Recovering an electromagnetic obstacle by a few phaseless backscattering measurements

TL;DR

This paper introduces a method to reconstruct convex polyhedral electromagnetic obstacles using only the magnitude of backscattered waves, identifying face orientations and areas without phase information.

Contribution

It extends previous 2D acoustic scattering techniques to 3D electromagnetic scattering, enabling obstacle reconstruction from phaseless measurements.

Findings

Local maximum behavior of far-field modulus helps determine obstacle face normals.

Reconstruction scheme effectively recovers obstacle shape from phaseless data.

Method extends to 3D electromagnetic scattering, a more complex setting.

Abstract

We consider the electromagnetic scattering from a convex polyhedral PEC or PMC obstacle due to a time-harmonic incident plane wave. It is shown that the modulus of the far-field pattern in the backscattering aperture possesses a certain local maximum behavior. Using the local maximum indicating phenomena, one can determine the exterior unit normal directions, as well as the face areas, of the front faces of the obstacle. Then we propose a recovery scheme of reconstructing the obstacle by phaseless backscattering measurements. This work significantly extends our recent study in [12] from two dimensions and acoustic scattering to the much more challenging three dimensions and electromagnetic scattering.