Directly traceable ultra-precision displacement metrology: a heterodyne self-traceable grating interferometer

The heterodyne grating interferometer, renowned for its superior resolution and robust environmental adaptability, is suitable for high-speed, ultra-precise displacement measurement and has been widely researched and applied. The heterodyne grating interferometer employs the grating pitch as its measurement reference. However, due to the lack of direct traceability for the grating pitch and the accumulation of errors during length measurement transfer in calibration, the accuracy, consistency, and comparability of displacement measurements are diminished. Self-traceable gratings (STG) fabricated using atomic lithography technology, whose pitch is directly traceable to the chromium atomic transition frequency, exhibit a line density of 4700 lines/mm with picometre-level accuracy and uniformity. Therefore, this paper proposes what we believe to be a novel approach for developing a heterodyne self-traceable grating interferometer (He-STGI) based on STG, which combines stable, ultra-high-precision heterodyne interferometric length metrology with intrinsically traceable displacement readout. Experimental results show excellent agreement with a traceable iodine-stabilized laser interferometer (IS-LI), demonstrating 2-nm-level resolution, a 1.23 nm standard deviation over a 2-min static record, and a ∼0.5 nm deviation in dynamic displacement repeatability. The proposed He-STGI provides a novel solution for ultra-precision displacement metrology and enables a shortened and simplified traceability chain for displacement calibration.