Warm-started Wavefront Reconstruction for Adaptive Optics

Future extreme adaptive optics (ExAO) systems have been suggested with up to 10^5 sensors and actuators. We analyze the computational speed of iterative reconstruction algorithms for such large systems. We compare a total of 15 different scalable methods, including multigrid, preconditioned conjugate-gradient, and several new variants of these. Simulations on a 128 by 128 square sensor/actuator geometry using Taylor frozen flow dynamics are carried out using both open-loop and closed-loop measurements, and algorithms are compared on a basis of mean squared error and floating-point multiplications required. We also investigate the use of warm-starting, where the most recent estimate is used to initialize the iterative scheme. In open-loop estimation or pseudo-open loop control, warm-starting provides a significant computational speedup; almost every algorithm tested converges in one iteration. In a standard closed-loop implementation, using a single iteration per timestep, most algorithms give the minimum error even in cold-start, and every algorithm gives the minimum error if warm-started. The best algorithm is therefore the one with the smallest computational cost per iteration, not necessarily the one with the best quasi-static performance.