Reconstructing Dielectric Scatterers

This chapter is devoted to quantitative reconstruction algorithms that are aimed at retrieving permittivities of dielectric scatterers from the knowledge of measured scattering data. It introduces the fundamentals of quantitative reconstruction algorithms and discusses the properties of uniqueness, stability, and nonlinearity. The chapter presents the formulation of the forward method, which is followed by casting the inverse problem to an optimization problem. It reviews noniterative inversion methods, of which there are two types. In particular, one type is Born‐type inversion algorithm and the other type is Rytov type approximations. The chapter also reviews several iterative inversion methods. In particular, for the inversion methods, their implementation steps are presented and their properties and characteristics are commented on. The chapter describes a subspace‐based optimization method (SOM), for which the implementation steps and numerical reconstruction results are presented. It also discusses several important issues in the theories and implementations of quantitative reconstruction algorithms.