Unified theory of near-field analysis and measurement: Scattering and inverse scattering

The many scanning procedures of the author's unified theory of near-field analysis and measurement are applied to the determination of complex bistatic scattering patterns of scalar and electromagnetic systems, both with and without correction for the patterns of the probes, one of which may be a compact range. For high accuracy, both the incident and scattered fields are expressed as linear combinations of exact solutions of the differential equations involved (Maxwell's in the electromagnetic cases). For high efficiency, natural orthogonalities with respect to summation are used to decouple the simultaneous equations expressing the measurements in terms of the desired pattern coefficients, implemented by the highly efficient fast Fourier transform as an approximation-free symmetry decomposition. The scanning procedures include spherical, a new, more accurate, more efficient type of plane polar, and many types of plane rectangular, plane radial, and circular cylindrical. All these results are expressed with a single notation and generally applicable equations, based upon symmetry analysis and relativistic invariances. The full apparatus of group representations is applied to reducing the measurement and computational effort, determining symmetries from scattering patterns, and determining Garbacz and singularity expansion method (SEM) modes. Further, Snell's laws, Fresnel's law, and conservation of momenta (e.g., propagation constants) are explained in terms of relativistic invariances.