| This dissertation explored the use of machine learning techniques, concentrating specifically on genetic algorithms (GAS), for solving beam shaping problems. In order to judge the effectiveness of this optimization-based method, four increasingly difficult beam shaping problems were solved. All four of these problems involved using a Gaussian input beam to a uniformly illuminate either spherical or planar surfaces placed some distance away. A computational method, which builds upon proven ray-tracing techniques, was developed for determining irradiance profiles. This method is the key to quantifying the efficacy of a beam shaper in terms of a merit function. When this merit function is coupled with a GA, an optimization technique can be employed.; The GA is able to find a satisfactory solution for all four cases in a significant but reasonable amount of time. This is particularly interesting since the GA requires little (often no) user input once the problem is started. In fact, in the last example, the GA is presented with a very general problem, and is allowed to determine the actual form of the system required to solve the problem, much as a human designer would. These examples demonstrate that the GA optimization-based method works, although the first two problems presented here can be solved in more general ways using analytical methods. With a general analytical solution, particular cases can be solved rapidly. However, the third and fourth examples illustrate two problems of such complexity that analytical methods become difficult, if not impossible, to apply. The most promising applications of GAs lie in these areas. |
