Accelerated convergence in multiple-plane phase retrieval via phase perturbations

Abstract

Single-Beam Multiple Intensity Reconstruction (SBMIR) is an iterative phase retrieval method that involves capturing the intensity of a beam at multiple axially-displaced planes. For smooth test objects, stemming from a lack of intensity variation, the iterative nature of this technique may sometimes lead to stagnation, where the solution converges at a local minimum, resulting in phase reconstruction errors. In this study, stagnation is prevented by introducing random perturbations to the phase estimate in order to hurdle the local minimum. The controlled phase perturbation allows the algorithm to explore alternative solutions during earlier iterations before focusing on refining the solution at later iterations. The viability of the modified SBMIR algorithm based on phase perturbation (SBMIR-PP) was tested by applying it to experimental data of a spherical wave. SBMIR-PP was found to have a consistently faster rate of convergence compared to the conventional SBMIR algorithm, resulting in higher-quality phase reconstructions at fewer iterations. The effects of various parameters were also investigated, and optimized. Faster convergence was achieved with an initial maximum perturbation strength of 2, and with lower values for the offset and slope of the perturbation schedule, for the test object wave used. SBMIR-PP proves to be a viable alternative to SBMIR, allowing for acceptable phase reconstruction outputs to be achieved at a faster rate affording fewer number of measurements.