Transmission eigenvalues with artificial background for explicit material index identification

TL;DR

This paper introduces a method to improve the retrieval of the refractive index of an inclusion by modifying the farfield operator with an artificial background, making transmission eigenvalues more informative.

Contribution

It proposes a novel approach of using an artificial background to modify the farfield operator, enhancing the extraction of transmission eigenvalues for better material index identification.

Findings

Modified farfield operator yields more accessible transmission eigenvalues.

Artificial background improves the accuracy of refractive index retrieval.

Method demonstrated through numerical computations.

Abstract

We are interested in the problem of retrieving information on the refractive index $n$ of a penetrable inclusion embedded in a reference medium from farfield data associated with incident plane waves. Our approach relies on the use of transmission eigenvalues (TEs) that carry information on $n$ and that can be determined from the knowledge of the farfield operator $F$. In this note, we explain how to modify $F$ into a farfield operator $F^{art}=F-\tilde{F}$, where $\tilde{F}$ is computed numerically, corresponding to well chosen artificial background and for which the associated TEs provide more accessible information on $n$.