THE NO RESPONSE TEST—A SAMPLING METHOD FOR INVERSE SCATTERING PROBLEMS∗

Abstract. We describe a novel technique, which we call the no response test, to locate the support of a scatterer from knowledge of a far field pattern of a scattered acoustic wave. The method uses a set of sampling surfaces and a special test response to detect the support of a scatterer without a priori knowledge of the physical properties of the scatterer. Specifically, the method does not depend on information about whether the scatterer is penetrable or impenetrable nor does it depend on any knowledge of the nature of the scatterer (absorbing, reflecting, etc.). In contrast to previous sampling algorithms, the techniques described here enable one to locate obstacles or inhomogeneities from the far field pattern of only one incident field—the no response test is a one-wave method. We investigate the theoretical basis for the no response test and derive a one-wave uniqueness proof for a region containing the scatterer. We show how to find the object within this region. We demonstrate the applicability of the method by reconstructing sound-soft, sound-hard, impedance, and inhomogeneous medium scatterers in two dimensions from one wave with full and limited aperture far-field data