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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 19, Iss. 9 — Sep. 1, 2002
  • pp: 1803–1816

Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques

Brent L. Ellerbroek  »View Author Affiliations

JOSA A, Vol. 19, Issue 9, pp. 1803-1816 (2002)

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The complexity of computing conventional matrix multiply wave-front reconstructors scales as O(n3) for most adaptive optical (AO) systems, where n is the number of deformable mirror (DM) actuators. This is impractical for proposed systems with extremely large n. It is known that sparse matrix methods improve this scaling for least-squares reconstructors, but sparse techniques are not immediately applicable to the minimum-variance reconstructors now favored for multiconjugate adaptive optical (MCAO) systems with multiple wave-front sensors (WFSs) and DMs. Complications arise from the nonsparse statistics of atmospheric turbulence, and the global tip/tilt WFS measurement errors associated with laser guide star (LGS) position uncertainty. A description is given of how sparse matrix methods can still be applied by use of a sparse approximation for turbulence statistics and by recognizing that the nonsparse matrix terms arising from LGS position uncertainty are low-rank adjustments that can be evaluated by using the matrix inversion lemma. Sample numerical results for AO and MCAO systems illustrate that the approximation made to turbulence statistics has negligible effect on estimation accuracy, the time to compute the sparse minimum-variance reconstructor for a conventional natural guide star AO system scales as O(n3/2) and is only a few seconds for n=3500, and sparse techniques reduce the reconstructor computations by a factor of 8 for sample MCAO systems with 2417 DM actuators and 4280 WFS subapertures. With extrapolation to 9700 actuators and 17,120 subapertures, a reduction by a factor of approximately 30 or 40 to 1 is predicted.

© 2002 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics

Original Manuscript: January 7, 2002
Revised Manuscript: April 1, 2002
Manuscript Accepted: April 9, 2002
Published: September 1, 2002

Brent L. Ellerbroek, "Efficient computation of minimum-variance wave-front reconstructors with sparse matrix techniques," J. Opt. Soc. Am. A 19, 1803-1816 (2002)

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  27. Matlab 6 no longer supports the FLOPS command included in previous versions to report the exact number of floating-point operations required by an algorithm. No other computationally significant tasks were running on this dual-processor system during the timing tests reported in this paper.

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