# A Surrogate Model Based Multi-Objective Optimization Method for Optical Imaging System
###### Abstract  
An optimization model for the optical imaging system was established in this paper. It combined the modern design of experiments (DOE) method known as Latin hypercube sampling (LHS), Kriging surrogate model training, and the multi-objective optimization algorithm NSGA-III into the optimization of a triplet optical system. Compared with the methods that rely mainly on optical system simulation, this surrogate model-based multi-objective optimization method can achieve a high-accuracy result with significantly improved optimization efficiency. Using this model, case studies were carried out for two-objective optimizations of a Cooke triplet optical system. The results showed that the weighted geometric spot diagram and the maximum field curvature were reduced 5.32% and 11.59%, respectively, in the first case. In the second case, where the initial parameters were already optimized by Code-V, this model further reduced the weighted geometric spot diagram and the maximum field curvature by another 3.53% and 4.33%, respectively. The imaging quality in both cases was considerably improved compared with the initial design, indicating that the model is suitable for the optimal design of an optical system.  
surrogate model; ray tracing; multi-objective optimization; experimental design; Kriging 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 2022 20222 2022 2 Therefore, optimal optical designs are limited to either a finite search in the global space or gradient-based searches that tend to become stuck in local optima. The current revival of surrogate models-based optimization algorithms [4; 5; 6] provides a possibility of overcoming the \"curse of dimensionality\". Currently, surrogate models have been used in the design of optical thin films [7], nanostructures [8; 9; 10; 11], and meta-surfaces [12; 13; 14] and have shown some promising results.  
For complex systems, the calculation cost is very high in the case of many parameters to be optimized and objective functions (dimension disaster). This paper proposes a multi-objective optimization method based on the Kriging surrogate model [15; 16; 17] for an optical imaging system; for a specific system, it greatly reduces the calculation cost in the optimization process and helps to conduct a more comprehensive search in the global design space. This surrogate model has a large number of applications in aerodynamics [18], weather prediction [19], and the structural reliability [20] of aircraft. Compared with the conventional methods, which mainly rely on optical system simulation using ray-tracing-based programs, the surrogate model-based method can greatly reduce the calculation cost and provide a possibility of using the saved computer power for more comprehensive searches in the design space.  
Section 2 of this paper will introduce the methodology used in the proposed model. The process flow of the model and the methods involved, including the experimental design method, surrogate model, and multi-objective optimization algorithm, will be introduced in detail in this section. Two case studies using the proposed method to optimize the design of a Cooke triplet system were carried out, and the results are presented in Section 3. A conclusion is given in Section 4.