Canonical illumination control problems are studied through the calculation of an appropriate ray mapping. We show that when the problem enjoys certain symmetries, the ray mapping can be calculated independently of the lens design. Once the ray mapping is known, the lens can be constructed. Such a separation of ray mapping and lens determination greatly simplifies the design task. We provide a few examples to illustrate this concept.
We analyze an algorithm for the design of a perfect cornea that exactly focuses a preselected object or a preselected wave front on the retina. The algorithm can be used, for example, in refractive surgery. We consider the sensitivity of the algorithm to various errors, including errors in the measurements of the aberrations, the original corneal topography and the ablation process.