Modeling of ghost reflections in grating interferometry and real-time suppression using Kalman filtering

Heterodyne grating interferometry plays a crucial role in various high-precision applications due to its superior performance across multiple fields. However, achieving picometer-level accuracy is hindered by multiple error sources. One of the critical challenges stems from optical component ghost reflections, which introduce significant measurement inaccuracies. Despite their impact, the error modeling of ghost reflections is complex, and current high-precision real-time error suppression algorithms are lacking. To address this, we establish an accurate error model for ghost reflections in the classical configuration of grating interferometers, focusing on phase and displacement calculation errors. Furthermore, we develop a real-time ghost reflection filtering algorithm based on the Kalman filter, which reduces the error by over 90% while maintaining real-time performance. In summary, the proposed ghost reflection modeling and error elimination methods significantly enhance the potential of heterodyne grating interferometers in achieving picometer-level precision.