Littrow 3D measurement based on 2D grating dual-channel equal-optical path interference

We propose a 3D measurement method based on 2D grating dual-channel and Littrow equal-optical path incidence to detect the 3D displacement of a 2D grating in the X-, Y-, and Z-directions. The 2D grating is combined with the Littrow incidence method and a turning element to cause the Littrow diffracted light with frequency f1 to interfere with the reference light at frequency f2, and the displacement data in the X-, Y-, and Z-directions are obtained using the separation-dual-channel phase decoupling algorithm. A corresponding test experimental platform is constructed, and linear error evaluation and step error evaluation experiments are performed to determine the displacements in the X-, Y-, and Z-directions. The results obtained show that all linearity errors are within ±60 nm in the 10 mm measurement ranges in the X-, Y-, and Z-directions, and the test resolution is within ±5 nm. The proposed method can thus realize nanoscale synchronous measurement of X-, Y-, and Z-direction 3D displacements.