A Novel Grating-Interferometric Comparator for Calibrating Baseline Errors of Linear Encoders

Accurate nanoscale calibration of linear encoders is essential for precision manufacturing and inspection. The conventional calibration method employs laser interferometric comparators, but these are susceptible to environmental disturbances and uncertainties in air refractive index compensation, making it challenging to achieve both operational convenience and high-accuracy traceability. To address this problem, a novel grating interferometric comparator based on Chromium Atomic Lithographic (CAL) gratings is proposed. By employing the grating pitch as the reference, this comparator eliminates refractive index corrections, thereby enhancing robustness and ease of use. The grating pitch is determined by the7S₃→7P₄ Cr atomic transition frequency, which is directly traceable to the SI with a relative standard uncertainty of 3.7×10-8. To validate the performance of the proposed comparator, a dual traceability chain comparison system was established, integrating a CAL Grating Interferometer (CGI) and a Stabilized Laser Interferometer (SLI) for synchronous calibration of linear encoder baseline errors. Experiments demonstrated that the two calibration methods showed good agreement within a travel range of 3 mm, with a maximum deviation of 1.9 nm. Furthermore, the CGI exhibited smaller standard deviations and superior repeatability. The expanded uncertainty of the novel comparator is U(k=2) = 2.7 nm + 8.6×10⁻8L, where L is in meters. This study provides a traceable and interference-resilient calibration solution for linear encoders, offering strong potential for industrial nanometrology.