Phase retrieval algorithms: a comparison

TLDR

Iterative phase‑retrieval algorithms are evaluated against gradient‑search methods for recovering phase from intensity data. The study examines phase retrieval from two intensity measurements (electron microscopy, wave‑front sensing) and from a single intensity measurement with a non‑negativity constraint (astronomy), focusing on the latter scenario. Both the error‑reduction algorithm (single‑measurement case) and the Gerchberg‑Saxton algorithm (two‑measurement case) converge, with the error‑reduction algorithm closely related to steepest descent, while input‑output and conjugate‑gradient methods converge markedly faster, as illustrated by examples.

Abstract

Iterative algorithms for phase retrieval from intensity data are compared to gradient search methods. Both the problem of phase retrieval from two intensity measurements (in electron microscopy or wave front sensing) and the problem of phase retrieval from a single intensity measurement plus a non-negativity constraint (in astronomy) are considered, with emphasis on the latter. It is shown that both the error-reduction algorithm for the problem of a single intensity measurement and the Gerchberg-Saxton algorithm for the problem of two intensity measurements converge. The error-reduction algorithm is also shown to be closely related to the steepest-descent method. Other algorithms, including the input-output algorithm and the conjugate-gradient method, are shown to converge in practice much faster than the error-reduction algorithm. Examples are shown.