空间分离式外差二自由度平面光栅干涉仪

To measure two Degree-Of-Freedom (DOF) in-plane displacement, a spatially separated heterodyne grating interferometer was designed and built. The optical configuration, measurement principle, and in-plane rotary assembling error of this instrument were investigated. Based on the diffraction of the planar grating and the spatially separated heterodyne grating interferometry, a symmetrical double-diffracted optical configuration was designed and analyzed. The measurement principle and the elimination of periodic nonlinear errors were modeled and studied using Jones matrices for the components. In-plane rotary assembling errors around the z-axis were measured to decouple the measurement results for the x-and y-axes using a two-dimensional rotation matrix. Then, the square and circular paths of the grating were driven to evaluate the functionality of the proposed interferometer. The experimental results indicate that the proposed interferometer is capable of measuring the in-plane displacements of a nanopositioning stage within the range of 30 μm after compensation for the 0.350° rotary assembling error. The error attributed to mechanical vibration is less than 0.15 μm. In this investigation, 2-DOF in-plane measurement was demonstrated using a spatially separated heterodyne grating interferometer.