The inverse electromagnetic scattering problem for an anisotropic medium

We consider the electromagnetic inverse scattering problem of determining the support of an orthotropic or anisotropic anomaly in a homogeneous background medium from a knowledge of the electric far-field pattern corresponding to the scattering of electromagnetic plane waves. Our aim is to derive a linear integral equation of the first kind from which the support of the anomaly can be found by examining the behaviour of the (regularized) solution. The analysis is based on a study of an interior transmission problem for Maxwell's equations.