Abstract: 

A new sampling method for inverse scattering problems is proposed to process far field data of one incident wave. As a sampling method, it sets up ill-posed integral equations and uses the solutions to reconstruct the unknown target. But in contrast to the classical linear sampling method, the method has the ability to process limited aperture data. We consider this method in both inverse acoustic problems and inverse elastic problems. Theoretical analysis and numerical examples show that the method can effectively determine the location and approximate the support with little a priori information of the unknown target.