An Inverse Uniqueness of a Phaseless Scattering Problem by Zero-Crossings

TL;DR

This paper investigates the inverse uniqueness in phaseless scattering problems by analyzing zero-crossings of the scattering amplitude's modulus, revealing how phase linearization affects zero distribution and relates to the index of refraction.

Contribution

It establishes inverse uniqueness results for phaseless scattering problems using zero-crossing analysis and connects zero distribution perturbations to the index of refraction.

Findings

Zero-crossings of the scattering amplitude are key to inverse problem uniqueness.

Phase linearization alters the zero distribution of the scattered wave.

Perturbations in the index of refraction influence the zero set of the modulus.

Abstract

We discuss the inverse uniqueness problem in phaseless scattering by counting the zeros of its modulus of the scattering amplitude. The phase linearization of scattered wave field disturbs the originally uniform distribution of the zero set. There is a connection between the perturbation of the index of refraction and the zero distribution of the modulus. We conclude the inverse uniqueness of the phaseless problem from the point of view of interior transmission problem.