Multipoles-based linear sampling method: impact of using multipole expansion

Abstract

In this article, we present a physical interpretation of the linear sampling method (LSM). The proposed interpretation is based on the multipole expansion of the induced currents at the sampling point, thus called multipoles-based linear sampling method (MLSM). MLSM does not interpret LSM as the focusing of fields at a sampling point. It rathers considers LSM as creating a current distribution that effectively radiates like a monopole at the sampling point. In this sense, MLSM brings LSM closer to the original scattering problem. We show that if infinite multipoles are considered, MLSM performs similar to LSM. This fact can be used to understand the poor performance of LSM in some particular cases, for example, circular and annular scatterers with specific permittivities. We show that it is not necessary to use infinite multipoles in MLSM. The truncation of higher order multipoles in MLSM serves as a regularization technique. As compared to the conventionally used Tikhonov regularization in LSM, the regularization in MLSM is not based on mathematical theory. It is rather a physics-based truncation technique as we truncate the multipoles which anyways do not contribute significantly to the scattered field. Such regularization is simple to understand and implement for practical engineering purposes.