Grating-based 2D displacement measurement with quadruple optical subdivision of a single incident beam

We propose a new symmetrical heterodyne grating displacement measurement method, based on 2D grating and single diffraction quadruple subdivision method. Using a dual-frequency laser with a wavelength of 632.8 nm, output power of 2.2 mW, and a 1200 l/mm 2D grating, eight diffracted light beams interfere in pairs in the X and Y directions through a turning element. The detection system's measurement accuracy was assessed experimentally. The system measurement resolution in the X and Y directions is better than 3 nm; the grating displacement measurement errors within a 10 mm range are better than ±30 nm and ±40 nm, and the repeatability error is better than ±25 nm. The method is not only applicable to nanoscale 2D displacement measurement technology but also can be used for ultra-precision positioning and ultra-precision processing, with the potential for picometer-level improvement.