Abstract

The use of a correcting element to compensate for higher-order aberrations in an optical system often requires accurate alignment of the correcting element. This is not always possible, as in the case of a contact lens on the eye. We propose a method consisting of partial correction of every aberration term to minimize the average variance of the residual wave-front aberration produced by Gaussian decentrations (translations and rotations). Analytical expressions to estimate the fraction of every aberration term that should be corrected for a given amount of decentration are derived. To demonstrate the application of this method, three examples are used to compare performance with total and with partial correction. The partial correction is more robust and always yields some benefit regardless of the amount of decentration.

© 2002 Optical Society of America

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References

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  1. 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]
  2. A. Guirao, D. R. Williams, I. G. Cox, “Effect of rotation and translation on the expected benefit of an ideal method to correct the eye’s higher-order aberrations,” J. Opt. Soc. Am. A 18, 1003–1015 (2001).
    [CrossRef]
  3. S. Bará, T. Mancebo, E. Moreno-Barriuso, “Positioning tolerances for phase plates compensating aberrations of the human eye,” Appl. Opt. 39, 3413–3420 (2000).
    [CrossRef]
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    [CrossRef] [PubMed]

2001

2000

1997

1980

Bará, S.

Cox, I. G.

Guirao, A.

Liang, J.

Mancebo, T.

Miller, D. T.

Moreno-Barriuso, E.

Silva, D. E.

Wang, J. Y.

Williams, D. R.

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Figures (2)

Fig. 1
Fig. 1

Illustration of the concept of the method. An optical system (OS) with pure spherical aberration is corrected by a correcting method (CM) that is decentered with respect to the pupil. When the total aberration of the OS is corrected, the residual aberrations are larger than those corresponding to the correction of only a fraction of the original aberration, as shown by the image intensity profiles. In the presence of decentration, the correction of spherical aberration produces coma that is proportional to the decentration and to the amount of spherical aberration corrected; with partial correction, a residual spherical aberration is uncorrected, but the amount of coma produced is smaller, giving minimum variance for the total aberrations.

Fig. 2
Fig. 2

Variance of the residual aberrations of the corrected system after Gaussian decentrations of the correcting element. Thin solid curves, aberrations totally corrected. Thick solid curves, aberrations partially corrected according to the fraction γn±m. Dotted and dashed curves, fraction of the aberration that is corrected. The WA consists of (a) spherical aberration, (b) the term Z66, and (c) two third-order aberrations, Z31 and Z33.

Tables (1)

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Table 1 Values of the Factor Fnm

Equations (7)

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bn±m=-γn±man±m.
WAresidual=WAOS+WACM=n,±m(1-γn±m)an±mZn±m.
Cn±m=-([T][R](γa))n±m,
WAresidual=WAOS+WACM(decentered)
=n,±m(an±m+Cn±m)Zn±m,
var=n,±m(an±m+Cn±m)2.
γn±m(σt, σr)=exp(-m2σr2/2)1+Fnmσt2/ro2,

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