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

This paper is concerned with the uniqueness of an 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 the use of the phaseless near-field data incurred by the cavity and the point sources, and thus the configuration is more feasible in practice.