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

Multi-conjugate adaptive optics (MCAO) systems with 10 − 10 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 (apply) the reconstruction matrix scales with the cube (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 10 actuators. The basic approach is the preconditioned 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 and analyze algorithm convergence.