Suppression Method for Stochastic Line Errors in Grating Interferometers Based on Spatial Wavefront Phase Analysis Theory

Grating interferometers have been extensively adopted in modern precision manufacturing industries. Diffraction grat-ings are the core components of grating interferometric displace-ment measurement systems. Notably, stochastic line errors of the grating introduce additional phase errors into the phase infor-mation of diffracted beams, ultimately degrading measurement precision. To eliminate the interference from stochastic line errors, this study establishes the spatial wavefront phase analysis theory (SWPAT). The adverse effects of stochastic line errors on the phase of diffracted beams are investigated, and a method of using large-diameter beams is proposed to suppress these errors. To val-idate this method, a heterodyne Littrow grating interferometric experimental setup is built, and controlled experiments with four different beam diameters are designed using the control variable method. Experimental results demonstrate that when the meas-urement beam diameter increases from 1 to 4 mm, the maximum displacement error is reduced by 34.3%, and the 3σ value is re-duced by 45.9%, thus verifying the correctness of SWPAT. This work enriches the theoretical framework for error compensation in grating interferometric displacement measurement systems and holds significant importance for improving displacement meas-urement precision.