Abstract

We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system.

© 2005 Optical Society of America

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2004 (1)

2003 (3)

2002 (3)

1994 (1)

1992 (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

1991 (1)

1989 (1)

1986 (1)

1978 (1)

1977 (2)

Base, J. M.

Bauman, B.

R. Dekany, J. E. Nelson, B. Bauman, “Design considerations for CELT adaptive optics,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 212–225 (2000).

Brack, G. L.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, R. G. Dekany, “Sparse matrix wavefront reconstruction: simulations and experiments,” in Adaptive Optical System Technologies II, P. Wizinowich, ed., Proc. SPIE4839, 1035–1044 (2002).

Burruss, R. S.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, R. G. Dekany, “Sparse matrix wavefront reconstruction: simulations and experiments,” in Adaptive Optical System Technologies II, P. Wizinowich, ed., Proc. SPIE4839, 1035–1044 (2002).

Dainty, J. C.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Dekany, R.

H. Ren, R. Dekany, “Fast wavefront reconstruction by solving the Sylvester equation with the alternating direction implicit method,” Opt. Express 12, 3279–3296 (2004), http://www.opticsexpress.org .
[CrossRef] [PubMed]

R. Dekany, J. E. Nelson, B. Bauman, “Design considerations for CELT adaptive optics,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 212–225 (2000).

Dekany, R. G.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, R. G. Dekany, “Sparse matrix wavefront reconstruction: simulations and experiments,” in Adaptive Optical System Technologies II, P. Wizinowich, ed., Proc. SPIE4839, 1035–1044 (2002).

Ellerbroek, B. L.

L. Gilles, C. R. Vogel, B. L. Ellerbroek, “A multigrid preconditioned conjugate gradient method for large-scale wave-front reconstruction,” J. Opt. Soc. Am. A 19, 1817–1822 (2002).
[CrossRef]

B. L. Ellerbroek, “Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques,” J. Opt. Soc. Am. A 19, 1802–1816 (2002).
[CrossRef]

Freischlad, K. R.

Fried, D. L.

Gavel, D. T.

Ghiglia, D. C.

Gilles, L.

Glindemann, A.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Golub, G. H.

G. H. Golub, C. F. van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, Baltimore, Md., 1996).

Hudgin, R. H.

Koliopoulos, C. L.

Lane, R. G.

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Macintosh, B.

MacMartin, D. G.

D. G. MacMartin, “Local, hierachic, and iterative reconstructors for adaptive optics,” J. Opt. Soc. Am. A 20, 1084–1093 (2003).
[CrossRef]

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, R. G. Dekany, “Sparse matrix wavefront reconstruction: simulations and experiments,” in Adaptive Optical System Technologies II, P. Wizinowich, ed., Proc. SPIE4839, 1035–1044 (2002).

Mooney, J. G.

R. J. Sasiela, J. G. Mooney, “An optical phase reconstructor based on using a multiplier-accumulator approach,” in Adaptive Optics, J. E. Ludman, ed., Proc. SPIE551, 170–176 (1985).

Nelson, J. E.

R. Dekany, J. E. Nelson, B. Bauman, “Design considerations for CELT adaptive optics,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 212–225 (2000).

Noll, R. J.

Poyneer, L. A.

Pritt, M. D.

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, 1998).

Rao, K. R.

K. R. Rao, P. Yip, Discrete Cosine Transform: Algorithm, Advantages, Applications (Academic, San Diego, Calif., 1990).

Ren, H.

Roddier, C.

Roddier, F.

Romero, L. A.

Rousset, G.

G. Rousset, “Wavefront sensors,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge U. Press, Cambridge, 1999).

Sasiela, R. J.

R. J. Sasiela, J. G. Mooney, “An optical phase reconstructor based on using a multiplier-accumulator approach,” in Adaptive Optics, J. E. Ludman, ed., Proc. SPIE551, 170–176 (1985).

Shi, F.

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, R. G. Dekany, “Sparse matrix wavefront reconstruction: simulations and experiments,” in Adaptive Optical System Technologies II, P. Wizinowich, ed., Proc. SPIE4839, 1035–1044 (2002).

Troy, M.

L. A. Poyneer, M. Troy, B. Macintosh, D. T. Gavel, “Experimental validation of Fourier-transform wavefront reconstruction at the Palomar Observatory,” Opt. Lett. 28, 798–800 (2003).
[CrossRef] [PubMed]

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, R. G. Dekany, “Sparse matrix wavefront reconstruction: simulations and experiments,” in Adaptive Optical System Technologies II, P. Wizinowich, ed., Proc. SPIE4839, 1035–1044 (2002).

van Loan, C. F.

G. H. Golub, C. F. van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, Baltimore, Md., 1996).

Vogel, C. R.

Watkins, D. S.

D. S. Watkins, Fundamentals of Matrix Computations, 2nd ed. (Wiley, New York, 2002).

Yip, P.

K. R. Rao, P. Yip, Discrete Cosine Transform: Algorithm, Advantages, Applications (Academic, San Diego, Calif., 1990).

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (6)

Opt. Express (1)

Opt. Lett. (3)

Waves Random Media (1)

R. G. Lane, A. Glindemann, J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves Random Media 2, 209–224 (1992).
[CrossRef]

Other (8)

D. C. Ghiglia, M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, 1998).

D. S. Watkins, Fundamentals of Matrix Computations, 2nd ed. (Wiley, New York, 2002).

G. H. Golub, C. F. van Loan, Matrix Computations, 3rd ed. (Johns Hopkins U. Press, Baltimore, Md., 1996).

K. R. Rao, P. Yip, Discrete Cosine Transform: Algorithm, Advantages, Applications (Academic, San Diego, Calif., 1990).

R. Dekany, J. E. Nelson, B. Bauman, “Design considerations for CELT adaptive optics,” in Optical Design, Materials, Fabrication, and Maintenance, P. Dierickx, ed., Proc. SPIE4003, 212–225 (2000).

F. Shi, D. G. MacMartin, M. Troy, G. L. Brack, R. S. Burruss, R. G. Dekany, “Sparse matrix wavefront reconstruction: simulations and experiments,” in Adaptive Optical System Technologies II, P. Wizinowich, ed., Proc. SPIE4839, 1035–1044 (2002).

R. J. Sasiela, J. G. Mooney, “An optical phase reconstructor based on using a multiplier-accumulator approach,” in Adaptive Optics, J. E. Ludman, ed., Proc. SPIE551, 170–176 (1985).

G. Rousset, “Wavefront sensors,” in Adaptive Optics in Astronomy, F. Roddier, ed. (Cambridge U. Press, Cambridge, 1999).

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