Abstract

A new, to my knowledge, procedure for retrieving the wave aberration from the point-spread function is presented. It uses the Levenberg–Marquardt optimization algorithm in a mutiresolution pyramidal scheme. The method, tested with simulated large aberrations without initial estimates, accelerates convergence and avoids stagnation in local minima.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  8. W. S. Rabadi, H. R. Myller, A. R. Weeks, “Iterative multiresolution algorithm for image reconstruction from the magnitude of its Fourier transform,” Opt. Eng. 35, 1015–1024 (1996).
    [CrossRef]

1998 (1)

1996 (1)

W. S. Rabadi, H. R. Myller, A. R. Weeks, “Iterative multiresolution algorithm for image reconstruction from the magnitude of its Fourier transform,” Opt. Eng. 35, 1015–1024 (1996).
[CrossRef]

1993 (1)

1992 (1)

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberration by using phase diversity,” J. Opt. Soc Am. A 9, 1072–1085 (1992).
[CrossRef]

1982 (1)

1977 (1)

1976 (1)

Artal, P.

Fienup, J. R.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, London, 1986).

Iglesias, I.

Lopez-Gil, N.

Myller, H. R.

W. S. Rabadi, H. R. Myller, A. R. Weeks, “Iterative multiresolution algorithm for image reconstruction from the magnitude of its Fourier transform,” Opt. Eng. 35, 1015–1024 (1996).
[CrossRef]

Noll, R. J.

Paxman, R. G.

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberration by using phase diversity,” J. Opt. Soc Am. A 9, 1072–1085 (1992).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, London, 1986).

Rabadi, W. S.

W. S. Rabadi, H. R. Myller, A. R. Weeks, “Iterative multiresolution algorithm for image reconstruction from the magnitude of its Fourier transform,” Opt. Eng. 35, 1015–1024 (1996).
[CrossRef]

Schulz, T. J.

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberration by using phase diversity,” J. Opt. Soc Am. A 9, 1072–1085 (1992).
[CrossRef]

Shouthwell, W. H.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, London, 1986).

Vettering, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, London, 1986).

Weeks, A. R.

W. S. Rabadi, H. R. Myller, A. R. Weeks, “Iterative multiresolution algorithm for image reconstruction from the magnitude of its Fourier transform,” Opt. Eng. 35, 1015–1024 (1996).
[CrossRef]

Appl. Opt. (2)

J. Opt. Soc Am. A (1)

R. G. Paxman, T. J. Schulz, J. R. Fienup, “Joint estimation of object and aberration by using phase diversity,” J. Opt. Soc Am. A 9, 1072–1085 (1992).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Opt. Eng. (1)

W. S. Rabadi, H. R. Myller, A. R. Weeks, “Iterative multiresolution algorithm for image reconstruction from the magnitude of its Fourier transform,” Opt. Eng. 35, 1015–1024 (1996).
[CrossRef]

Other (1)

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes (Cambridge U. Press, Cambridge, London, 1986).

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Figures (3)

Fig. 1
Fig. 1

Pyramidal implementation of the LM algorithm to retrieve the wave aberration from the PSF.

Fig. 2
Fig. 2

Error evolution in the retrieval of the wave aberration with 14 free parameters from the PSF with S = 0.10 by use of the LM algorithm (dashed curve) and the pyramidal algorithm (solid curve). NRMSE, normalized rms error.

Fig. 3
Fig. 3

(a) Test wave aberration (64-pixel pupil radius) corresponding to the PSF with S = 0.08. The P-V is 4.6λ. (b) Retrieved wave aberration; the P-V is 4.4λ and S = 0.10. (c) Residual wave aberration (S = 0.23). The height axis is plotted in units of wavelength.

Tables (1)

Tables Icon

Table 1 Two Different Sets of Test Parameters and the Sets Recovereda

Equations (5)

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w ν ,   a = k   a k Z k r ,   θ ,
g ν ,   a = m ν exp i 2 π w ν ,   a / λ ,
E a = x A x - | G x ,   a | 2 ,
α kl = ν   h k ν ,   a h l ν ,   a ,
h k ν ,   a = 2 Re - i 2 π / λ g * ν ,   a Z k r ,   θ × FT G x ,   a / | G x ,   a | .

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