Target reconstruction from scattered far field data

The problem of finding the shape of a perfectly conducting cylinder when illuminated by an E-polarized incident electromagnetic wave is considered. The given problem is cast in the form of a penalized optimization problem in which we seek a surface in some suitably constrained class which minimizes a functional involving two terms. The first term measures the mean square deviation of the far field of the solution to the direct scattering problem for a surface in the admissible class from given, measured, far field data whilst the second term, penalty, measures the error in satisfying the imposed boundary conditions. An optimisation algorithm is used which does not require that a direct problem be solved in the updating process. Explicit reconstructions are presented which illustrate the effectiveness of the method. Some results indicating the sensitivity of the algorithm to the choice of penalty parameter and the number of incident waves are also given.