We consider in this work a direct and inverse problem in scattering theory. We construct an arc g of the boundary from the far field pattern  of the scattered wave at fixed energy. This leads to the direct scattering problem for the Helmholtz equation in a perturbed half-plane with Dirichlet condition on the boundary. Using the integral method, we show that the direct problem is well posed. For the identification of the arc, we prove a uniqueness theorem by using the point source method and a reciprocity relation.

scattering theory, far field, inverse problem, integral equation method.