Radar cross sections for two dielectric spheroids in arbitrary configuration

By expanding the incident, scattered, and transmitted electric and magnetic fields in terms of an appropriate set of vector spheroidal eigenfunctions, an exact solution is obtained to the problem of scattering of a uniform plane electromagnetic wave by two dielectric spheroids in arbitrary configuration. The boundary conditions at the surface of each spheroid are imposed by expressing both electric and magnetic fields scattered by one spheroid in terms of the spheroidal coordinates attached to the other, using the rotational-translational addition theorems for vector spheroidal wave functions. As in the case of two perfectly conducting spheroids, the column matrix of the total scattered field expansion coefficients is equal to the product of a square matrix, which is independent of the direction and polarization of the incident wave, and the column matrix of the known incident field expansion coefficients. The solution of the associated set of simultaneous linear equations gives the unknown scattered field expansion coefficients. Numerical results are presented for backscattering cross sections of a system of two prolate spheroids with nonparallel axes for different axial ratios and separations.<>