The no response test - a sampling method for inverse
scattering problems
Roland Potthast
Institute for Numerical and Applied Mathematics
University of Goettingen, Germany
We describe a novel scheme, 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. Specially, the method does not
depend on information about whether the scatterer is penetrable
or impenetrable. If the scatterer is penetrable, the nature of
the inhomogeneity is not used. In contrast to previous sampling
methods, the methodology described here enables one to locate
obstacles or inhomogeneities from the far field pattern of only
one or a few incident fields - the no response test is a
one-wave-method. We investigate the theoretical basis for the
no response test and derive a new 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 pattern data.