  We discuss the use of differential sampling method to image local
perturbations in anisotropic periodic layers, extending earlier works on the
isotropic case. We study in particular the new interior transmission problem
that is associated with the inverse problem when only a single Floquet-Bloch
mode is used. We prove Fredholm properties of this problem under similar
assumptions as for classical interior transmission problems. The result of the
analysis is then exploited to design an indicator function for the local
perturbation. The resulting numerical algorithm is validated for two
dimensional numerical experiments with synthetic data.
