Determination of the Electrical Radius ka of a Circular Cylindrical Scatterer from the Scattered Field

Abstract

The inverse problem of scattering for a circular cylindrical scattering geometry is considered. The transverse far field components are related to the Fourier coefficients of the circular cylindrical wave expansion in terms of the scattered field matrix. The associated determinant which describes the scattering geometry is formulated in closed form. To achieve nonsingular matrix inversion, a novel, determinate optimization procedure for the measurement aspect angles is derived and proved. Measurement techniques or experimental results are not presented. Yet, it is shown analytically that the unknown expansion coefficients can be recovered with standard double precision matrix inversion techniques to the degree of accuracy dictated only by any suitable measurement technique. Assuming the required set of expansion coefficients {an}TM and/or {bn}TE is found, it is shown that the electrical radius ka of the scatterer can be determined from four contiguous expansion coefficients in the TM as well as the mixed TM–TE cases. Only the TE case is an exception for which a more elaborate formulation exists. The relationships between contiguous expansion coefficients of both electric and magnetic type are relevant to the general cylindrical inverse problem, since the electrical radius can be directly recovered from the scattered field data. Furthermore, the scattered field can be uniquely expressed in terms of only one set of expansion coefficients associated with either the electric or magnetic vector wave functions.