Computationally efficient wavefront reconstructor for simulation of multiconjugate adaptive optics on giant telescopes

Multi-conjugate adaptive optical (MCAO) systems with from 10,000 to 100,000 degrees of freedom have been proposed for future giant telescopes. Using standard matrix methods to compute, optimize, and implement wavefront reconstruction algorithms for these systems is impractical, since the number of calculations required to compute (apply) the reconstruction matrix scales as the cube (square) of the number of AO degrees of freedom. Significant improvements in computational efficiency are possible by exploiting the sparse and/or periodic structure of the deformable mirror influence matrices and the atmospheric turbulence covariance matrices appearing in these calculations. In this paper, we review recent progress in developing an iterative sparse matrix implementation of minimum variance wavefront reconstruction for MCAO. The basic method is preconditioned conjugate gradients, using a multigrid preconditioner incorporating a layer-oriented, iterative smoothing operator. We outline the key elements of this approach, including special considerations for laser guide star (LGS) MCAO systems with tilt-removed LGS wavefront measurements and auxiliary full aperture tip/tilt measurements from natural guide stars. Performance predictions for sample natural guide star (NGS) and LGS MCAO systems on 8 and 16 meter class telescopes are also presented.