Characterization of rarefied gas flows within narrow-confined spaces in grating interferometers

High-speed motion of the reading head in grating interferometers induces rarefied gas flow perturbations in narrow-confined microstructure spaces with micro- and nano-periodic structures, leading to the fluctuations of air-refractive index and nanometer-scale interferometric measurement errors. To address this, an integrated fluid–solid-optical framework combining the Information Preservation Direct Simulation Monte Carlo (IP-DSMC) method, a modified Edlén refractive index model, and a ray-tracing method is developed. The IP-DSMC method is implemented within the OpenFOAM framework and validated against benchmark Couette flow cases. This study systematically characterizes the effects of Knudsen numbers and geometric parameters on flow perturbations and interferometric measurement errors. Results reveal that interferometric measurement errors are highly sensitive to refractive index non-uniformities induced by flow perturbations, jointly governed by rarefaction effects and microstructure geometries. A dynamic fluctuation model of air-refractive index incorporating Kn- and geometry-dependent corrections achieves high accuracy, showing that pressure-driven fluctuations of air-refractive index dominate interferometric measurement errors, reaching 13.2 nm at Kn is 0.25. The ray-tracing result confirms the reduction of the optical path difference with rising Kn, while geometric effects are secondary. This study provides a foundation for the error compensation in the high-precision grating interferometer under rarefied flow conditions.