Deterministic phase retrieval: a Green’s function solution

TLDR

An appendix discusses the local validity of the parabolic‑wave equation based on the factorized Helmholtz equation approach to Rayleigh–Sommerfeld and Fresnel diffraction theories. The study derives equations for phase and irradiance propagation and presents a Green’s function solution for phase in terms of irradiance and perimeter phase values, along with expressions for the near‑field diffracted wave. The authors consider both circular and slit pupils, discuss a measurement scheme, and provide numerical simulation results to validate the derived equations. Numerical simulations confirm the measurement scheme and demonstrate the validity of the Green’s function approach.

Abstract

Equations for the propagation of phase and irradiance are derived, and a Green's function solution for the phase in terms of irradiance and perimeter phase values is given. A measurement scheme is discussed, and the results of a numerical simulation are given. Both circular and slit pupils are considered. An appendix discusses the local validity of the parabolic-wave equation based on the factorized Helmholtz equation approach to the Rayleigh–Sommerfeld and Fresnel diffraction theories. Expressions for the diffracted-wave field in the near-field region are given.