Globally optimal first-order design of zoom systems with fixed foci as well as high zoom ratio.

In this paper, we propose a systematic approach to automatically retrieve the first-order designs of three-component zoom systems with fixed spacing between focal points based on Particle Swarm Optimization (PSO) algorithm. In this method, equations are derived for the first-order design of a three-component zoom lens system in the framework of geometrical optics to decide its basic optical parameters. To realize the design, we construct the mathematical model of the special zoom system with two fixed foci based on Gaussian reduction. In the optimization phase, we introduce a new merit function as a performance metric to optimize the first-order design, considering maximum zoom ratio, total optical length and aberration term. The optimization is performed by iteratively improving a candidate solution under the specific merit function in the multi-dimensional parametric space. The proposed method is demonstrated through several examples, which cover almost all the common application scenarios. The results show that this method is a practical and powerful tool for automatically retrieving the optimal first-order design for complex optical systems.