Multi-extremum optimization in lens design: navigation through merit function valleys maze

Lens designers routinely use optimization in their everyday practice. Local optimization algorithms lead to the nearest minimum. In this paper, a new deterministic approach for multi-extremum optimization is proposed. Optimal solutions for even moderate complexity optical architectures are shown to be located within extended merit function valleys. Merit function minimums are separated by saddle points. An effective algorithm to travel over these valleys from one local minimum through a saddle point to another minimum is proposed. From this new minimum, a new valley is found which leads through another saddle point to another minimum and so on.. In a finite number of steps, a complete mutually connected system of stationary points (minimums and saddle points) are revealed, giving a reasonable assurance that the search is completed.