Enhanced phase retrieval using nonlinear dynamics

Abstract

Historically, phase retrieval algorithms have relied on linear propagation between two different amplitude (intensity) measurements. While generally successful, these algorithms have many issues, including susceptibility to noise, local minima, and indeterminate initial and final conditions. Here, we show that nonlinear propagation overcomes these issues, as intensity-induced changes to the index of refraction create additional constraints on the phase. More specifically, phase-matching conditions (conservation of wave energy and momentum) induce an object-dependent resonance between the measured amplitudes and the unknown phase. The result is a non-classical convergence profile in the reconstruction algorithm that contains a zero crossing, where the observable minimum in amplitude error and the unobservable minimum in phase error align at the same iteration number. We demonstrate this convergence experimentally in a photorefractive crystal, showing that there is a clear rule for stopping iterations. We find that the optimum phase retrieval occurs for a nonlinear strength that gives minimal correlation between the linear and nonlinear output amplitudes, i.e. a condition that maximizes the information diversity between linear and nonlinear propagation. The corresponding algorithm greatly improves the conventional Gerchberg-Saxton result and holds much potential for enhancing other methods of diffractive imaging.