

1980 (1)

1979 (1)

1977 (1)

1976 (1)

B. Howland, H. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1976).
[CrossRef] [PubMed]

1975 (1)

1971 (1)

B. Platt, R. V. Shack, “Lenticular Hartmann–screen,” Opt. Sci. Center Newsl. 5 (1), 15–16 (1971).

1966 (1)

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

1961 (1)

M. S. Smirnov, “Measurement of the wave aberrations of the eye,” Biophysics (USSR) 6, 776–794 (1961).

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,H. Dickson, ed. (Oriel, London, 1970), pp. 375–386.

Bille, J. F.

A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 28, 804–808 (1989).
[CrossRef] [PubMed]

J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Hartmann– Shack sensor as a component in an active optical system to improve the depth resolution of the laser tomographic scanner,” in Active and Adaptive Optical Systems,M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 543–554 (1991).
[CrossRef]

Campbell, F. W.

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

Campbell, M.

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

Charman, W. N.

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.
[CrossRef]

Cox, J.

J. Cox, “Evaluation of peak location algorithms with subpixel accuracy for mosaic focal planes,” in Processing of Images and Data from Optical Sensors,W. H. Carter, ed., Proc. Soc. Photo-Opt. Instrum. Eng.292, 288–299 (1981).
[CrossRef]

Cubalchini, R.

Dreher, A. W.

A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 28, 804–808 (1989).
[CrossRef] [PubMed]

A. W. Dreher, “Aufbau eines konfokalen Laser-Augentomographen mit aktiv-optischer Fokuskontrolle zur Topographie des Meschlichen Augenhintergrundes,” Ph.D. dissertation (University of Heidelberg, Heidelberg, Germany, 1988).

Freeman, R. H.

J. E. Pearson, R. H. Freeman, H. C. Reynolds, “Adaptive optical techniques for wave front correction,” in Applied Optics and Optical Engineering,R. Shannon, J. Wyant, eds. (Academic, New York, 1979), Vol. 7, pp. 245–340.
[CrossRef]

Goelz, S.

J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Hartmann– Shack sensor as a component in an active optical system to improve the depth resolution of the laser tomographic scanner,” in Active and Adaptive Optical Systems,M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 543–554 (1991).
[CrossRef]

Grimm, B.

J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Hartmann– Shack sensor as a component in an active optical system to improve the depth resolution of the laser tomographic scanner,” in Active and Adaptive Optical Systems,M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 543–554 (1991).
[CrossRef]

Gubish, R. W.

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

Harrison, E.

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

Howland, B.

Howland, H.

Ivanoff, A.

A. Ivanoff, Les Aberrations de l’oeil (Éditions de la Revue d’Optique, Theorie et Instrumentale, Paris, 1953).

Liang, J.

J. Liang, “A new method to precisely measure the wave aberrations of the human eye with a Hartmann–Shack wavefront sensor,” Ph.D. dissertation (University of Heidelberg, Heidelberg, Germany, 1991).

J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Hartmann– Shack sensor as a component in an active optical system to improve the depth resolution of the laser tomographic scanner,” in Active and Adaptive Optical Systems,M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 543–554 (1991).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1991), pp. 472–484.

D. Malacara, Optical Shop Testing (Wiley, New York, 1991), p. 465.

D. Malacara, Optical Shop Testing (Wiley, New York, 1991), p. 67.

Merkle, F.

F. Merkle, “Adaptive optics,” in International Trends in Optics,J. Goodman, ed. (Academic, Boston, Mass., 1991), pp. 379–390.

Pearson, J. E.

J. E. Pearson, R. H. Freeman, H. C. Reynolds, “Adaptive optical techniques for wave front correction,” in Applied Optics and Optical Engineering,R. Shannon, J. Wyant, eds. (Academic, New York, 1979), Vol. 7, pp. 245–340.
[CrossRef]

Platt, B.

B. Platt, R. V. Shack, “Lenticular Hartmann–screen,” Opt. Sci. Center Newsl. 5 (1), 15–16 (1971).

Reynolds, H. C.

J. E. Pearson, R. H. Freeman, H. C. Reynolds, “Adaptive optical techniques for wave front correction,” in Applied Optics and Optical Engineering,R. Shannon, J. Wyant, eds. (Academic, New York, 1979), Vol. 7, pp. 245–340.
[CrossRef]

Rimmer, M.

