On the global interpolation of shaped reflector surfaces

Geometrical optics (GO) synthesis of reflector antennas involve the numerical solution of a system of partial differential equations obtained by enforcing the primary field along ray tubes emanating from the feed phase-center to map after reflections onto the prescribed far field. As a result, reflector profiles defined by a discrete set of points are obtained. It is then necessary to fit an analytically defined surface to this set of data-points in order to permit the evaluation of the antenna secondary field and its check against designer specifications. The implementation of two global interpolating functions is explored