Abstract-The scattering of a plane electromagnetic wave by a perfectly conducting prolate or oblate spheroid is considered analytically by a shape perturbation method. The electromagnetic field is expressed in terms of spherical eigenvectors only, while the equation of the spheroidal boundary is given in spherical coordinates. There is no need for using any spheroidal eigenvectors in our solution. Analytical expressions are obtained for the scattered field and the scattering cross-sections, when the solution is specialized to small values of the eccentricity h = d/(2a), (h 1), where d is the interfocal distance of the spheroid and 2a the length of its rotation axis. In this case exact, closed-form expressions, valid for each small h, are obtained for the expansion coefficients g (2) and g (4) in the relation

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In this paper, we study the electromagnetic scattering of a plane wave by a prolate or oblate dielectric spheroid, which can be lossless or lossy. The presented efficient solution is obtained by applying a perturbation technique to the problem of the sphere using the spherical eigenvectors. This method allows a closed-form solution for the fields and the scattering cross sections, which is valid for small eccentricities of the spheroid. Alternatively, we construct the exact solution of the problem using the separation of variables in terms of the spheroidal eigenvectors and updated spheroidal algorithms that allow complex arguments. We compare the closed-form solution versus the exact solution and we conclude about its accuracy. Both polarizations are studied and numerical results are given for various values of the parameters.

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