Optimal simplex optimization for optical design

Simplex optimization is a powerful method of finding minima in noisy merit function spaces, such as those for illumination. The standard simplex routine and a modified one developed by the author are. applied to three lens design problems found in the literature: singlet, cemented doublet, and triplet. The starting conditions of the size of the simplex and the location in merit function space are investigated. It is found that the modified simplex routine provides better results than the standard one as the solution converges to the optimal solution, which is called the "end game". The standard simplex tends to provide better results than the modified one when operating in the "start game". The simplex results are compared to those from a commercially available lens design code. In most circumstances the commercially available code provides better performance in both iterations to convergence and quality of the result. The results presented herein provide confirmation that the modified simplex algorithm is a viable means of optimization for noisy merit function determination when in the neighborhood of local optima.