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.
[CrossRef]

Salomon, P.

P. Salomon, “Charge-coupled device (CCD) trackers for highaccuracy guidance applications,” Opt. Eng. 20, 135–142 (1981).
[CrossRef]

Shack, R. V.

B. Platt, R. V. Shack, “Lenticular Hartmann–screen,” Opt. Sci. Center Newsl. 5 (1), 15–16 (1971).

Simonet, P.

M. Campbell, E. Harrison, P. Simonet, “Psychophysical measurement of blur on the retina due to optical aberrations 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,H. Dickson, ed. (Oriel, London, 1970), pp. 375–386.

Sliney, D.

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

Smirnov, M. S.

M. S. Smirnov, “Measurement of the wave aberrations of the eye,” Biophysics (USSR) 6, 776–794 (1961).

Southwell, W. H.

Walsh, G.

Weinreb, R. N.

Wolbarsht, M.

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

Wyant, J.

Appl. Opt. (2)

Biophysics (USSR) (1)

M. S. Smirnov, “Measurement of the wave aberrations of the eye,” Biophysics (USSR) 6, 776–794 (1961).

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (1)

J. Physiol. (London) (1)

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

Opt. Eng. (1)

P. Salomon, “Charge-coupled device (CCD) trackers for highaccuracy guidance applications,” Opt. Eng. 20, 135–142 (1981).
[CrossRef]

Opt. Sci. Center Newsl. (1)

B. Platt, R. V. Shack, “Lenticular Hartmann–screen,” Opt. Sci. Center Newsl. 5 (1), 15–16 (1971).

Science (1)

B. Howland, H. Howland, “Subjective measurement of high-order aberrations of the eye,” Science 193, 580–582 (1976).
[CrossRef] [PubMed]

Vision Res. (1)

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

Other (13)

F. Berny, S. Slansky, “Wavefront determination resulting from Foucault test as applied to the human eye and visual instruments,” in Optical Instruments and Techniques,H. Dickson, ed. (Oriel, London, 1970), pp. 375–386.

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.
[CrossRef]

A. Ivanoff, Les Aberrations de l’oeil (Éditions de la Revue d’Optique, Theorie et Instrumentale, Paris, 1953).

F. Merkle, “Adaptive optics,” in International Trends in Optics,J. Goodman, ed. (Academic, Boston, Mass., 1991), pp. 379–390.

J. E. Pearson, R. H. Freeman, H. C. Reynolds, “Adaptive optical techniques for wave front correction,” in Applied Optics and Optical Engineering,R. Shannon, J. Wyant, eds. (Academic, New York, 1979), Vol. 7, pp. 245–340.
[CrossRef]

D. Malacara, Optical Shop Testing (Wiley, New York, 1991), pp. 472–484.

D. Malacara, Optical Shop Testing (Wiley, New York, 1991), p. 465.

J. Liang, “A new method to precisely measure the wave aberrations of the human eye with a Hartmann–Shack wavefront sensor,” Ph.D. dissertation (University of Heidelberg, Heidelberg, Germany, 1991).

A. W. Dreher, “Aufbau eines konfokalen Laser-Augentomographen mit aktiv-optischer Fokuskontrolle zur Topographie des Meschlichen Augenhintergrundes,” Ph.D. dissertation (University of Heidelberg, Heidelberg, Germany, 1988).

J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Hartmann– Shack sensor as a component in an active optical system to improve the depth resolution of the laser tomographic scanner,” in Active and Adaptive Optical Systems,M. A. Ealey, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1542, 543–554 (1991).
[CrossRef]

J. Cox, “Evaluation of peak location algorithms with subpixel accuracy for mosaic focal planes,” in Processing of Images and Data from Optical Sensors,W. H. Carter, ed., Proc. Soc. Photo-Opt. Instrum. Eng.292, 288–299 (1981).
[CrossRef]

D. Malacara, Optical Shop Testing (Wiley, New York, 1991), p. 67.

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

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Figures (10)

Fig. 1
Fig. 1

Construction of a Hartmann–Shack wave-front sensor.

Fig. 2
Fig. 2

Actual Hartmann–Shack wave-front sensor, whose aperture is 20 mm in diameter.

