In this paper the problem of synthesis of offset shaped single reflector antenna is considered. This problem has to be solved when a reflector antenna system is required to control the field amplitude and/or phase on the far-field or on the output aperture in the near-field. Achieving high efficiency is a very important objective of the design and shaped reflector antennas are used for that purpose.
The equations of the problem are strongly nonlinear partial differential equations which can not be analyzed by standard techniques. Though the problem has been the subject of study by many authors for over 40 years, up until recently, there were no rigorous theoretical results resolving completely the questions of existence and uniqueness. With few exceptions, authors have attacked the problem with heuristic numerical procedures, and, depending on the specific formulation, obtained different results not always in agreement with each other.
In this paper a new method for solving the single reflector problem is presented. The new method allows a complete and mathematically rigorous investigation of this problem. Furthermore, the proposed method lends itself to a numerical implementation and we present here several examples.