Geometric error correction in micro-probe fiber interferometry based on mode field matching for nanometer positioning

Geometric errors introduced by angular deflection of linear-motion targets severely limit the accuracy of laser interferometric positioning measurement. This study addresses the geometric error induced by target deflection in nanoscale linear motion positioning measurement by innovatively proposing a compensation method based on optical mode field matching. By establishing a mode field matching model and combining it with wavelength-scanning interferometry for precise working distance measurement, the target deflection angle is accurately determined without any auxiliary angle sensing components (e.g., quadrant detectors), and the corresponding geometric error is effectively compensated. The system utilizes a compact fiber micro-probe and eliminates the need for auxiliary optics, thereby significantly enhancing system compactness and robustness. Experimental results demonstrate that within 200 mm travel range, the deviation between the proposed system and a commercial interferometric system was reduced to ± 30 nm after applying the proposed correction. Furthermore, tests with a piezoelectric stage verify sub-nanometer displacement resolution. This study provides an effective geometric error compensation method for high-precision linear positioning measurements in confined spaces, holding significant application value in fields such as ultra-precision machine tool linear motion positioning measurement.