Generalized algorithm for finding the catacaustics of an optical system

Abstract

The author of the work has proposed an algorithm for determining catacaustics in a “source-reflector” optical system on a plane. Katakaustika is called the envelope of reflected rays from a given curve and the study of catacaustics in the design of optical systems is one of the main tasks. The paper gives examples of solving this problem and presents the corresponding visualization. Particular attention is paid to problems where the source and reflector are curved, because these tasks in the scientific literature have not been previously considered. The presented algorithm is based on the cyclographic projection of the spatial curve of the line and its optical property. It is versatile and suitable for all tasks where the source of optical radiation is given in the form of a central (point), parallel or scattered beam of direct (light rays). The main advantage of the algorithm is that in the end it turns out analytical, i.e. exact solution to the problem of determining catacaustics. The results of the study can be used in applied fields of geometric optics, as well as in various computer-aided design systems specializing in modeling lighting of geometric objects.