Towards multi-dimensional atomic-level measurement: integrated heterodyne grating interferometer with zero dead-zone

This study proposes a novel heterodyne grating interferometer designed to meet the multi-dimensional atomic-level measurement demands of next-generation lithography systems and large-scale atomic-level manufacturing. By utilizing a dual-frequency laser source, the interferometer enables simultaneous three-degree-of-freedom (3-DOF) displacement measurements. Key innovations include a compact, zero dead-zone optical path architecture, which enhances measurement robustness by minimizing sensitivity to laser source instabilities and atmospheric refractive index fluctuations. In addition, we present a systematic crosstalk error analysis, coupled with a corresponding compensation algorithm, effectively reducing crosstalk-induced errors to below 5%. Experimental evaluation of the 90 × 90 × 40 mm3 prototype demonstrates outstanding performance metrics: sub-nanometer resolutions (0.25 nm for X/Y-axes, 0.3 nm for Z-axis), superior linearity coefficients (6.9 × 10−5, 8.1 × 10−5, 16.2 × 10−5 for X-, Y-, and Z-axes, respectively), high repeatability (0.8 nm@1000 nm for all axes), exceptional long-term stability (20 nm XY-plane drift, 60 nm Z-axis drift over 1000 s), and practical measurement ranges exceeding 10 mm in-plane and 2 mm axially. Comparative analysis with state-of-the-art sensors demonstrates significant advantages in measurement precision, system integration, and multi-axis capability. This advancement highlights excellent potential for applications in integrated circuit fabrication, atomic-scale manufacturing, and ultra-precision metrology for aerospace systems.