Multimode fiber ruler for detecting nanometric displacements

Light is a perfect tool for numerous metrology applications. To deliver light to hard-to-reach places, fiber probes are widely used. Hair-thin endoscopes based on multimode fibers offer exceptional performance in terms of information density and instrument footprint. Here, we integrate optical metrology into a flexible fiber probe and present a multimode fiber ruler for detecting nanometric displacements. A fast single-shot measurement demonstrates two-dimensional resolving power of 1.8 nm, which is 670 times smaller than the diffraction limit of the optical system and 24 times smaller than the demagnified image pixel size. The multimode fiber ruler does not require detailed field mapping; therefore, low-magnification optical systems can be used to increase the light intensity on a sensor. Moreover, the proposed approach does not rely on any special structures, such as optical grating or metasurfaces. A high-resolution two-dimensional fingerprint is naturally "printed"on the multimode fiber output facet. Our results enable fiber-based displacement measurements with nanometer precision, establishing a new benchmark for fiber-based optical alignment sensors and metrology.