Gemini Preprint #84

Layer-Oriented Multigrid Wavefront Reconstruction Algorithms for Multi-Conjugate Adaptive Optics

L.Gillesa, B.L.Ellerbroekb and C.R.Vogelc

aMichigan Technological University, Dept. of Electrical and Computer Engineering, Houghton, MI 49931-1295

bGemini Observatory, 670 N. A'Ohoku Place, Hilo, HI 96720

cMontana State University, Dept. of Mathematical Sciences, Bozeman, MT 59717-2400


Multi-conjugate adaptive optics (MCAO) systems with 104 - 105 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront control algorithms for these systems is impractical, since the number of calculations required to compute and apply the reconstruction matrix scales respectively with the cube and the square of the number of AO degrees of freedom. In this paper, we develop an iterative sparse matrix implementation of minimum variance wavefront reconstruction for telescope diameters up to 32m with more than 104 actuators. The basic approach is the pre-conditioned conjugate gradient method, using a multigrid preconditioner incorporating a layer-oriented (block) symmetric Gauss-Seidel iterative smoothing operator. We present open-loop numerical simulation results to illustrate algorithm convergence.

Keywords: Multi-Conjugate Adaptive Optics, Wavefront Reconstruction, Multigrid

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Virginia M. Smith / / July 25, 2002