Computation of reflector surfaces for bivariate beamshaping in the elliptic case
Abstract
A numerical method for designing reflector surfaces that produce a specified farfield over a given solid angle when illuminated by an isotropic source is presented. The technique, which uses the geometrical optics approximation, requires the solution of a particular nonlinear, elliptic partial differential equation, previously derived by the authors. The equation is solved iteratively by applying a finite difference model to a linearized form. Examples of some generated reflector surfaces are given showing the existence of two distinct solutions for each case. The method is applicable to problems in microwave antenna design, optics and acoustics.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 December 1976
 DOI:
 10.1088/03054470/9/12/020
 Bibcode:
 1976JPhA....9.2159N
 Keywords:

 Antenna Design;
 Antenna Radiation Patterns;
 Computer Aided Design;
 Elliptic Differential Equations;
 Far Fields;
 Reflectors;
 Cassegrain Antennas;
 Finite Difference Theory;
 Iterative Solution;
 Microwave Antennas;
 Nonlinear Equations;
 Surface Geometry;
 Physics (General)