Fig. 3
Fig. 3

Principle of a Hartmann–Shack wave-front sensor14: (A) single element illustrating how a lens can be used to sense a wave front and (B) multiple-element version that senses local tilts of a large wave front.

Fig. 4
Fig. 4

Wave aberrations of the eye. (A) Definition of the wave aberrations of the eye in the image space of the eye. The dashed arc represents the reference sphere, and the solid arc illustrates the real wave front. (B) Equivalent definition of the ocular aberrations in front of the eye. The dashed line and the solid arc illustrate the reference plane and the real wave front emerging from the eye, respectively.

Fig. 5
Fig. 5

Schematic diagram of the experimental setup. In this configuration the pupil plane is set to be conjugate to the Hartmann–Shack wave-front sensor (HSS) plane, while the fovea is conjugate to the target (the pinhole). The CCD image module is at the focal plane of the lens array (HHS). NDF, neutral density filter; B1 and B2, beam splitters; T, target; GGP, ground-glass plate; L1–L6, lenses.

Fig. 6
Fig. 6

Detected image pattern from test of a plane wave. The region that covers the central 7 × 7 points is the tested area in this study.

Fig. 7
Fig. 7

Detected image pattern from tests of the eyes. (A) and (B) are the tests of subject L (L1 and L2, respectively), conducted sequentially in two days. (C) and (D) are the tests of subject B (B1 and B2, respectively), conducted one after the other in half an hour.

Fig. 8
Fig. 8

Equal-level contours of the reconstructed wave front W(x, y) for the two tested eyes. L1 and L2 are for tests of subject L, and B1 and B2 are for tests of subject B. X and Y are the coordinates normalized to the distance from the center to the corner. The grid distance is 0.5 mm in the pupil plane. Z represents W(X, Y). The difference between neighboring curves is one wavelength of 0.63 μm.

Fig. 9
Fig. 9

Equal-level contours of the high-order aberrations of the tested eyes. (A) and (B) are for subject L’s tested eye, and (C) and (D) are for subject B’s tested eye. X and Y are the coordinates normalized to the distance from the center to the corner. The grid distance is 0.5 mm in the pupil plane. Z represents Whigh(X, Y). The difference between neighboring curves is one fourth of the wavelength of 0.63 μm.

Fig. 10
Fig. 10

Intensity distribution of the typical focus spots of the Hartmann–Shack wave-front sensor in an image pattern for the tested eyes. (A) and (B) are two points in Fig. 7(D). X and Y are in pixels, and each pixel has an angular size of 20 arcsec on the retina.

Tables (3)

Tables Icon

Table 1 Zernike Polynomials up to Fourth Degreea

Tables Icon

Table 2 Estimated Zernike Coefficients for the Tested Eyesa

Tables Icon

Table 3 Measured Defocus and Astigmatism of the Tested Eyesa

Equations (12)

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W ( x , y ) x = Δ x f ,
W ( x , y ) y = Δ y f ,
P ( x , y ) = W ( x , y ) x + μ ( x , y ) ,
Q ( x , y ) = W ( x , y ) y + ν ( x , y ) ,
W ( x , y ) = i = 0 14 C i Z i ( x , y ) ,
W ( x , y ) x = i = 0 14 C i Z i ( x , y ) x ,
W ( x , y ) y = i = 0 14 C i Z i ( x , y ) y .
C = ( T M ) ( P Q ) ,
C = ( C 1 , C 2 , C 3 , , C 14 ) T ,
P Q = [ P ( x 1 , y 1 ) , P ( x 2 , y 1 ) , , P ( x N , y 1 ) , P ( x 1 , y 2 ) , P ( x 2 , y 2 ) , , P ( x N , y 2 ) , P ( x 1 , y N ) , P ( x 2 , y N ) , , P ( x N , y N ) , Q ( x 1 , y 1 ) , Q ( x 2 , y 1 ) , , Q ( x N , y 1 ) , Q ( x 1 , y 2 ) , Q ( x 2 , y 2 ) , , Q ( x N , y 2 ) , Q ( x 1 , y N ) , Q ( x 2 , y N ) , , Q ( x N , y N ) ] T .
W lens ( x , y ) = 2 C 3 x y + 2 C 4 ( x 2 + y 2 ) + C 5 ( y 2 x 2 ) .
W high ( x , y ) = i = 6 14 C i Z i ( x , y ) .

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