Lens design and optimization using multi-objective evolutionary algorithms.

摘要

Non-Dominated Sorting Genetic Algorithm 2 (NSGA 2) was used to optimize optical systems with multiple objectives. The systems selected for study are Cooke triplets, Petzval lens and double Gauss lens. The objectives are minimization of aberration coefficients for spherical aberration, distortion, and the sum of coefficients of all third order monochromatic aberrations. CODE V RTM was used as a ray tracer. A set of trade-off solutions representing the optima, known as Pareto-Optima in multi-objective analysis, was obtained. A comparison of obtained optima to the known optima was done. Pareto-Optima in objective space for the selected Petzval lens design problem are shown to exhibit saddle points having unique trade-off features, which can not be detected in traditional gradient-based scalar optimization. Various optimization strategies are illustrated which ensure a diverse set of Pareto-Optima offering alternate manufacturing choices. Based on the results, a fourth objective was identified (sum of lateral and axial color coefficients) that is necessary to make valid trade-off decisions. The expansion of objectives followed by re-optimization provided unique trade-off solutions. Based on power and symmetry distribution of the component elements for the Cooke triplet system, addition and deletion of elements were carried out. The fourth objective added for that study is the minimization of the required number of elements. For the double Gauss lens system, the Pareto optimal surface indicated alternate manufacturing choices. There is a clear diversity of the Pareto optimal front in both objective and decision vector space. These studies have clearly illustrated the advantages of evolutionary multi-objective optimization techniques in optical system design.