Dual-Axis Micro-Displacement Sensing Based on a Grating Pair with a Quasi-Common-Mode Optical Configuration

This paper presents a dual-axis micro-displacement measurement system based on double-layer grating interference adopting a quasi-common-mode optical configuration. Utilizing the diffraction and interference effects of the grating pair, the system realizes decoupled high-precision dual-axis displacement measurement by detecting diffracted light intensity induced by out-of-plane and in-plane motions of the movable grating. The light-intensity response originating from grating-pair diffraction is theoretically derived to establish the quantitative relationship between displacement and optical intensity. An experimental setup is constructed to record intensity variation curves for out-of-plane and in-plane motions. Measurement accuracy along the two axes is systematically analyzed over a 1 mm working range. Experimental results yield a full-scale accuracy of 0.0039% and a resolution of 0.38 nm for out-of-plane displacement, while the in-plane displacement measurement achieves a full-scale accuracy of 0.08% with 19 nm resolution. Benefiting from its compact architecture, nanoscale resolution, and superior measurement precision, the proposed grating-pair scheme opens a new avenue for multi-dimensional micro-displacement sensing.