A near-field to far-field transformation for spheroidal geometry utilizing an eigenfunction expansion

This paper presents a near-field to far-field (NF-FF) transformation for antenna and scatterer radiation evaluation. The transformation allows practical computation by making use of a sampling surface in the near-field that is spheroidal in shape: namely a prolate or oblate spheroid. The resulting vector wave equation does not support orthogonal vector solutions in spheroidal coordinates and instead rectangular field components are solved for using the scalar wave equation in spheroidal coordinates. The new transformation only requires knowledge of the completely-specified near-field electric field along the spheroidal transformation surface and does not need any information associated with the corresponding magnetic field. The benefit of using a spheroidal near-field geometry is its ability to closely conform to both linear and planar radiating structures while still permitting evaluation of the full far-field radiation pattern. Our approach makes use of an eigenfunction expansion of spheroidal wave-harmonics to develop two distinct, yet closely related, NF-FF transformation algorithms for each type of spheroidal surface. The spheroidal NF-FF transformation is validated and performance assessed using a well-characterized radiation structure. By applying the prolate and oblate algorithms to a radiating structure with known analytical near- and far-field electric fields, viz., a filament dipole with sinusoidal current distribution, we are able to setup and conduct multiple numerical tests that serve as a proof-of-concept for the spheroidal NF-FF transformation.