Asymptotic formulas for phase recovering from phaseless data of biharmonic waves at a fixed frequency

TL;DR

This paper establishes the uniqueness of phase retrieval from phaseless biharmonic wave data and derives explicit asymptotic formulas for phase recovery at a fixed frequency, advancing inverse scattering theory.

Contribution

It proves unique determination of phased biharmonic waves from modulus data and provides explicit asymptotic formulas for phase retrieval, which was previously unexplored.

Findings

Unique determination of biharmonic wave from modulus data

Explicit asymptotic formulas for phase retrieval

Advancement in inverse biharmonic scattering theory

Abstract

This paper focuses on phase retrieval from phaseless total-field data in biharmonic scattering problems. We prove that a phased biharmonic wave can be uniquely determined by the modulus of the total biharmonic wave within a nonempty domain. As a direct corollary, the uniqueness for the inverse biharmonic scattering problem with phaseless total-field data is established. Moreover, using the Atkinson-type asymptotic expansion, we derive explicit asymptotic formulas for the problem of phase retrieval.