# Imaging polarizable dipoles

## TL;DR

This paper develops an electromagnetic imaging method for polarizable dipoles, providing resolution estimates and error analysis, and addresses artifacts in the imaging process with numerical validation.

## Contribution

It introduces a Kirchhoff imaging approach for electromagnetic dipoles, analyzing resolution and errors, and extends to active imaging of scatterers' polarizability tensors.

## Key findings

- Range and cross-range resolution match acoustic estimates.
- Error bounds for dipole orientation reconstruction are established.
- Naive imaging methods suffer from artifacts, which are characterized and corrected.

## Abstract

We present a method for imaging the polarization vector of an electric dipole distribution in a homogeneous medium from measurements of the electric field made at a passive array. We study an electromagnetic version of Kirchhoff imaging and prove, in the Fraunhofer asymptotic regime, that range and cross-range resolution estimates are identical to those in acoustics. Our asymptotic analysis provides error estimates for the cross-range dipole orientation reconstruction and shows that the range component of the dipole orientation is lost in this regime. A naive generalization of the Kirchhoff imaging function is afflicted by oscillatory artifacts in range, that we characterize and correct. We also consider the active imaging problem which consists in imaging both the position and polarizability tensors of small scatterers in the medium using an array of collocated sources and receivers. As in the passive array case, we provide resolution estimates that are consistent with the acoustic case and give error estimates for the cross-range entries of the polarizability tensor. Our theoretical results are illustrated by numerical experiments.