Formulas for phase recovering from phaseless scattering data at fixed frequency

TL;DR

This paper derives explicit formulas for phase recovery from phaseless scattering data at fixed frequency, enabling unique inverse scattering solutions for quantum and acoustic waves with compact support.

Contribution

It introduces explicit phase recovery formulas and proves global uniqueness for inverse scattering problems without phase data at fixed frequency.

Findings

Explicit formulas for phase recovery from phaseless data

Global uniqueness results for inverse scattering

Applicable to quantum and acoustic wave problems

Abstract

We consider quantum and acoustic wave propagation at fixed frequency for compactly supported scatterers in dimension $d\ge 2$. In these framework we give explicit formulas for phase recovering from appropriate phaseless scattering data. As a corollary, we give global uniqueness results for quantum and acoustic inverse scattering at fixed frequency without phase information.