| Expressions are presented for describing incoming and outgoing fields about an antenna in terms of a series of exciting and emergent vector spherical-wave functions. The exciting and emergent fields around the antenna's exterior are related to the field in the antenna feed via a source-scattering matrix representation. A series of these so called spherical-wave source-scattering matrix coefficients are then related to more conventional antenna parameters such as gain and receiving cross section. An overview of rotation and translation theorems for transforming vector spherical-wave functions between two distinct coordinate systems is given, followed by a general solution to the problem of expressing the coupling between two coupled antennas in terms of each antenna's spherical-wave source-scattering matrix representation. We go on to consider special results to substantiate our formulation, such as showing equivalence between the coupling equations for transmission in opposite directions when the antennas are reciprocal, showing uniform convergence of the series representations for antenna coupling and simultaneously obtaining a coordinate-system translation theorem for the dyadic Green's function, and lastly showing that our two-antenna coupling equations reduce to expressions for the incident and emergent fields about a single antenna when the other antenna is an elementary dipole. Efficient probe-corrected spherical and hemispherical scanning algorithms are then developed for processing measured near-field data to obtain an antenna's far-field pattern. Finally, we describe a number of self-consistency tests and theoretical-data simulations that were developed to validate our spherical-scanning algorithm, and we describe an independent experimental verification. |
