Abstract

It is well known that the eye’s optics exhibit temporal instability in the form of microfluctuations in focus; however, almost nothing is known of the temporal properties of the eye’s other aberrations. We constructed a real-time Hartmann–Shack (HS) wave-front sensor to measure these dynamics at frequencies as high as 60 Hz. To reduce spatial inhomogeneities in the short-exposure HS images, we used a low-coherence source and a scanning system. HS images were collected on three normal subjects with natural and paralyzed accommodation. Average temporal power spectra were computed for the wave-front rms, the Seidel aberrations, and each of 32 Zernike coefficients. The results indicate the presence of fluctuations in all of the eye’s aberration, not just defocus. Fluctuations in higher-order aberrations share similar spectra and bandwidths both within and between subjects, dropping at a rate of approximately 4 dB per octave in temporal frequency. The spectrum shape for higher-order aberrations is generally different from that for microfluctuations of accommodation. The origin of these measured fluctuations is not known, and both corneal/lenticular and retinal causes are considered. Under the assumption that they are purely corneal or lenticular, calculations suggest that a perfect adaptive optics system with a closed-loop bandwidth of 1–2 Hz could correct these aberrations well enough to achieve diffraction-limited imaging over a dilated pupil.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. N. Charman, G. Heron, “Fluctuations in accommodation: a review,” Ophthalmic Physiol. Opt. 8, 153–163 (1988).
    [CrossRef] [PubMed]
  2. J. Liang, D. R. Williams, D. T. Miller, “Supernormal vision and high-resolution retinal imaging through adaptive optics,” J. Opt. Soc. Am. A 14, 2884–2892 (1997).
    [CrossRef]
  3. A. Roorda, D. R. Williams, “The arrangement of the three cone classes in the living human eye,” Nature (London) 397, 520–522 (1999).
    [CrossRef]
  4. F. Vargas-Martin, P. Prieto, P. Artal, “Correction of the aberrations in the human eye with liquid crystal spatial light modulators: limits to the performance,” J. Opt. Soc. Am. A 15, 2552–2562 (1998).
    [CrossRef]
  5. A. W. Dreher, J. F. Bille, R. N. Weinreb, “Active optical depth resolution improvement of the laser tomographic scanner,” Appl. Opt. 24, 804–808 (1989).
    [CrossRef]
  6. J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651 (1978).
    [CrossRef]
  7. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophysics (USSR) 6, 776–794 (1961).
  8. H. C. 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]
  9. I. Iglesias, E. Berrio, P. Artal, “Estimates of the ocular wave aberration from pairs of double-pass retinal images,” J. Opt. Soc. Am. A 15, 2466–2476 (1998).
    [CrossRef]
  10. J. Liang, B. Grimm, S. Goelz, J. F. Bille, “Objective measurement of the wave aberrations of the human eye using a Hartmann–Shack wavefront sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
    [CrossRef]
  11. J. Liang, D. R. Williams, “Aberrations and retinal image quality of the normal human eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
    [CrossRef]
  12. 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).
  13. N. Lopez-Gil, P. Artal, “Comparison of double-pass estimates of the retinal image quality obtained with green and near infrared light,” J. Opt. Soc. Am. A 14, 961–971 (1997).
    [CrossRef]
  14. American National Standard for the Safe Use of Lasers, ANSI Z136.1 (Laser Institute of America, Orlando, Fla., 1993).
  15. H. J. Polland, Technolas, Munich, Germany (personal communication, March25, 1999).
  16. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  17. R. W. Ditchburn, Eye-Movements and Visual Perception (Clarendon, Oxford, UK, 1973).
  18. I. Miro, N. Lopez-Gil, P. Artal, “Pupil meter and tracking system based in a fast image processing algorithm,” in Ophthalmic Technologies IX, P. O. Rol, K. M. Joos, F. Manns, B. E. Stuck, M. Belkin, eds., Proc. SPIE3591, 63–70 (1999).
    [CrossRef]
  19. L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711–716 (1995).
    [CrossRef]
  20. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985).

1999

A. Roorda, D. R. Williams, “The arrangement of the three cone classes in the living human eye,” Nature (London) 397, 520–522 (1999).
[CrossRef]

1998

1997

1995

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711–716 (1995).
[CrossRef]

1994

1989

1988

W. N. Charman, G. Heron, “Fluctuations in accommodation: a review,” Ophthalmic Physiol. Opt. 8, 153–163 (1988).
[CrossRef] [PubMed]

1978

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651 (1978).
[CrossRef]

1977

1976

1961

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

Artal, P.

