On a Set of Continuous Wave Electromagnetic Inverse Scattering Boundary Conditions

The inverse problem of continuous wave electromagnetic scattering is considered. The shape and the material constituents of an unknown scatterer need to be determined from bistatic measurement data for a given transmitted field. Although methods have been outlined on how to determine the material constituents of a semi-transparent scatterer, no suitable method has been found which may be employed to simultaneously specify the shape and the material constituents of an unknown smooth, convex-shaped, close, and imperfectly conducting scatterer. Namely, such boundary conditions are sought which do not depend on either the shape or the material constituents of the scattering body and its enclosing surface, but allow one to specify the relevant characteristic parameters uniquely from the recovered near field.The main incentive of this study is to show that the unknown geometrical and material surface parameters can be determined from a set of equations which is derived from the Leontovich impedance boundary condition. The resulting inverse scattering boundary conditions are analyzed in detail and it is shown that in the perfectly conducting case these boundary conditions degenerate to those conditions investigated by Weston and Boerner.The theoretical analysis is verified by computation proving the importance of the result to the inverse theory of electromagnetic scattering.