Subreflector shaping for antenna distortion compensation: an efficient Fourier-Jacobi expansion with GO/PO analysis

Technological demands have brought a renewed interest in the application of large reflector antennas with steadily increasing operating frequencies and antenna dimensions. The high surface accuracy of the main reflector required by these antennas can often not be achieved with available manufacturing technologies. The utilization of a shaped subreflector for main reflector-distortion compensation is considered an effective measure to enhance the overall radiation performance of an antenna system. In the process of evaluating the suitability of the subreflector shaping, however, it is crucial to accurately assess the most suitable subreflector shape within a reasonable amount of computational time. This is especially true for electrically large reflectors, where simple analysis of the radiation characteristics already creates a serious computational burden, moreover, since reflector shaping is a synthesis process that necessitates repeated computation of the radiation characteristics. In this paper, the development of an efficient computational tool for subreflector shaping is presented. The subreflector shaping is performed through a combination of geometrical optics (GO) and physical optics (PO) on the subreflector and the main reflector, respectively. To significantly limit the number of parameters subject to optimization, the subreflector surface is parameterized by the coefficients of a global, orthogonal Fourier-Jacobi set (related to Zernike polynomials), which allows us to accurately represent a surface with only a small number of coefficients. The incorporation of this surface expansion into a GO/PO synthesis technique is detailed, representative results are given for a computationally challenging reflector configuration, and the tolerances for the shaped subreflector surface are studied.