Tolerance Inversion for Lens Support Loads Based on Feature-Enhanced Active-Learning Gaussian Process Regression

Support load fluctuations in lithographic objectives can induce additional surface figure errors in lenses. Conventional Monte Carlo-based tolerance analysis is computationally expensive in high-dimensional load spaces, and surrogate models based only on raw load inputs often fail to accurately capture local-extremum responses such as peak-to-valley (PV). To address the load tolerance inversion problem under prescribed PV and root mean square (RMS) constraints, a tolerance inversion framework integrating Regional Peak-to-Valley Fluctuation Features, Active-Learning Gaussian Process Regression, and dual-metric tolerance boundary search (RPVF-ALGPR) is proposed. The framework transforms the local fluctuation information in low-order Zernike-reconstructed wavefronts into regional peak-to-valley fluctuation features and combines them with the original support loads as inputs to the GPR surrogate models. It further combines posterior-uncertainty-driven active learning to construct surrogate models for both metrics, thereby enabling the inverse determination of the critical load fluctuation boundary. One set of training results from a biconvex lens case study shows that the proposed method effectively improves PV and RMS prediction accuracy and reduces the number of samples required to reach the prescribed accuracy threshold by 35.7% compared with random sampling. The results provide a reference for support-load tolerance allocation and optomechanical stability evaluation of high-precision lenses.