# Uniqueness in inverse cavity scattering problems with phaseless near-field data

## TL;DR

This paper proves the first known uniqueness result for determining the shape, location, and boundary condition of a cavity using only the modulus of near-field data, making inverse scattering more practical.

## Contribution

It introduces a novel proof of uniqueness in inverse cavity scattering problems using phaseless near-field data with the reference ball technique.

## Key findings

- Unique determination of cavity shape and location from phaseless data
- Use of superpositions of point sources enhances practical feasibility
- First rigorous proof of uniqueness in this setting

## Abstract

This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique and the superpositions of two point sources as the incident waves, we rigorously prove that the location and shape of the cavity as well as its boundary condition can be uniquely determined by the modulus of near-fields at an admissible surface. To our knowledge, this is the first uniqueness result in inverse cavity scattering problems with phaseless near-field data. In this paper, we make use of the phaseless near-field data incurred by the cavity and the point sources, and thus the configuration is more feasible in practice.