An evaluation of the data space dimension in phase retrieval: results in Fresnel zone

TL;DR

This paper investigates the data space dimension in phase retrieval within the Fresnel zone, using a linear operator approach to analyze the singular values related to a 2D electric current problem.

Contribution

It introduces an analytical method to compute the data space dimension in phase retrieval using lifting and singular value analysis for a specific 2D electromagnetic scenario.

Findings

Derived the linear representation of the phase retrieval data

Analytically computed the relevant singular values of the data operator

Provided insights into the data space dimension in a Fresnel zone setting

Abstract

In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval,the analysis is performed in two steps. First, we exploit the lifting technique to obtain a linear representation of the data. Later, we evaluate the dimension of data space by computing analytically the number of relevant singular values of the linear operator that represents the data. The study is done with reference to a 2D scalar geometry consisting of an electric current strip whose square amplitude of the electric radiated field is observed on a twodimensional extended domain in Fresnel zone.