Theoretical Investigation of Iterative Phase Retrieval Algorithm for Quasi-Optical Millimeter-Wave RF Beams

In this paper, we present a detailed analysis of the iterative phase retrieval approach (IPRA) for determining the phase profile of the output microwave beam of a gyrotron from known intensity patterns emphasizing the field propagation techniques which are used to propagate the RF field of the microwave beam between known intensity planes. The propagation method, based on first Rayleigh-Sommerfeld diffraction integral (RSDI), is solved using fast Fourier transform (FFT) technique and zero padding. It is observed that the use of FFT and, therefore, the discretization of the RSDI propagation kernel introduce aberrations in the propagated field due to the superposition of the original field with its replicated versions. This problem is solved by approximations leading to the Huygens-Fresnel propagation method which further imposes the restrictions on the distances of propagation depending on the size of the transverse plane used to discretize the intensity pattern. This constraint of the distance of propagation causes problem in the iterative phase retrieval approach (IPRA) when more than two intensity planes are used. A method based on interpolation is proposed to overcome this restriction. IPRA is then further discussed to optimize several parameters, such as plane separation, plane dimension, mesh size, and measurement accuracies, which become more of an issue during the measurements of infrared intensity thermograms of the output microwave beam.