Single-shot common-path Fizeau interferometer for vibration-insensitive nanometric displacement measurement

We present a single-shot, common-path Fizeau interferometer for high-precision micro-displacement measurement. By integrating a wire-grid polarizer with a pixelated polarization camera, the system implements spatial polarization phase-shifting for real-time phase retrieval. The common-path configuration and single-exposure acquisition significantly enhance robustness against environmental vibrations and air turbulence. The polarization-multiplexing scheme enables single-exposure measurement, granting the system the capability for real-time dynamic displacement monitoring. Experimental results demonstrate that the proposed method is capable of measuring displacements as small as 2 nm with high repeatability. This compact, vibration-insensitive design offers a robust solution for dynamic nanometric metrology in precision engineering.