Abstract

Future extreme adaptive optics (ExAO) systems have been suggested with up to 105 sensors and actuators. We analyze the computational speed of iterative reconstruction algorithms for such large systems. We compare a total of 15 different scalable methods, including multigrid, preconditioned conjugate-gradient, and several new variants of these. Simulations on a 128×128 square sensor/actuator geometry using Taylor frozen-flow dynamics are carried out using both open-loop and closed-loop measurements, and algorithms are compared on a basis of the mean squared error and floating-point multiplications required. We also investigate the use of warm starting, where the most recent estimate is used to initialize the iterative scheme. In open-loop estimation or pseudo-open-loop control, warm starting provides a significant computational speedup; almost every algorithm tested converges in one iteration. In a standard closed-loop implementation, using a single iteration per time step, most algorithms give the minimum error even in cold start, and every algorithm gives the minimum error if warm started. The best algorithm is therefore the one with the smallest computational cost per iteration, not necessarily the one with the best quasi-static performance.

© 2008 Optical Society of America

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2007

2006

2005

2004

2003

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

L. Gilles, “Order-N sparse minimum-variance open-loop reconstructor for extreme adaptive optics,” Opt. Lett. 28, 1927-1929 (2003).
[CrossRef]

B. L. Ellerbroek and C. R. Vogel, “Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes,” Proc. SPIE 5169, 206-217 (2003).

D. T. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890-901 (2003).

2002

2000

B. L. Ellerbroek and F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” Proc. SPIE 4007, 1088-1099 (2000).
[CrossRef]

1993

1983

Anderson, D. J.

Brase, J. M.

Britton, M.

Britton, M. C.

M. C. Britton, “Arroyo,” Proc. SPIE 5497, 290-300 (2004).

M. C. Britton, “Arroyo C++ library: object oriented class libraries for the simulation of electromagnetic wave propagation through turbulence,” http://eraserhead.caltech.edu/arroyo/arroyo.html (April 8, 2008).

Conan, J.-M.

Dekany, R.

Ellerbroek, B.

L. Gilles, B. Ellerbroek, and C. Vogel, “A comparison of multigrid V-cycle versus Fourier domain preconditioning for laser guide star atmospheric tomography,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JTuA1.

Ellerbroek, B. L.

Fusco, T.

Gavel, D. T.

Gilles, L.

L. Gilles, “Closed-loop stability and performance analysis of least-squares and minimum-variance control algorithms for multiconjugate adaptive optics,” Appl. Opt. 44, 993-1002 (2005).
[CrossRef]

L. Gilles, “Order-N sparse minimum-variance open-loop reconstructor for extreme adaptive optics,” Opt. Lett. 28, 1927-1929 (2003).
[CrossRef]

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

L. Gilles, B. Ellerbroek, and C. Vogel, “A comparison of multigrid V-cycle versus Fourier domain preconditioning for laser guide star atmospheric tomography,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JTuA1.

Hardy, J. W.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).

Kulcsár, C.

Le Roux, B.

Macintosh, B. A.

MacMartin, D. G.

Mugnier, L. M.

Oosterlee, C. W.

U. Trottenberg, A. Schüller, and C. W. Oosterlee, Multigrid Methods (Academic, 2000).

Paschall, R. N.

Piatrou, P.

P. Piatrou and M. Roggemann, “Performance analysis of Kalman filter and minimum variance controllers for multiconjugate adaptive optics,” Proc. SPIE 5894, 288-296 (2005).

Poyneer, L. A.

Raynaud, H.-F.

Ren, H.

Rigaut, F. J.

B. L. Ellerbroek and F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” Proc. SPIE 4007, 1088-1099 (2000).
[CrossRef]

Roggemann, M.

P. Piatrou and M. Roggemann, “Performance analysis of Kalman filter and minimum variance controllers for multiconjugate adaptive optics,” Proc. SPIE 5894, 288-296 (2005).

Schüller, A.

U. Trottenberg, A. Schüller, and C. W. Oosterlee, Multigrid Methods (Academic, 2000).

Tatarskii, V. I.

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

Trottenberg, U.

U. Trottenberg, A. Schüller, and C. W. Oosterlee, Multigrid Methods (Academic, 2000).

Véran, J.-P.

Vogel, C.

L. Gilles, B. Ellerbroek, and C. Vogel, “A comparison of multigrid V-cycle versus Fourier domain preconditioning for laser guide star atmospheric tomography,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JTuA1.

Vogel, C. R.

Wallner, E. P.

Wiberg, D.

D. T. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890-901 (2003).

Yang, Q.

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Lett.

Proc. SPIE

D. T. Gavel and D. Wiberg, “Toward Strehl-optimizing adaptive optics controllers,” Proc. SPIE 4839, 890-901 (2003).

P. Piatrou and M. Roggemann, “Performance analysis of Kalman filter and minimum variance controllers for multiconjugate adaptive optics,” Proc. SPIE 5894, 288-296 (2005).

B. L. Ellerbroek and C. R. Vogel, “Simulations of closed-loop wavefront reconstruction for multiconjugate adaptive optics on giant telescopes,” Proc. SPIE 5169, 206-217 (2003).

M. C. Britton, “Arroyo,” Proc. SPIE 5497, 290-300 (2004).

B. L. Ellerbroek and F. J. Rigaut, “Scaling multiconjugate adaptive optics performance estimates to extremely large telescopes,” Proc. SPIE 4007, 1088-1099 (2000).
[CrossRef]

Other

L. Gilles, B. Ellerbroek, and C. Vogel, “A comparison of multigrid V-cycle versus Fourier domain preconditioning for laser guide star atmospheric tomography,” in Adaptive Optics: Analysis and Methods/Computational Optical Sensing and Imaging/Information Photonics/Signal Recovery and Synthesis Topical Meetings on CD-ROM, OSA Technical Digest (CD) (Optical Society of America, 2007), paper JTuA1.

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford U. Press, 1998).

V. I. Tatarskii, Wave Propagation in a Turbulent Medium (McGraw-Hill, 1961).

U. Trottenberg, A. Schüller, and C. W. Oosterlee, Multigrid Methods (Academic, 2000).

M. C. Britton, “Arroyo C++ library: object oriented class libraries for the simulation of electromagnetic wave propagation through turbulence,” http://eraserhead.caltech.edu/arroyo/arroyo.html (April 8, 2008).

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