Identification of Electromagnetic Dipoles from Multi-frequency Sparse Electric Far Field Patterns

TL;DR

This paper presents a method to uniquely identify and locate electric and magnetic dipoles using multi-frequency sparse electric far field data, along with algorithms for determining their polarization strengths.

Contribution

It introduces a novel approach for unique identification and localization of dipoles from sparse multi-frequency data, including indicator functions and computational formulas.

Findings

Successful localization of dipoles in numerical tests

Robustness of the method against sparse data

Effective computation of polarization strengths

Abstract

The inverse electromagnetic source scattering problem from multi-frequency sparse electric far field patterns is considered. The underlying source is a combination of electric dipoles and magnetic dipoles. We show that the locations and the polarization strengths of the dipoles can be uniquely determined by the multi-frequency electric far field patterns at sparse observation directions. The unique arguments rely on some geometrical discussions and ingenious integrals of the electric far field patterns with properly chosen functions. Motivated by the uniqueness proof, we introduce two indicator functions for locating the magnetic dipoles and the electric dipoles, respectively. Having located all the dipoles, the formulas for computing the corresponding polarization strengths are proposed. Finally, some numerical examples are presented to show the validity and robustness of the proposed algorithm.