Modelling surface raw data for reflector antenna applications

The usual methods of synthesis of reflector antennas yield numerically defined surfaces in the form of a set of arbitrarily (though ordered) located data points. These must then be interpolated for subsequent evaluation of the radiation field as a means of checking if design specifications were attained. It is then desirable to use a global (for the sake of computational efficiency) and smooth (in order to satisfy inherent principles of the synthesis technique, e.g. geometrical optics) interpolating function, with reasonable assurance that if the specifications have not been met, one should refine the synthesis step and not the interpolation itself. The family of pseudosplines obtained from the minimization of appropriate functionals, comprise a set of interpolating functions satisfying the above requirements, with polynomial degrees resulting from forcing the continuity of derivatives up to a certain order. Cubic pseudosplines (CPS) present continuous first-order derivatives, adequate for physical optics (PO) field computations. Quintic pseudosplines (QPS) present continuous derivatives up to second order, a requisite for employing ray-optical methods of analysis, 7^th-degree ones present up to third-order continuous derivatives, and so on. Unknown coefficients in these expansions are obtained by point-matching at (known) data points and imposing a boundary condition by which higher-order continuous derivatives remain finite away from each data point