Target signatures for thin surfaces

TL;DR

This paper develops a method to detect changes in thin surface materials using target signatures derived from a mixed Steklov eigenvalue problem, computed via modified scattering data and the linear sampling method.

Contribution

It introduces a novel approach to characterize thin surface scatterers through eigenvalues obtained from scattering data, enhancing detection capabilities.

Findings

Eigenvalues can be determined from scattering data using the generalized linear sampling method.

The proposed target signature effectively detects material property changes in thin surfaces.

Numerical experiments validate the theoretical approach and its practical applicability.

Abstract

We investigate an inverse scattering problem for a thin inhomogeneous scatterer in R^m, m = 2,3, which we model as a m-1 dimensional open surface. The scatterer is referred to as a screen. The goal is to design target signatures that are computable from scattering data in order to detect changes in the material properties of the screen. This target signature is characterized by a mixed Steklov eigenvalue problem for a domain whose boundary contains the screen. We show that the corresponding eigenvalues can be determined from appropriately modified scattering data by using the generalized linear sampling method. A weaker justification is provided for the classical linear sampling method. Numerical experiments are presented to support our theoretical results.