The three-dimensional inverse scattering problem for the Helmholtz equation

Abstract

In this paper we are concerned with solutions of the three-dimensional Helmholtz equation which are of class C2 (i.e. regular) in the exterior of a bounded domain D. In cylindrical polar coordinates (r, z, φ) such solutions satisfy the equationin which we have dimensionalized the radial coordinate r so that the wave number is normalized to unity. If we further assume that u satisfies the Sommerfeld radiation conditionthen u may be regarded as being generated by volume sources, surface sources, or point singularities, all of which are contained in D.