Multigrid approach to predictive wave-front reconstruction in adaptive optical systems

A computationally efficient approach, based on the principles of multigrid methods, to predictive wave-front reconstruction in adaptive optical systems is described. Local predictive estimators are computed by use of recursive least squares on multiple grids. Each grid is increasingly coarse, allowing for temporal prediction of the behavior of both high- and low-spatial-frequency aberrations. Example numerical simulation results are given, showing that implementing the recursive least-squares algorithm for predictive estimation in a multigrid fashion greatly accelerates convergence to the steady-state optimal estimator condition. By implementation of the multigrid predictive reconstructor in parallel, the computational cost of implementing a predictive wave-front reconstruction scheme that uses recursive least squares for each processor at each cycle can be reduced from [symbol: see text](m2) to [symbol: see text](2m), where m is the number of actuators.