Novel grating interferometer self-traceable to Cr atomic transition frequency

We present a self-traceable grating interferometer (STGI) based on chromium (Cr) atomic transition frequency ( ⁷ S₃ → ⁷ P₄), achieving direct length traceability to a natural constant. Cr gratings fabricated by atom lithography provide a pitch of 212.7779 nm (4700 lines mm⁻¹) with a measurement uncertainty of 0.0021 nm ( k  = 1), demonstrating excellent pitch precision. Combining the direct traceability of laser interferometry with the environmental robustness of grating interferometry, the STGI achieves sub-nanometre repeat positioning accuracy. Comparison with a laser interferometer calibrated by the national metrology institute shows excellent consistency, while 1 nm and 0.3 nm displacement tests reveal lower noise and higher sensitivity. This work establishes a novel length traceability chain linking atomic frequency standards to solid gratings, offering a compact, calibration-free, and highly stable approach for precise displacement metrology in advanced manufacturing and nanoscopic instrumentation.