ABSTRACT

This chapter presents rigorous approaches to optical design producing effective tools for development, analysis, and description of required freeform optics. In the far-field problem the reflected directions are identified with points on the unit sphere double-struckS2. Traditional methods for designing optics for prescribed irradiance problems are often based on an a priori assumption that the sources, targets, and light patterns have rotational or some other symmetry. However, designers of optics often encounter practical tasks in which optical surfaces are expected to accommodate light sources, targets, and illumination patterns without special symmetries such as rotational or rectangular. The chapter outlines the issues involved in the development of methods for design with freeform surfaces. In the geometrical optics approximation the derivation of equations of freeform optical surface(s) transforming a given input radiation into a prescribed irradiance pattern is based on a systematic application of the ray-tracing equations and energy conservation law.