Comprehensive evaluation framework for measured freeform surfaces integrating imaging quality simulation and assembly tolerance analysis

Abstract Freeform surfaces are widely applied in high-performance optical systems, such as augmented reality/VR displays and remote sensing instruments. However, the complexity of their surface errors poses significant challenges for quality evaluation. Conventional metrics cannot directly relate surface deviations to imaging performance, while fitting approaches—such as global polynomials or parametric local models—often suffer from smoothing effects or parameter sensitivity. In this work, we propose a generalized, measurement-data-driven evaluation framework for practically fabricated freeform mirrors. The framework employs piecewise bicubic Hermite interpolation to represent measured surfaces, providing a deterministic analytic reconstruction with high representation accuracy and numerical robustness. Realistic ray tracing simulations are then performed to comprehensively evaluate both imaging performance and assembly tolerance sensitivity. This framework enables the decoupling of imaging degradation caused by specific surface errors, thereby supporting precise process optimization. In a case study of a dual-freeform augmented reality head-up display optical system, the simulation based on Hermite-interpolated data demonstrated a deviation of only 1.17% from experimental results regarding horizontal local magnification at the edge eye position. Using this framework, we identified and corrected the primary manufacturing errors, reducing the surface form error peak-to-valley of the M1 from 123.3 µm to 93.56 µm. Both simulation and experimental validation confirmed that the optimized system met design requirements, demonstrating the effectiveness of the proposed framework for high-precision quality control in freeform manufacturing.