Herein, a mathematical model of the relationship between grating rotation angle and diffraction beam deflection angle was established based on the theory of mosaic gratings. An optical path was designed to detect the grating rotation angle using interferometry. A Zygo interferometer was used to detect the zero- and first-order diffraction wavefronts of a grating. In addition, the model error caused by the reflector installation error was studied. The experimental results show that in the range of 0-500 μrad, the maximum relative measurement error of grid line parallelism between gratings is 3.85% when the theoretical model is used to adjust the grating attitude. When pitch and yaw angles of the reflector vary in the range of 0″-20″, the maximum relative measurement errors of grid line parallelism between gratings are 4.99% and 3.77%, respectively.