High-Accuracy prediction and efficient adjustment of surface shape distortion in optical elements: Model correction based on uncertainty quantification-driven transfer learning

The surface shape of optical elements is a key determinant of opto-mechanical system performance, as its distortion directly affects optical wavefront distortion and can even render systems unusable. To address the challenge of compromised prediction accuracy due to high data dimensionality, this paper proposes a transfer learning model driven by uncertainty quantification, enabling high-accuracy prediction and efficient adjustment of optical element surface shape distortion using small-sample experimental data. First, a transfer learning prediction model for optical surface shape distortion is developed, integrating theoretical data from mechanical models with small-sample experimental data. Second, based on the principle of equal probability density, the uncertainty quantification of assembly preload is used to correct the transfer learning prediction model, enabling accurate prediction of high-dimensional surface reconstruction data and determining assembly process parameters in conjunction with surface shape distortion patterns. Third, an inverse model for preload in the assembly process is established, and an adjustment theory based on confidence levels is proposed, leading to a digital adjustment strategy aimed at minimizing beam wavefront distortion. Finally, experimental validation is conducted to verify the effectiveness of the adjustment strategy. Experimental validation shows that after three adjustments, surface distortion decreased by 13.66%, with only a 0.60% deviation from the theoretical minimum. Compared to traditional methods, this approach improves adjustment efficiency by 483.76%, offering a precise and efficient solution for optical surface shape distortion adjustment in opto-mechanical systems.