Absolute testing of weakly aspheric surfaces with pixel-level resolution and subnanometer accuracy

In this study, the shift-rotation absolute testing method is extended to weakly aspheric surfaces, providing a direct, null-compensator-free solution for subnanometer figure testing. A key limitation of existing shift-rotation methods, namely the tradeoff between high-resolution and low-noise propagation, is addressed. Accordingly, a pixel-level-resolution absolute testing method based on multiple rotations and two orthogonal lateral shifts is proposed. Rotationally asymmetric errors are calibrated via rotation averaging, while rotationally symmetric errors are reconstructed by dividing shift-induced differential wavefronts into subapertures for least-squares fitting and stitching. These components are then fused to achieve pixel-level absolute surface figure reconstruction. The proposed method preserves high-frequency surface information while maintaining a low noise-propagation ratio, thereby achieving subnanometer accuracy. Numerical simulations and absolute testing experiments on a weakly aspheric surface validate the effectiveness and reliability of the proposed method for high-precision optical surface testing.