Extrapolative phase retrieval based on a hybrid of PhaseCut and alternating projection techniques

Abstract

Phase retrieval is an important research topic in the optics field. It is aimed to reconstruct the wave-front from the intensity of the far-field diffracted field. To deal with the local stagnation of conventional iterative Fourier-based algorithms, an interesting recent approach formulates the phase retrieval problem as a tractable relaxation (called PhaseCut). Despite its powerful global capability, the operation of recasting a vector problem into a matrix problem leads to higher computational cost, which limits its use in far-field patterns with high resolution. In this paper, we develop an extrapolative alternating projection algorithm to cope with the reconstruction of high-resolution phase pattern. The algorithm starts with a low-resolution phase estimation solved by PhaseCut from the far-field amplitudes in the low frequency range, and then refines the initial estimation by an extrapolative iterative projection method, which has a low computational complexity. The iterative process is divided into various periods where the inputs of the algorithm (far-field amplitudes) are extrapolated to include more high frequency information. The main contribution is that the algorithm can quickly converge to the globally optimal and high-resolution solution with a high probability. We verified the validity of the algorithm with various numerical simulations.