Optimization of active support layout for mirrors based on an RBF neural network and a hybrid optimization algorithm

The optimization of active support layout for mirrors is crucial for ensuring the performance of optical systems. To address the issues of low computational efficiency, long optimization cycles, and susceptibility to local optima in traditional optimization methods, this study proposes a strategy coupling RBF neural networks with hybrid optimization algorithms for optimizing the active support layout of a 450 mm meniscus thin mirror under horizontal working conditions. With the diameters <i>R</i>₁ and <i>R</i>₂ of the mirror's back support rings taken as design variables and the RMS and PV values of the mirror surface under vertical gravity defined as optimization targets, a parametric finite element model of the mirror is established. A dataset is then generated through the design of experiments to train the RBF neural network, after which the hybrid optimization algorithm is employed for multi-objective optimization. The results show that the RBF neural network exhibits excellent fitting performance and predictive accuracy, with all correlation coefficients of its objective functions exceeding 0.9 and error metrics significantly below the threshold. After optimization, the surface peak-to-valley (PV) and root mean square (RMS) values are reduced to 5.689 and 1.1775 nm, with improvements of approximately 43.78% and 43.11%, respectively, compared with the initial support scheme. The surface shape results achieved via this optimization surpass those obtained by existing optimization methods and single multi-objective algorithms, while the single optimization efficiency is improved by 96%. This optimization method offers significant engineering application value for enhancing both surface accuracy and optimization efficiency.