Minimax optimization of shaped reflector antennas by polygon sequencing

Optimization of shaped reflector antennas for satellite applications is often performed using an iterative process that adjusts coefficients of the surface expansion based on some norm of the far-field directivity. Traditionally, this involves sampling the far-field directivity pattern on a fixed uniform grid within the specification polygon (see Sorensen, S.B., 1993). We present a procedure that optimizes shaped reflector antennas using the minimax criteria. The new procedure exploits the spatial filtering aspects of the antenna pattern in order to obtain improved results from the optimization. The specification coverage polygon is analogous to the mask of a harmonic filter. We replace this polygon by a sequence of contracting polygons beginning with a circumscribing ellipse and ending with the specification polygon. The problem is solved essentially by a sequence of optimizations. We also use an adaptive grid method which more efficiently samples the antenna pattern by recognizing the filtering aspects of its shape. The method has achieved significantly improved results at the cost of an extremely slow convergence. It is anticipated that for many commercial applications this cost can be justified, given the significant improvement in antenna performance that is possible.