Inverse Source Solutions with Spectral Filtering

The radiation model of inverse source solvers representing an antenna under test (AUT) relies on a discretized spatial equivalent source distribution and the source expansion coefficients are found such that their radiation reproduces known field observations. The required number of field observations, where in particular its spatial density is of interest, depends on the number of degrees of freedom of the radiation fields and, thus, on the spatial extent of the sources. For source distributions producing a narrow far-field radiation pattern, the number of degrees of freedom is reduced as compared to the general case and the spatial observation density can, thus, be reduced considerably. Since a general purpose inverse source solver requires the full set of observation samples as possibly supported by its spatial source distribution, we consider a solver with a spectrally filtered radiation operator, where the filtering is performed in the translation step of the underlying propagating plane-wave representation as known from the multilevel fast multipole method. The spectrally filtered inverse source solver is shown to reliably work with observation data with considerably reduced sample densities as compared to the commonly necessary sample densities, thus, allowing also considerably reduced acquisition times in antenna measurements. The spectral filtering can, moreover, lead to considerable computational speed-ups and it is still possible to identify possibly occurring problems of the AUT, which destroy the assumption of the narrow far-field radiation pattern and which do need to be detected in antenna testing.