On raytracing via caustic geometry
Abstract
It is shown that results from the mathematical theory of singularities of differentiable mappings make it possible to understand the local structure of typical caustics in fields of two and three dimensions, and that this local information can be pieced together to give an effective visualization of the overall ray configuration. For simplicity, the work is done in the context of geometrical optics only, assuming the region of space under consideration to be homogeneous, so that ray paths are straight lines. No account is taken of edge diffraction, although the methods can be extended to incorporate such effects using the geometric theory of diffraction. Quantitative results concerning numbers and configurations of specular points are obtained for source and field points, the positions of which are allowed to vary.
 Publication:

IEEE Transactions on Antennas and Propagation
 Pub Date:
 May 1990
 DOI:
 10.1109/8.53490
 Bibcode:
 1990ITAP...38..625C
 Keywords:

 Caustics (Optics);
 Geometrical Optics;
 Ray Tracing;
 Reflector Antennas;
 Singularity (Mathematics);
 Optics