Fast FFT-based algorithm for phase estimation in speckle imaging

This paper describes a fast direct algorithm for obtaining least-squares phase estimates from arrays of noisy phase differences. The algorithm uses the fast Fourier transform to diagonalize and decouple the system of equations which results from the application of the least-squares criterion. It is accurate and stable, and is perhaps an order of magnitude faster than the best iterative method. The effectiveness of the algorithm has been demonstrated by using it in connection with the Knox-Thompson speckle-imaging procedure to restore an optical object perturbed by simulated atmospheric turbulence. Representative results are discussed in the paper.