Optimal, blind-search modal wavefront correction in atmospheric turbulence. Part I: simulations

Modal control is an established tool in adaptive optics. It allows not only for the reduction in the controllable degrees of freedom, but also for filtering out unseen modes and optimizing gain on a mode-by-mode basis. When Zernike polynomials are employed as the modal basis for correcting atmospheric turbulence, their cross-correlations translate to correction errors. We propose optimal modal decomposition for gradient-descent-based wavefront sensorless adaptive optics, which is free of this problem. We adopt statistically independent Karhunen-Loève functions for iterative blind correction and analyze performance of the algorithm in static as well as in dynamic simulated turbulence conditions.