A comparison between techniques for global surface interpolation in shaped reflector analysis

The usual geometrical-optics-based synthesis of shaped reflector antennas provides numerically defined surfaces which must be interpolated to permit the evaluation of the antenna secondary field to be checked against design specifications. An interpolating function capable of describing the surfaces in a global fashion as smoothly as possible is then desirable, especially when ray-optical methods of analysis are employed. The implementation of two global interpolating functions is explored. One is a polynomial-Fourier series while the other is a quintic pseudo-spline. Two cases are studied: a shaped reflector antenna synthesized for a cosecant squared beam in the vertical plane with an azimuthally uniform radiation, offset-fed by a 90 degrees corrugated horn, for use in a nodal station for point-to-multipoint transmission in metropolitan areas; and an offset dual reflector system for satellite communications, synthesized by 300 points on each surface, with both shapings controlled so as to meet a prescribed sidelobe envelope.<>