A direct inverse scattering method for imaging obstacles with unknown surface conditions

A new technique is described for imaging obstacles using the acoustic far "eld response for plane wave incidence. The method requires no a priori information about the surface, nor does it depend upon prior knowledge of the surface boundary conditions. The algorithm is straightforward to implement and is illustrated by imaging multiple targets simultaneously for various surface boundary conditions: soft, hard, and impedance. The input data is the full acoustic scattering matrix at a single frequency, from which the eigenvalues and eigenfunctions of the far "eld operator are determined. Associated incident wave functions are then used to compute a spatial indicator function which takes on large values in the exterior of the target but is bounded inside the obstacle, or obstacles when there are multiple disconnected surfaces. Inverse scattering methods may be categorized as direct or indirect, depending upon how the algorithm arrives at the unknown quantity. Here we consider the target identi"cation problem: to "nd the surface or surfaces of targets given the far "eld data. Indirect approaches to this problem include optimization or least squares methods, based on an assumed form for the surface. The error between the predicted and measured data is minimized over the class of assumed surfaces, using a direct scattering solver at each step of the solution. Examples on this approach are Angell et al. (1989,1997) who use an alternating iteration procedure. This has the advantage that only limited data are needed, but it requires prior knowledge of the target: the assumption that it is a single closed surface with known impedance boundary condition. A related method for obstacle reconstruction is described by Roy et al. (1997) which also requires solving the direct problem iteratively. The method of Kirsch and Kress (Colton & Kress 1992) is more direct in that it seeks a