Based on Talbot effect of optical microgratings, we report an ultra-compact sensor for displacement and vibration measurement with resolution down to sub-nanometer level. With no need of optical components such as reflectors, splitters, polarizers, and wave plates, the proposed sensor based on a common-path structure shows a high compactness. Using gratings with period of 3 µm, displacement measurement within a range of 1 mm is demonstrated experimentally. Associated with an interpolation circuit with subdividing factor of 4096, a resolution of 0.73 nm is obtained. The experimental results also show the ability for the sensor to detect in-plane vibration with frequency below 900 Hz. With a sub-nanometer resolution and an ultra-compact structure, the miniature sensor shows potential in applications such as high-precision machinery manufacturing and semiconductor processing.

C.G. Xin, Z.Y. Yang, J. Qi, Q.Q. Niu, X.C Ma, C.J. Fan et al., Opt. Express 30, 22(2022).