Diffraction synthesis of reflector antennas using pseudospline global interpolating functions

Geometrical optics (GO) synthesis of reflector antennas usually yield numerically defined surfaces which must then be interpolated for subsequent evaluation of the radiation patterns and its checking against design specifications. With respect to this, global interpolating functions capable of handling a set of arbitrarily located data points while observing the smoothness characteristics implied by GO synthesis are preferably used. For highly shaped reflectors, a previous study revealed the adequacy of quintic pseudosplines (QPS) and its superior stability when compared with the implementation of other global interpolating functions, namely the polynomial-Fourier series (PFS) and Jacobi polynomial-sinusoidal expansions (JPSE). The main advantage of the algorithm implemented for QPS was revealed by the use of a relatively small number of data points, chosen among the larger synthesis set in a step-by-step localized reduction of coordinate residues at critical portions of the surface, in order to obtain convergence of the corresponding physical-optics (PO) radiation patterns to within specified limits. Conversely, for the same class of surface, the oscillatory behavior of the expansion functions in the PFS and JPSE interpolations was shown to cause unstable interference patterns in the corresponding radiation fields as the number of terms in the series is varied in order to accommodate local fittings.