Inverse elastic surface scattering with far-field data

TL;DR

This paper introduces a mathematical and computational approach for inverse elastic surface scattering that enhances resolution using far-field data and a high-density elastic slab, with a single illumination and nonlinear correction.

Contribution

It presents a novel method combining far-to-near field data conversion and an explicit inversion formula for elastic surface reconstruction with improved resolution.

Findings

Capable of stable surface reconstruction with resolution controlled by slab density

Uses only a single illumination for the inverse problem

Employs nonlinear correction for improved accuracy

Abstract

A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced resolution can be achieved by using more easily measurable far-field data. The surface is assumed to be a small and smooth perturbation of an elastically rigid plane. By placing a rectangular slab of a homogeneous and isotropic elastic medium with larger mass density above the surface, more propagating wave modes can be utilized from the far-field data which contributes to the reconstruction resolution. Requiring only a single illumination, the method begins with the far-to-near (FtN) field data conversion and utilizes the transformed field expansion to derive an analytic solution for the direct problem, which leads to an explicit inversion formula for the inverse problem. Moreover, a nonlinear correction scheme is developed to improve the accuracy of the reconstruction. Results show that the proposed method is capable of stably reconstructing surfaces with resolution controlled by the slab's density.