As part of our efforts to design imaging algorithms for unknown complex backgrounds, we propose and analyze a new sampling method to recover the support of a local perturbation in a periodic layer from measurements of scattered waves at a fixed frequency. Our method is capable of directly reconstructing the geometry of the perturbation, without the need for knowing or reconstructing the background periodic media. The related analysis is based on studying sampling methods using a single Floquet-Bloch mode. This analysis introduces a new type of interior transmission problems that couple usual interior transmission problems for one mode with scattering problems for the other modes. We shall discuss and analyze this problem as well as the sampling method for differential imaging and present some related numerical results. This is a joint work with Thi-Phong Nguyen.