Two-dimensional optical micro displacement sensing and crosstalk elimination based on the self-imaging effect of a grating pair

This paper proposes a straightforward method for measuring micro-displacement synchronously along two orthogonal axes. A single structure consists of a pair of two-dimensional gratings and a quadrant detector aligned with a collimated laser is used to detect the micro-displacement. The crosstalk and the common-mode noise are eliminated through a two-step differential process. Experimental results demonstrate that the displacement measurement resolution can reach 40 nm with a sensitivity of 0.483 V/µm within the linear range. The accuracy obtained is 0.29% on the X-axis and 0.31% on the Y-axis within a 500 µm range. The signal-to-noise ratio is improved by 4.56 dB after differential. The simplicity and high compactness of this measurement structure make it suitable for fabrication and alignment using microfabrication processes, which show great potential in many applications such as gyroscopes, accelerators, and multi-dimensional displacement measurements.