Fast method to detect and calculate displacement errors in a Littrow grating-based interferometer

Grating-based interferometers play important roles in precision displacement measurements. Gratings are the core components of grating-based interferometers, and grating surface errors and line errors seriously affect measurement accuracy, especially in systems with Littrow configurations. A fast, accurate method to calculate displacement errors caused by grating surface errors and line errors in a grating-based interferometer with a Littrow configuration is proposed. Displacement errors are calculated using the diffracted wavefronts at the ±1st orders of the grating. Experimental comparison of the displacements of a grating-based interferometer and a laser interferometer verifies the correctness of the proposed method. The differences between the calculated and measured displacement error results are within 40 nm. The method is accurate, fast, and low cost and is highly significant for system error compensation and improvement of the measurement accuracy of grating-based interferometers.