Berrio, E.

Bille, J. F.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985).

Charman, W. N.

W. N. Charman, G. Heron, “Fluctuations in accommodation: a review,” Ophthalmic Physiol. Opt. 8, 153–163 (1988).
[CrossRef] [PubMed]

Ditchburn, R. W.

R. W. Ditchburn, Eye-Movements and Visual Perception (Clarendon, Oxford, UK, 1973).

Dreher, A. W.

Fercher, A. F.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711–716 (1995).
[CrossRef]

Goelz, S.

Grimm, B.

Hardy, J. W.

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651 (1978).
[CrossRef]

Heron, G.

W. N. Charman, G. Heron, “Fluctuations in accommodation: a review,” Ophthalmic Physiol. Opt. 8, 153–163 (1988).
[CrossRef] [PubMed]

Howland, B.

Howland, H. C.

Iglesias, I.

Lexer, F.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711–716 (1995).
[CrossRef]

Liang, J.

Lopez-Gil, N.

N. Lopez-Gil, P. Artal, “Comparison of double-pass estimates of the retinal image quality obtained with green and near infrared light,” J. Opt. Soc. Am. A 14, 961–971 (1997).
[CrossRef]

I. Miro, N. Lopez-Gil, P. Artal, “Pupil meter and tracking system based in a fast image processing algorithm,” in Ophthalmic Technologies IX, P. O. Rol, K. M. Joos, F. Manns, B. E. Stuck, M. Belkin, eds., Proc. SPIE3591, 63–70 (1999).
[CrossRef]

Miller, D. T.

Miro, I.

I. Miro, N. Lopez-Gil, P. Artal, “Pupil meter and tracking system based in a fast image processing algorithm,” in Ophthalmic Technologies IX, P. O. Rol, K. M. Joos, F. Manns, B. E. Stuck, M. Belkin, eds., Proc. SPIE3591, 63–70 (1999).
[CrossRef]

Noll, R. J.

Polland, H. J.

H. J. Polland, Technolas, Munich, Germany (personal communication, March25, 1999).

Prieto, P.

Roorda, A.

A. Roorda, D. R. Williams, “The arrangement of the three cone classes in the living human eye,” Nature (London) 397, 520–522 (1999).
[CrossRef]

Sattmann, H.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711–716 (1995).
[CrossRef]

Schmetterer, L. F.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711–716 (1995).
[CrossRef]

Smirnov, M. S.

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

Unfried, C. J.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711–716 (1995).
[CrossRef]

Vargas-Martin, F.

Weinreb, R. N.

Williams, D. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985).

Appl. Opt.

Biophysics (USSR)

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

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature (London)

A. Roorda, D. R. Williams, “The arrangement of the three cone classes in the living human eye,” Nature (London) 397, 520–522 (1999).
[CrossRef]

Ophthalmic Physiol. Opt.

W. N. Charman, G. Heron, “Fluctuations in accommodation: a review,” Ophthalmic Physiol. Opt. 8, 153–163 (1988).
[CrossRef] [PubMed]

Opt. Eng.

L. F. Schmetterer, F. Lexer, C. J. Unfried, H. Sattmann, A. F. Fercher, “Topical measurement of fundus pulsations,” Opt. Eng. 34, 711–716 (1995).
[CrossRef]

Proc. IEEE

J. W. Hardy, “Active optics: a new technology for the control of light,” Proc. IEEE 66, 651 (1978).
[CrossRef]

Other

American National Standard for the Safe Use of Lasers, ANSI Z136.1 (Laser Institute of America, Orlando, Fla., 1993).

H. J. Polland, Technolas, Munich, Germany (personal communication, March25, 1999).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1985).

R. W. Ditchburn, Eye-Movements and Visual Perception (Clarendon, Oxford, UK, 1973).

I. Miro, N. Lopez-Gil, P. Artal, “Pupil meter and tracking system based in a fast image processing algorithm,” in Ophthalmic Technologies IX, P. O. Rol, K. M. Joos, F. Manns, B. E. Stuck, M. Belkin, eds., Proc. SPIE3591, 63–70 (1999).
[CrossRef]

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).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1
Fig. 1

Experimental apparatus. Light from the SLD (1-mm beam size) enters the eye, forming a diffraction-limited spot on the retina. This light scatters from the retina, passes through the eye’s optics, and emerges as an aberrated wave front in the pupil plane. The microlens array, which is conjugate with the pupil plane, collects the light and forms a HS spot image on the CCD. The scanning mirror, conjugate with the pupil, scans the laser spot across the retina at 600 Hz. Because the same light is also descanned, there is no movement of the spots on the CCD camera, or of the light distribution in the pupil plane with respect to the microlens array.

