Abstract: I will discuss the scattering problem for a quantum particle in dimension three in the presence of a semitransparent unbounded obstacle, modeled by a surface. The generator of the dynamics is the operator formally defined as the Laplacian plus a delta-interaction supported by the surface. I will consider the case in which the surface is obtained through a local deformation of a plane, it can be identified by the graph of a compactly supported, Lipschitz continuous function. In this configuration, the reference dynamics is the one generated by the Laplacian plus a delta-interaction supported by the plane. I will discuss existence and asymptotic completeness of the wave operators, provide a representation formula for the scattering matrix, and show that the scattering matrix converges to the identity as the deformation goes to zero (with a quantitative estimate on the rate of convergence).