Fixed angle inverse scattering for almost symmetric or controlled perturbations

TL;DR

This paper proves unique determination of certain potentials in fixed angle inverse scattering problems, including almost symmetric and horizontally controlled cases, by establishing equivalences between frequency and time domain formulations and extending Carleman estimate methods.

Contribution

It introduces new uniqueness results for fixed angle inverse scattering of almost symmetric and controlled potentials, extending existing methods with novel analytical techniques.

Findings

Unique determination of potentials from two fixed angles

Extension of Carleman estimate methods to new classes of potentials

Equivalence established between frequency and time domain formulations

Abstract

We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally controlled potentials are uniquely determined by their fixed angle scattering data. This is done by establishing an equivalence between the frequency domain and the time domain formulations of the problem, and by solving the time domain problem by extending the methods of [RS19] which adapts the ideas introduced in [BK81] and [IY01] on the use of Carleman estimates for inverse problems.