Deterministic phase retrieval: a Green’s function solution

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.