Formation, measurement, and correction of intrinsic positional deviations in the beam space at the end effector of a five-axis laser micro-machining system

The five-axis laser micro-machining system (FALMMS) enables beam control in five spatial dimensions and is widely used for fabricating complex components. However, optical lens control and focusing inevitably introduce beam distortions, leading to intrinsic positional errors that limit machining accuracy. Effective error correction across all five dimensions remains challenging. This work systematically analyzes the sources of intrinsic beam deviations in FALMMS and proposes a full-dimensional calibration method based on indirect measurement and polynomial interpolation. The novelty lies in designing dimension-specific feature patterns and applying interpolation algorithms tailored to error characteristics. An n×n grid pattern with bilinear interpolation is used for the XY-plane, layered focal measurements with cubic polynomial interpolation address Z-axis errors, and cross-shaped (“+”) marks on different planes enable angular error calibration for α and β. Experiments show that, within a 20 × 20 mm² field, the residual XY error is below 8 µm; Z-axis errors are ∼10 µm within ±2 mm; and angular accuracy of 0.1° is achieved for α and β within ±4°. An integrated test pattern further validates the effectiveness of the method. This study extends error correction from 2D/3D to five dimensions, providing a feasible strategy for high-precision FALMMS.