Abstract

The wave aberration of the human eye has been measured by means of a Hartmann–Shack wave-front sensor in a population of normal subjects. The set of data has been used to compute the phase distribution, the power spectrum, and the structure function for the average eye to analyze the statistics of the ocular aberration considered as a phase screen. The observed statistics fits the classical Kolmogorov model of a statistically homogeneous medium. These results can be of use in understanding the average effect of aberrations on the retinal image and can serve as a tool to analyze the consequences of ocular-aberration compensation by adaptive optics, customized ophtalmic elements, or refractive surgery.

© 2002 Optical Society of America

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References

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  1. M. S. Smirnov, “Measurement of the wave aberration of the human eye,” Biophys. 6, 776–794 (1961).
  2. J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurements of wave aberrations of the human eye with use of a Hartmann–Shack wave-front sensor,” J. Opt. Soc. Am. A 11, 1949–1957 (1994).
    [CrossRef]
  3. J. Liang and D. R. Williams, “Aberrations and retinal image quality of the normal eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
    [CrossRef]
  4. P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann–Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000).
    [CrossRef]
  5. J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistic in a normal young population,” submitted to Vis. Res.
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  9. J. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, New York, 1998).
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    [CrossRef]
  11. M. P. Cagigal and V. F. Canales, “Generalized Fried parameter after adaptive optics partial wave-front compensation,” J. Opt. Soc. Am. A 17, 903–910 (2000).
    [CrossRef]

2000

M. P. Cagigal and V. F. Canales, “Generalized Fried parameter after adaptive optics partial wave-front compensation,” J. Opt. Soc. Am. A 17, 903–910 (2000).
[CrossRef]

P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann–Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000).
[CrossRef]

M. P. Cagigal and V. F. Canales, “Residual phase variance in partial correction: application to the estimate of the light intensity statistics,” J. Opt. Soc. Am. A 17, 1312–1318 (2000).
[CrossRef]

1997

1996

1994

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

1976

1961

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

Artal, P.

P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann–Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000).
[CrossRef]

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistic in a normal young population,” submitted to Vis. Res.

Benito, A.

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistic in a normal young population,” submitted to Vis. Res.

Bille, J. F.

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

Cagigal, M. P.

M. P. Cagigal and V. F. Canales, “Residual phase variance in partial correction: application to the estimate of the light intensity statistics,” J. Opt. Soc. Am. A 17, 1312–1318 (2000).
[CrossRef]

M. P. Cagigal and V. F. Canales, “Generalized Fried parameter after adaptive optics partial wave-front compensation,” J. Opt. Soc. Am. A 17, 903–910 (2000).
[CrossRef]

Canales, V. F.

M. P. Cagigal and V. F. Canales, “Generalized Fried parameter after adaptive optics partial wave-front compensation,” J. Opt. Soc. Am. A 17, 903–910 (2000).
[CrossRef]

M. P. Cagigal and V. F. Canales, “Residual phase variance in partial correction: application to the estimate of the light intensity statistics,” J. Opt. Soc. Am. A 17, 1312–1318 (2000).
[CrossRef]

Castejón-Mochón, J. F.

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistic in a normal young population,” submitted to Vis. Res.

Goelz, S.

P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann–Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000).
[CrossRef]

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

Grimm, B.

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

Hardy, J.

J. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, New York, 1998).

Kumar, G.

Liang, J.

J. Liang and D. R. Williams, “Aberrations and retinal image quality of the normal eye,” J. Opt. Soc. Am. A 14, 2873–2883 (1997).
[CrossRef]

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

López-Gil, N.

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistic in a normal young population,” submitted to Vis. Res.

Noll, R. J.

Prieto, P. M.

P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann–Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000).
[CrossRef]

Roggemann, M. C.

M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC, Boca Raton, Fla., 1996).

Schmitt, J. M.

Smirnov, M. S.

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

Vargas-Martín, F.

P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann–Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000).
[CrossRef]

Welsh, B.

M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC, Boca Raton, Fla., 1996).

Williams, D. R.

Biophys.

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

J. Opt. Soc. Am. A

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

P. M. Prieto, F. Vargas-Martín, S. Goelz, and P. Artal, “Analysis of the performance of the Hartmann–Shack sensor in the human eye,” J. Opt. Soc. Am. A 17, 1388–1398 (2000).
[CrossRef]

M. P. Cagigal and V. F. Canales, “Generalized Fried parameter after adaptive optics partial wave-front compensation,” J. Opt. Soc. Am. A 17, 903–910 (2000).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Vis. Res.

J. F. Castejón-Mochón, N. López-Gil, A. Benito, and P. Artal, “Ocular wave-front aberration statistic in a normal young population,” submitted to Vis. Res.

Other

M. C. Roggemann and B. Welsh, Imaging Through Turbulence (CRC, Boca Raton, Fla., 1996).

J. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, New York, 1998).

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Figures (4)

Fig. 1
Fig. 1

Distribution of the phase across subjects and pupil positions for a 7-mm pupil diameter, for two different levels of compensation (thin curves, j=3; thick curves, j=6). Solid curves, normalized experimental density functions; dashed curves, Gaussian fits.

Fig. 2
Fig. 2

Power spectra for two different compensation levels (thin solid curves, three modes corrected, thick solid curves, ten modes corrected), compared with a -11/3 power law (thin dotted curves, three modes corrected; thick dashed curve, ten modes corrected).

Fig. 3
Fig. 3

Radial evolution of the phase variance for two compensation levels (solid curve, three modes corrected; dashed curve, ten modes corrected).

Fig. 4
Fig. 4

Structure function calculated with concentric circles of different diameter d. The pupil diameter is fixed D=7 mm, and the distance between points Δr is in D units. Long-dashed curve, d=0.9D; solid curve, d=0.7D; circles, d=0.5D; short-dashed curve, d=0.3D.

Equations (1)

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ϕr=i=1aiZir,

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