Abstract
The problem considered is that of determining the shape of a three-dimensional scattering object, illuminated by an acoustic field, from a knowledge of scattered far-field data. The far-field data are the asymptotic form of the solution of an exterior transmission problem for the Helmholtz equation. The problem is reformulated as an optimisation problem, specifically, finding that surface, in a suitably restricted class, which minimises an appropriate functional of the far field generated by the surface through the solution of the direct problem. Through the use of complete families of solutions, the problem is further reduced to finding a surface which minimises error in satisfying the transmission conditions.
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