Multigrid algorithm for least-squares wavefront reconstruction

Multigrid (MG) methods are presented for fast, efficient, flexible, and robust least-squares wavefront reconstruction in extremely high-resolution conventional adaptive optics, or ExAO. We demonstrate that MG can robustly handle a variety of sensor-actuator geometries, and it can accommodate deformable mirror influence function models that are more realistic than the common piecewise bilinear model. With MG one can also easily incorporate additional penalty, or regularization, terms to damp out the waffle mode in Fried geometry and to damp out instabilities due to actuators near the pupil boundary with poorly sensed influence. We present closed-loop simulation results that suggest that only one or two MG iterations per time step are needed to control an ExAO system.