Observability-driven double-rotation self-calibration of non-rotational symmetry errors in laser direct writing lithography.

Coaxial computer-generated holograms (CGHs) are widely applied in high-precision wavefront testing of coaxial optical systems. Non-rotational symmetry error of these CGHs is one of the dominant error sources, which is critically determined by the stage errors of the laser direct writing system. However, existing approaches typically require high-precision reference masks, and the calibration area cannot exceed 6 inches, which limits their applicability and efficiency. In this study, an observability-driven self-calibration method was proposed to reconstruct non-rotational symmetry errors based on double-rotation measurements. A mask written by the same writing system was used as the reference mask, eliminating the requirement for external references. By introducing an observability-driven basis selection strategy, the decomposition and stable reconstruction of non-rotational symmetry errors have been successfully achieved. Experimental results demonstrated that the proposed method enabled the stage error to converge by 73.7% and 64.3% on the X-axis and Y-axis, respectively. Through comparative verification, the low-frequency consistency of the decomposed non-rotational symmetry errors was verified to be better than 9 nm (1σ) on both axes, providing an efficient and feasible solution for improving the placement accuracy of large-aperture CGHs.