Fig. 2
Fig. 2

HS images taken (a) without and (b) with the scanning mirror. Both images were taken under identical conditions with a He–Ne laser and 20-ms exposure on the same human subject. Spot compactness and uniformity are much better in (b) than in (a).

Fig. 3
Fig. 3

Illustration of the centroiding algorithm. The top panel shows the centroiding error that would be obtained with a simple algorithm that determines spot centroids by computing the center of mass within each search box. Successive panels show the result of the new algorithm after each iteration, until finally in the bottom panel the spot centroid is accurately determined.

Fig. 4
Fig. 4

Temporal traces of the total rms wave-front error, the coefficient of the Zernike defocus term, the magnitude of the Zernike astigmatism terms, the magnitude of the Zernike coma terms, and the coefficient of the Zernike spherical aberration term for subject HH when accommodating on a target at 2 D. For reference, a trace showing the variation in the total rms wave-front error for an artificial eye is included at the top of the plot. All aberrations were computed for a 4.7-mm pupil size.

Fig. 5
Fig. 5

Comparison of the power spectrum of the fluctuations in the total rms wave-front error for an artificial eye and for a human subject with paralyzed accommodation. Aberrations were computed for a 4.7-mm pupil size. The solid curve shows the spectrum for the human eye, and the dashed curve shows the power spectrum for the artificial eye. Both the power and frequency axes are logarithmic.

Fig. 6
Fig. 6

Averaged power spectra for Zernike modes of different orders for a human subject with paralyzed accommodation. Aberrations were computed for a 4.7-mm pupil size. The scale on the ordinate is applicable only to the curve for defocus; the spectra for the fluctuations in astigmatism and those for the higher orders of aberration have been vertically shifted for clarity. The numbers in parentheses next to the descriptions of the curves indicate the original power of these fluctuations, in log units, relative to those of defocus.

Fig. 7
Fig. 7

Relationship between accommodative state and spherical aberration for HH and PA. Plots show the measurement results from three trials in which the subjects voluntarily changed their accommodation over a range of approximately 2 D within a 5-s interval. Zero defocus represents the subject’s far point. Each point on the graph is the Zernike coefficient of spherical aberration plotted against the Zernike coefficient of defocus for one of the 128 measurements made during the 5-s interval of each trial. The three different symbols within each plot indicate individual points taken from each of the three separate measurements. For better slope comparison, the values of spherical aberration have been plotted for each subject relative to that subject’s value of spherical aberration when accommodating at 1 D (which was approximately the middle of the accommodative range over which measurements were taken). The lines indicate the best-fitting linear regression curves for each subject; the slopes of these lines are indicated on the plots.

Fig. 8
Fig. 8

Averaged power spectra of the fluctuations in defocus, astigmatism, and the third-, fourth-, and fifth-order Zernike modes for subjects HH and PA for the conditions of (a) paralyzed accommodation and natural accommodation on (b) near and (c) far targets.

Fig. 9
Fig. 9

Simulated effect of pupil translation. The solid curve shows the actual variation measured during a typical trial in PA’s total rms wave-front error computed for a 4.7-mm pupil size. The various dotted and dashed curve show the expected variation that one would measure in total rms wave-front error if the wave front were perfectly stable but the pupil center were moving with different amplitudes of displacement.

Fig. 10
Fig. 10

Power spectra for fluctuations in total rms wave-front error with and without the scanning mirror averaged across two subjects. The curves are nearly parallel, demonstrating that spatial inhomogeneity in real eyes does not act as a random noise source but causes a multiplicative increase in the power spectra of the measured fluctuations in the wave aberration.

Fig. 11
Fig. 11

Time-averaged Strehl ratio versus bandwidth for a perfect adaptive optics system, calculated for 4.7- and 5.8-mm pupils for paralyzed accommodation and for natural accommodation on a far target. Error bars on each subject’s curve represent the standard deviations of the calculated results for that subject. Values of Strehl ratio higher than 0.8 are considered to correspond to diffraction-limited imaging.

Metrics