Optical design algorithm utilizing continuous-discrete variables grounded on stochastic processes

This work proposes an optimization algorithm in optical design based on the concepts of ergodic and stochastic processes in statistical mechanics. In mixed-variable optimization problems, pseudo-random number and discrete-to-continuous variable conversion dramatically increase the speed at which the system solves for the optimal solution. Pseudo-random numbers are mainly applied in two important steps in the optimization algorithm: determining the combination of glasses involved and the order in which the successive glass parameters are replaced by real glasses. After two series of stochastic processes, the merit function value decreases rapidly along the steepest descent path, and thus the optical system approaches the optimal solution within a very short duration of time. By using the method proposed in this paper, a plan apochromatic objective with a long working distance was optimized, and finally, a high-quality optical system was obtained.