Uniqueness in inverse scattering with phaseless near-field data generated by superpositions of two incident plane waves

TL;DR

This paper proves that the shape of an unknown scatterer can be uniquely identified using phaseless near-field data generated by superpositions of two incident plane waves, advancing inverse scattering theory.

Contribution

It establishes the uniqueness of inverse scattering problems with phaseless data using superpositions of two plane waves, employing phase analysis and classical integral formulas.

Findings

Unique determination of scatterers from phaseless data

Application of Rellich's lemma and Green's formula

Extension to electromagnetic and acoustic scattering

Abstract

This paper is concerned with the uniqueness in inverse acoustic and electromagnetic scattering with phaseless near-field data generated by superpositions of two incident plane waves at a fixed frequency. It can be proved that the unknown scatterer can be uniquely determined by the phaseless near-field data. The proof is based on the analysis of the phase information and the application of Rellich's lemma together with the Green's formula for the radiating solutions to the Helmholtz equation or the Stratton--Chu formula for the radiating solutions to the Maxwell equations.