An inverse problem without the phase information

TL;DR

This paper proves a new uniqueness theorem for an inverse scattering problem involving the 3-D Helmholtz equation, where only the modulus of the scattered wave is measured, and the phase information is absent.

Contribution

It introduces a novel uniqueness result for inverse scattering without phase data in three dimensions, expanding the understanding of such inverse problems.

Findings

Established uniqueness of the dielectric constant from modulus-only measurements

Extended inverse scattering theory to phase-less data scenarios

Provided mathematical proof for the 3-D Helmholtz equation case

Abstract

We prove a new uniqueness theorem for an inverse scattering problem without the phase information for the 3-D Helmholtz equation. The spatially distributed dielectric constant is the subject of the interest in this problem. We consider the case when the modulus of the scattered wave field |u_{sc}| is measured. The phase is not measured.