Mathematics and Computers in Simulation 66 (2004) 281–295 A set-handling approach for the no-response test and related methods Roland Potthast Institut for Numerical and Applied Mathematics, University of Göttingen, Göttingen, Germany Available online 19 June 2004 Abstract 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. In the pilot paper [SIAM J. Appl. Math.] a rather tricky visualization method is described to determine the unknown scatterer. The authors use rotations and translations of some test domain, construct special images and then take minima of several images. Here, our goal is to considerably simplify this method and find the unknown scatterer as the intersection of all test domains for which the response is small for all special incident fields. We will describe the new realization of the no-response test, link it to the theoretical results and show numerical reconstructions for sound-soft, sound-hard, impedance, and inhomogeneous medium scatterers. The proceeding can be used to work with related methods as the range test [Inverse Problems] as well. © 2004 IMACS. Published by Elsevier B.V. All rights reserved. Keywords: No-response test; Scatterers; Inverse scattering 1. Introduction Inverse scattering is concerned with the detection of unknown objects or their properties from measured acoustic, electric or elastic fields. One of the fundamental problems the area is the determination of the location and the shape of scatterers which are either buried or located in some inaccessible region. Applications range from such diverse areas as geoscience and mine detection to medical imaging and E-mail address: potthast@scienceatlas.de (R. Potthast). URL: http://www.scienceatlas.de/nfg. 0378-4754/$30.00 © 2004 IMACS. Published by Elsevier B.V. All rights reserved. doi:10.1016/j.matcom.2004.02.012