Modeling and design optimization of off-axis beam expanders using super element method and active learning-based Kriging model

Aiming at the low computational efficiency and the difficulty in balancing accuracy and efficiency in the integrated opto-mechanical modeling and optimization of off-axis beam expanders, this paper proposes a novel design optimization method combining the super element method and the active learning Kriging model. The frame, primary mirror and its support are condensed into a super element to reduce the degrees of freedom and computational scale of the model. An active learning Kriging surrogate model is constructed to fit the mapping between secondary mirror support design parameters and beam pointing error, with gradient-based nonlinear programming adopted for multi-parameter optimization. Results show that the super-element model yields a maximum displacement error of 1.053% and a maximum stress error of 4.781%, while improving computational efficiency by 8.6 times. The coefficient of determination (R2) of the Kriging model reaches 0.966, representing an 11.162% improvement over uniform sampling with the same sample size. The beam pointing error is reduced by 54.739% after optimization. This approach achieves a balance between accuracy and efficiency, providing technical support for the rapid optimization of precision opto-mechanical systems.