Saddle Point Methods in Global Optimization of Complex Optical Systems

Global optimization in optical design is a challenging task, especially with complex optical systems with large numbers of variables e.g. sophisticated multilayer structures or imaging systems with advanced surface profiles. We will report on the methods saddle point detection and saddle point construction that are developed at TU Delft, in order to improve the global optimization of such complex optical systems. These methods are used both to solve distinct design problems and to provide a more general insight in the structure of the solution space by means of a systematic analysis in order to improve the optimization process of similar design tasks. The discovery of the network of the positive triplet lens system is one milestone of this approach. Also the reduction of the number of variables in lithographic systems i.e. individual lenses or surface parameters, while maintaining or even exceeding the performance of the initial designs will be discussed. Moreover, the presented optimization methods are conceptually not limited to applications in optical design, but are in general applicable to global optimization problems.