Developing optical systems, particularly those consisting of spherical lenses, is relevant for various applications such as lithographic scanners and metrology equipment. The design process of an optical system typically involves the optimization of specific objectives to ensure the best performance. As a common example of such an objective, we consider the problem of determining the lens curvatures that result in a sufficiently small root mean square spot size. Optimization algorithms are commonly employed to solve this problem by heuristically eliminating suboptimal optical designs. This class of algorithms includes the damped least squares widely applied in commercial software and advanced methods such as saddle-point construction. However, within a restricted computational budget, these optimizers are limited in exploring potentially promising novel solutions because they heavily rely on the initial specific designs that must conform to complex or unknown requirements. We address the considered problem with a modified Hill Valley Evolutionary Algorithm, which has proved itself as one of the best state-of-the-art metaheuristics for multimodal black-box optimization. We demonstrate that our algorithm locates a diverse set of high-quality optical designs with four lenses in a single run, even when initialized with random starting curvatures. This is the first result in this domain when an optimization algorithm that does not take specific optical properties into account can still generate relevant and high-performing optical systems. Furthermore, we show the benefits of the proposed methodology for the diversity of the obtained set of solutions while maintaining a solution of the same quality as the one found by the most prominent algorithm in the domain. We provide analyses of the obtained solutions according to: (1) tolerance to the alignment of lenses and (2) susceptibility to small variations of lens curvatures.
Antonov et al. (Wed,) studied this question.