Analysis of sampling methods for imaging a periodic layer and its defects

We revisit the differential sampling method introduced in (Haddar and Nguyen 2017 Comput. Math. Appl. 74 2831–55) for the identification of a periodic domain and some local perturbation. We provide a theoretical justification of the method that avoids assuming that the local perturbation is also periodic. Our theoretical framework uses functional spaces with continuous dependence with respect to the Floquet–Bloch variable. The corner stone of the analysis is the justification of the generalized linear sampling method in this setting for a single Floquet–Bloch mode.