Evaluation of Periodic Nonlinear Error in a Directly Traceable Grating Interferometer

Periodic nonlinear error (PNE) is a key factor limiting the accuracy of displacement measurement instruments. For grating interferometers, which are widely used in high-precision displacement measurement, reliable characterization of PNE is essential. Conventional evaluation methods that rely on higher-precision instruments become unsuitable for ultra-high-accuracy systems. Although the self-evaluation method based on Lissajous figures are commonly used, their results inherently depend on the grating parameters and the interferometric signals themselves, leading to a lack of traceability and reduced credibility of the results. In this work, we propose a traceable self-evaluation method for assessing the PNE of a directly traceable grating interferometer (DTGI). The DTGI employs a chromium (Cr) atom lithography grating, whose pitch is directly traceable to the atomic transition frequency of Cr (7S3 → 7P4), as its displacement reference, thereby overcoming the traceability deficiencies of conventional self-evaluation methods. Numerical simulations confirm the validity of the proposed method, and experiments performed on a laboratory-built DTGI demonstrate 10-picometer-level PNE after Heydemann correction within micrometer range displacements. These results confirm the method’s suitability for metrological applications requiring stringent linearity performance in nanometric displacement measurement.