On the theory of the synthesis of offset dualshaped reflectors  Case examples
Abstract
In an earlier paper by GalindoIsrael et al. (1987), the geometrical optics (GO) principles, constraints, and requirements of the dual and singleoffsetshaped reflector synthesis problem were collected and developed into a set of nonlinear firstorder PDEs. An extension of the methods by which solutions to the PDEs can be obtained is presented, together with several case examples. These examples are independently analyzed by GO and physical optics diffraction methods. The starting point for the integration over each reflector can be taken on the outer rim, at the center, or at an intermediate pointthe intermediate starting point being the more general case. The utility of the speed of this synthesis method is demonstrated. For example, the program utilized completes a synthesis in less than 45 s on a 386/20 personal computer and within a fraction of a second on a mainframe Cray. This makes practical the incorporation of the synthesis into a search algorithm that can optimize one or more parameters of the reflector system. As an example, the optimization of the mapping equations for low cross polarization is discussed.
 Publication:

IEEE Transactions on Antennas and Propagation
 Pub Date:
 May 1991
 DOI:
 10.1109/8.81489
 Bibcode:
 1991ITAP...39..620G
 Keywords:

 Antenna Radiation Patterns;
 Geometrical Optics;
 Gregorian Antennas;
 Partial Differential Equations;
 Physical Optics;
 Two Reflector Antennas;
 Computer Techniques;
 Cross Polarization;
 Parabolic Antennas;
 Personal Computers;
 Radio Astronomy;
 Communications and Radar