Improving Initial Phase Estimates for Phase Retrieval Algorithms

Two extensions of our previously reported ‘crude phase estimation’ procedure are developed. They both serve to provide starting phases (for Fienup's iterative algorithms) which are ‘improved’ in the sense that rates of convergence of these algorithms are accelerated. The theory is illustrated by examples of phase retrieval from phaseless Fourier data. Images are reconstructed from Fourier magnitudes which were either computer-generated or measured in our optical laboratory, set up to simulate Labeyrie's speckle interferometry.