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. Whereas the required design procedure is well known for situations in which the source can be approximated as a point or as a line, the development of a general analytical design method for extended sources began only recently. One can obtain a solution for extended sources by establishing a one-to-one correspondence between target points and edge rays. Here the possible solutions in two dimensions (cylindrical sources) are identified, based on only one reflection for the edge rays. The solutions depend on whether the "image" on the reflector is bound by rays from the near or 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. Counting the topological choices for the boundaries of the "image" we obtain a complete classification of the buildingblocks from which luminaires can be designed. One can construct interesting hybrid configurations 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 the target at infinity.