Analytical modeling of adaptive optics: foundations of the phase spatial power spectrum approach.

End-to-end simulation of adaptive optics (AO) systems allows high-fidelity modeling of system performance, but at the cost of long computation time. Analytical modeling, on the other hand, can provide much faster first-order performance estimates for a rapid exploration of the AO parameter space. In this paper, we present the foundations of a modeling method for the AO optical transfer function, based on an analytical description of the residual phase spatial power spectrum. The method has been implemented in an IDL-based code, PAOLA, and comparison with end-to-end simulations demonstrates the validity of the analytical approach.