# Orthogonality Sampling Method for the Electromagnetic Inverse Scattering Problem

## TL;DR

This paper develops a theoretical foundation and resolution analysis for the orthogonality sampling method in electromagnetic inverse scattering, demonstrating its effectiveness for locating and shaping anisotropic scatterers from far field data.

## Contribution

It provides a new theoretical basis and resolution analysis for the orthogonality sampling method, linking it to the direct sampling and factorization methods.

## Key findings

- The method is fast, robust, and effective for 3D anisotropic scatterers.
- Theoretical resolution limits are established.
- Numerical examples validate the method's performance.

## Abstract

This paper is concerned with the electromagnetic inverse scattering problem that aims to determine the location and shape of anisotropic scatterers from far field data (at a fixed frequency). We study the orthogonality sampling method which is a simple, fast and robust imaging method for solving the electromagnetic inverse shape problem. We first provide a theoretical foundation for the sampling method and a resolution analysis of its imaging functional. We then establish an equivalent relation between the orthogonality sampling method and direct sampling method as well as resolution analysis for the latter. The analysis used to justify the Factorization method for the far field operator plays an important role in the justifications. Finally, we present some numerical examples to validate the performance of the sampling methods for anisotropic scatterers in three dimensions.