24 December 2003 Sparse minimum-variance open-loop reconstructors for extreme adaptive optics: order N multigrid versus preordered Cholesky factorization
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Abstract
A scalable sparse minimum-variance open-loop wavefront reconstructor for extreme adaptive optics (ExAO) systems is presented. The reconstructor is based on Ellerbroek's sparse approximation of the wavefront inverse covariance matrix. The baseline of the numerical approach is an iterative conjugate gradient (CG) algorithm reconstructing a spatially sampled wavefront at N grid points on a computational domain of size equal to the telescope primary mirror diameter D, using a multigrid (MG) accelarator to efficiently speed up convergence and enhance its robustness. The combined MGCG scheme is order N, and requires only 2 conjugate gradient iterations to converge to the asymptotic average Strehl ratio (SR) and root mean squared (RMS) reconstruction error. Average SR and RMS reconstruction error comparison with figures obtained from a previously proposed MGCG FFT-based minimum-variance reconstructor incorporating the exact wavefront inverse covariance matrix on a computational domain of size equal to 2D, indicates relative deviations below 1-2% at realistic measurement noise levels below π/2 rad RMS phase difference. A cost comparison between the sparse MGCG algorithm and a symmetric approximate minimum degree (SYMAMD) preordered Cholesky factorization, indicates that this last method is competitive for real-time ExAO wavefront reconstruction for systems with up to N ≈ 104 since the update rate of the Cholesky factor is typically several orders of magnitude lower than the temporal sampling rate.
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Luc Gilles, "Sparse minimum-variance open-loop reconstructors for extreme adaptive optics: order N multigrid versus preordered Cholesky factorization", Proc. SPIE 5169, Astronomical Adaptive Optics Systems and Applications, (24 December 2003); doi: 10.1117/12.506893; https://doi.org/10.1117/12.506893
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