Reconstruction of the three-dimensional refractive index in electromagneticscattering by using a propagation–backpropagation method

Abstract

This paper is concerned with the development of an iterative algorithm forthe reconstruction of the three-dimensional complex-valued refractiveindex of an object in electromagnetic scattering. The inverse problem ismodelled by a second-order Maxwell equation for the electric field atfixed frequency with plane, time-harmonic microwave irradiation. Thecomplex-valued scattered electric field is measured at some distance from theobject for a finite number of directions of the incident waves. Each ofthese measurements is used to improve iteratively a starting guess forthe true refractive index of the object. For each iteration one forwardand one adjoint problem of a system of a second-order equation haveto be solved. The complexity of each step is O(N3log(N)).The algorithm solves the full nonlinear inverse problem. It can be consideredas a nonlinear generalization of the algebraic reconstruction techniquein x-ray tomography. The practical usefulness of the algorithm is shown in threenumerical simulations.