Abstract

Phase-diverse wave-front sensing (PDWFS) is a methodology for estimating aberration coefficients from multiple incoherent images whose pupil phases differ from one another in a known manner. With the use of previous work by other authors, the Cramér–Rao lower-bound (CRLB) expression for the phase diversity aberration estimation problem is developed and is generalized slightly to allow for multiple phase-diverse images, various beam-splitting configurations, and imaging of known extended objects. The CRLB for a given problem depends implicitly on the true underlying value of the aberration being estimated. Therefore we use numerical evaluation and Monte Carlo analysis of the PDWFS CRLB expressions. The numerical evaluation is performed on an ensemble of aberration phase screens while simulating a number of different imaging configurations. We demonstrate the use of average CRLB values as figures of merit in comparing these various PDWFS configurations. For simulated point-source imaging we quantify the effects of varying the amounts and the types of diversity phase and briefly address the issue of the number of diversity images. Our results show that there is a diversity defocus configuration that is optimal in a Cramér–Rao sense for estimating certain aberrations. We also show that PDWFS Cramér–Rao squared-error values can be orders of magnitude higher for imaging of an extended target object than those from a point-source target.

© 1999 Optical Society of America

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1995 (1)

1994 (1)

M. G. Lofdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys., Suppl. Ser. 107, 243–264 (1994).

1993 (1)

1992 (1)

1988 (1)

1983 (1)

1982 (1)

1977 (1)

1976 (1)

Chidlaw, R.

R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).

Ellerbroek, B. L.

Fienup, J. R.

Fried, D. L.

Gaskill, J. D.

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

Gonsalves, R. A.

R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).

R. A. Gonsalves, “Fundamentals of wavefront sensing by phase retrieval,” in Wavefront Sensing, N. Bareket, C. L. Koliopoulos, eds., Proc. SPIE351, 56–65 (1982).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Kay, S. M.

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).

Lofdahl, M. G.

M. G. Lofdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys., Suppl. Ser. 107, 243–264 (1994).

Marron, J. C.

Miller, M. I.

D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space (Springer, New York, 1991).

Noll, R. J.

Paxman, R. G.

Pennington, T. L.

Roggemann, M. C.

Scharmer, G. B.

M. G. Lofdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys., Suppl. Ser. 107, 243–264 (1994).

Schulz, T. J.

Seldin, J. H.

Snyder, D. L.

D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space (Springer, New York, 1991).

Wallner, E. P.

Welsh, B. M.

Appl. Opt. (3)

Astron. Astrophys., Suppl. Ser. (1)

M. G. Lofdahl, G. B. Scharmer, “Wavefront sensing and image restoration from focused and defocused solar images,” Astron. Astrophys., Suppl. Ser. 107, 243–264 (1994).

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (2)

Other (8)

D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space (Springer, New York, 1991).

R. A. Gonsalves, “Fundamentals of wavefront sensing by phase retrieval,” in Wavefront Sensing, N. Bareket, C. L. Koliopoulos, eds., Proc. SPIE351, 56–65 (1982).

J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics (Wiley, New York, 1978).

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

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

R. A. Gonsalves, R. Chidlaw, “Wavefront sensing by phase retrieval,” in Applications of Digital Image Processing III, A. G. Tescher, ed., Proc. SPIE207, 32–39 (1979).

S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).

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