Aperture amplitude and phase control of offset dual reflectors

An approximate synthesis method is presented for solving the problem of offset dual-shaped reflectors. It is shown that the equations obtained by this method are partial differential equations that can be integrated numerically, except that these equations are generally not total and therefore do not have a 'smooth' solution. However, it is demonstrated that these equations form a nearly total differential that enables one to generate a smooth subreflector by integrating the differential equations and then synthesizing a main reflector which gives an exact solution for the specified aperture phase distribution. Several important illustrative examples are treated, which validate the adequacy of the proposed method.