Two-Dimensional Nanoruler Based on Optical Scale

Displacement sensing with subnanometer precision is a crucial technology across various fields. There is a pressing need for a rapid, compact, long-range, and highly accurate lateral displacement measurement method that does not rely on postprocessing algorithms. In this study, we demonstrate a nanoruler based on confocal micrometalens arrays (MMLAs) for two-dimensional (2D) transverse displacement metrology. We have developed an 'optical scale' by constructing a blazed grating with a tunable blaze angle proportional to the relative displacement between the MMLAs, enabling high-precision sensing of displacements as small as 0.5 nm when environmental noise is minimized. Our system is characterized by its simplicity and compactness, comprising only a laser, two MMLAs, a Fourier transform lens, and an image sensor. This work introduces innovative concepts for metasurface-based photonic devices and high-precision displacement metrology.