Out-of-plane displacement sensor based on the Talbot effect in angular-modulated double-layer optical gratings

Based on the Talbot effect of optical gratings, we propose a novel out-of-plane optical displacement sensor with an ultracompact structure, to the best of our knowledge. Using two optical gratings with a slight angle between them, two angular-modulated signals with a phase difference of 90° are obtained associated with a two-quadrant photodetector, which are in sinusoidal relationship with the displacement in the direction perpendicular to the grating plane. Using an interpolation subdivision circuit with a subdivision factor of 1000, out-of-plane displacement measurement with a resolution of 11.23 nm within a range of 1 mm is obtained.