An Asymptotic Formalism for Reconstructing Small Perturbations of Scatterers from Electric or Acoustic Far-Field Measurements

TL;DR

This paper introduces an asymptotic formalism to reconstruct small boundary perturbations of scatterers from far-field electric or acoustic data, using a linearized relation and Fourier analysis.

Contribution

It develops a novel linearized approach based on Dirichlet-to-Neumann operator expansion for shape reconstruction of nearly circular scatterers.

Findings

Successfully relates far-field data to boundary perturbations.

Provides a method to compute Fourier coefficients of shape changes.

Applicable to electric and acoustic scattering problems.

Abstract

We consider the problem of determining the boundary perturbations of an object from far-field electric or acoustic measurements. Assuming that the unknown object boundary is a small perturbation of a circle, we develop a linearized relation between the far-field data that result from fixed Dirichlet boundary conditions, entering as parameters, and the shape of the object, entering as variables. This relation is used to find the Fourier coefficients of the perturbation of the shape and makes use of an expansion of the Dirichlet-to-Neumann operator.