A set-handling approach for the no-response test and related methods Original Research Article

We describe a new realization for the no-response test by Luke and Potthast [SIAM J. Appl. Math.] to locate the unknown support of scatterers from the knowledge of the far field pattern of one scattered acoustic wave. The method uses a sampling set of surfaces and a special indicator function to detect the support of a scatterer from which the physical properties do not need to be known. In particular, we neither need to know whether the scatterer is penetrable or impenetrable nor do we need to know the nature of the inhomogeneity. In contrast to previous sampling methods, this approach does need to know the far field pattern only for one or a few incident fields, i.e. the method is a natural one-wave-method.