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Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Vol. 28, Iss. 20 — Oct. 15, 2003
  • pp: 1927–1929

Order-N sparse minimum-variance open-loop reconstructor for extreme adaptive optics

L. Gilles  »View Author Affiliations


Optics Letters, Vol. 28, Issue 20, pp. 1927-1929 (2003)
http://dx.doi.org/10.1364/OL.28.001927


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Abstract

A scalable sparse minimum-variance open-loop wave-front reconstructor for extreme adaptive optics (ExAO) systems is presented. The reconstructor is based on Ellerbroek’s sparse approximation of the wave-front inverse covariance matrix [J. Opt. Soc. Am. A 19, 1803 (2002)]. The baseline of the numerical approach is an iterative conjugate gradient (CG) algorithm for reconstructing a spatially sampled wave front at N grid points on a computational domain of size equal to the telescope’s primary mirror’s diameter D that uses a multigrid (MG) accelerator to speed up convergence efficiently and enhance its robustness. The combined MGCG scheme is order N and requires only two CG iterations to converge to the asymptotic average Strehl ratio (SR) and root-mean-square reconstruction error. The SR and reconstruction squared error are within standard deviation with figures obtained from a previously proposed MGCG fast-Fourier-transform based minimum-variance reconstructor that incorporates the exact wave-front inverse covariance matrix on a computational domain of size equal to 2D . A cost comparison between the present sparse MGCG algorithm and a Cholesky factorization based algorithm that uses a reordering scheme to preserve sparsity indicates that the latter method is still competitive for real-time ExAO wave-front reconstruction for systems with up to N ∼ 104 degrees of freedom because the update rate of the Cholesky factor is typically several orders of magnitude lower than the temporal sampling rate.

© 2003 Optical Society of America

OCIS Codes
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.7350) Atmospheric and oceanic optics : Wave-front sensing

Citation
L. Gilles, "Order-N sparse minimum-variance open-loop reconstructor for extreme adaptive optics," Opt. Lett. 28, 1927-1929 (2003)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-20-1927

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