Reflector design for illumination with extended sources: The basic solutions

The goal of the optical design of luminaires and other radiation distributors is to attain the desired illumination on the target with a given source, while minimizing losses. While the required design procedure is well known for situations where the source can be approximated as a point or as a line, the development of general design methods for extended sources has begun only very recently. A solution for extended sources can be obtained by establishing a one-to-one correspondence between target points and edge rays. In the present paper the possible solutions in two dimensions (cylindrical sources) are identified, and are based on only one reflection for the edge rays. The solutions depend on whether the "image" on the reflector is bounded by rays from the near or from the far edge of the source. For each case there are two solutions that could be called converging and diverging by analogy with imaging optics. Hence four building blocks emerge from which luminaires can be designed. Interesting hybrid configurations can be constructed by combining these building blocks. Thus one can gain a great deal of flexibility for tailoring designs to specific requirements. The differential equation for the reflector is shown to have an analytical solution. Explicit results are presented for symmetric configurations with target at infinity.