The Determination of an Obstacle from its Scattering Cross Section

The inverse acoustic obstacle scattering problem, in its most general

form, seeks to determine the nature of an unknown scatterer from knowl-

edge of its far eld or radiation pattern. The problem which is the main

concern here is:

If the scattering cross section, i.e the absolute value of the radiation

pattern, of an unknown scatterer is known determine its shape.

In this talk we explore the problem from a number of points of view.

These include questions of uniqueness, methods of solution including it-

erative methods, the Minkowski problem and level set methods. We con-

clude by looking at the problem of acoustically invisible gateways and its

connections with cloaking