The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory. It is based on solving a linear integral equation and then using the equation's solution as an indicator function for the determination of the support of the scattering object. This book describes the linear sampling method for a variety of electromagnetic scattering problems. It presents uniqueness theorems and the derivation of various inequalities on the material properties of the scattering object from a knowledge of the far field pattern of the scattered wave. Also covered are: the approximation properties of Herglotz wave functions; the behavior of solutions to the interior transmission problem, a novel interior boundary value problem; and numerical examples of the inversion scheme.

F. Cakoni received her Ph.D. degree in 1996 from the University of Tirana (Albania) and University of Patras (Greece). Since 2000 she has been on the Faculty of the Department of Mathematical Sciences at the University of Delaware, where she became Professor in 2010.

Preface; 1. Inverse scattering in two dimensions; 2. Maxwell's equations; 3. The inverse problem for obstacles; 4. The inverse scattering problem for anisotropic media; 5. The inverse scattering problem for thin objects; 6. The inverse scattering problem for buried objects; Bibliography; Index.