On ray-tracing via caustic geometry

The objective of this study is to show how 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 how 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