Differential imaging of local perturbations in anisotropic periodic media

We develop a differential sampling method to image local perturbations in anisotropic periodic layers, extending earlier works on the isotropic case. We study in particular a new interior transmission problem that is associated with the inverse problem when only a single Floquet-Bloch mode is used. This 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.