Abstract

Phase diversity algorithms allow a wavefront to be reconstructed from through-focus measurements of a point source or extended scene. These algorithms have traditionally been limited to systems that are Nyquist sampled. Many optical systems for remote sensing applications are designed to be undersampled, however. One approach to phase diversity with undersampled systems is to employ superresolution techniques to first create properly sampled scenes. This is demonstrated experimentally for a point object, but is applicable to extended scenes as well.

© 2012 Optical Society of America

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References

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S. C. Park, M. K. Park, and M. G. Kang, IEEE Signal Process. Mag. 20, 21 (2003).
[CrossRef]

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D. S. C. Biggs and M. Andrews, Appl. Opt. 36, 1766 (1997).
[CrossRef]

A. S. Fruchter and R. N. Hook, Proc. SPIE 3164, 120 (1997).
[CrossRef]

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1992 (1)

1982 (2)

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).

J. R. Fienup, Appl. Opt. 21, 2758 (1982).
[CrossRef]

1976 (1)

Andrews, M.

Biggs, D. S. C.

Brady, G. R.

DeRosa, R. T.

Fienup, J. R.

Fiete, R. D.

R. D. Fiete, Opt. Eng. 38, 1229 (1999).
[CrossRef]

Fletcher, R.

R. Fletcher, Practical Methods of Optimization, 2nd ed. (Wiley, 1987).

Fruchter, A. S.

A. S. Fruchter and R. N. Hook, Proc. SPIE 3164, 120 (1997).
[CrossRef]

Gonsalves, R. A.

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).

Guizar-Sicairos, M.

Hook, R. N.

A. S. Fruchter and R. N. Hook, Proc. SPIE 3164, 120 (1997).
[CrossRef]

Hu, X. J.

Kang, M. G.

S. C. Park, M. K. Park, and M. G. Kang, IEEE Signal Process. Mag. 20, 21 (2003).
[CrossRef]

Li, S. Y.

Noll, R. J.

Park, M. K.

S. C. Park, M. K. Park, and M. G. Kang, IEEE Signal Process. Mag. 20, 21 (2003).
[CrossRef]

Park, S. C.

S. C. Park, M. K. Park, and M. G. Kang, IEEE Signal Process. Mag. 20, 21 (2003).
[CrossRef]

Paxman, R. G.

Schulz, T. J.

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 3rd ed. (McGraw-Hill, 2000).

Thurman, S. T.

Wu, Y. L.

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Figures (3)

Fig. 1.
Fig. 1.

Test configurations for (a) interferometry and (b) phase-diverse phase retrieval. Note that for (b) the interferometer is only used as a laser source.

Fig. 2.
Fig. 2.

Input PSFs for (a)–(c) undersampled reconstruction and (d)–(f) Nyquist-sampled reconstruction. Figures 2(a)2(c) result from superresolution reconstruction and deconvolution.

Fig. 3.
Fig. 3.

(a) Interferometrically measured wavefront; (b) Nyquist-sampled reconstructed wavefront; and (c) undersampled reconstructed wavefront. Wavefront units are waves.

Tables (1)

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Table 1. Interferometrically Measured Zernike Coefficients and Reconstruction Errorsa

Equations (1)

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Q=λf#p,

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