The Inverse Electromagnetic Scattering Problem for a Perfectly Conducting Cylinder

摘要

We consider the problem of determining the shape of the cross section of a simply connected perfectly conducting infinite cylinder from a knowledge of the far field pattern for all angles of observation and small values of the wave number. The method we propose relies heavily on conformal mapping techniques. In particular we show that module the transfinite diameter each Fourier coefficient of the far field pattern of the electric field determines a Laurent coefficient of the conformal mapping taking the exterior of the unit disk onto the exterior of the unknown cross section. The transfinite diameter is determined by changing the polarization of the incoming wave and measuring the far field pattern of the resulting magnetic field. Of particular interest is the case when only a finite number of the Fourier coefficients of the far field pattern are known, and in this situation we obtain error estimates by using results on coefficients estimates for univalent functions. (Author)