DIFFRACTION BY A SPHEROID

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Abstract
The diffraction of a spherical scalar wave by a hard or soft spheroid is investigated theoretically. First the diffracted field is determined by the geometrical theory of diffraction. Then for comparison the corresponding boundary value problem is solved exactly in terms of a series of products of spheroidal functions. The series involves the "radial" eigenfunctions which correspond to appropriate complex eigenvalues. Asymptotic expansions are derived for these functions for large values of the variable and the parameter. When used in the series solution, these expansions yield the asymptotic form of the diffracted field for incident wavelengths small compared to the spheroid dimensions. This result coincides precisely with that given by the geometrical theory. This agreement provides another verification of that theory. The expression for the field is used to calculate the backscattering and the field on the spheroid. The electromagnetic backscattering is finally computed with the aid of a theorem which relates it to the two scalar results.

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