Abstract

The simple laws of geometric optics allow to calculate how a ray is changed by reflection or refraction at an optical surface. Performing this calculation for a large number of rays allows to infer the entire output distribution of rays given an input dis tribution and an optical system. Ray tracing may be tedious but it is conceptually straight forward. Alas, the problem faced by the optical designer is the inverse of that described: given a distribution of light as input to the optical system, as well as the desired output distribution of light, the designer needs to find the appropriate optical system. Certainly, for a single input ray the relationship can be inverted. But each point on each optical surface is intersected by a set of rays. There are not enough degrees of freedom to transform the entire set. In mathematics many functional relations are well known which are easily evaluated in one direction, but which can not easily be inverted, i.e. evaluated in the reverse direction. Notably cryptography relies on such transformations. In geometrical optics there is equally no general procedure or theory available at this time to determine the appropriate optical system given the input radiation distribution and the desired output distribution. With few exc eptions, it is not even possible to assert whether a solution exists or not in the general case.

© 2003 Optical Society of America