Stability of the determination of the surface impedance of an obstacle from the scattering amplitude

TL;DR

This paper establishes a logarithmic stability estimate for determining an obstacle's surface impedance from scattering data, using a straightforward proof based on elliptic Carleman inequalities.

Contribution

It provides the first simple and direct proof of stability estimates for this inverse scattering problem, enhancing understanding of the problem's stability properties.

Findings

Logarithmic stability estimate proven

Proof based on elliptic Carleman inequality

Simplifies previous approaches

Abstract

We prove a stability estimate of logarithmic type for the inverse problem consisting in the determination of the surface impedance of an obstacle from the scattering amplitude. We present a simple and direct proof which is essentially based on an elliptic Carleman inequality.