Abstract: The assembly and angular commissioning errors in the grating interference system are the direct causes of the geometric misalignment of the detection light and its deviation from the detector sensing center. To clarify the influence of the integrated attitude error of the detection light on the interferometric phase and displacement measurement results, based on the 4D expression of the wave vector of special relativity, this paper directly relates the optical frequency and optical wave vector to the grating equation, constructs a Doppler frequency shift theory system with any arbitrary angle of incidence and grating motion along any direction, and demonstrates the physical characteristics that the frequency shift relationship of diffraction light at the same level is consistent under different grating incidence angles. By comparing the physical images between laser and grating interference systems, it is clarified that even if the optical geometric path of the system does not change with the motion, the reason for the phase change is the special wave vector modulation relationship on the grating surface. The conclusion shows that the grating interference system maintains the displacement transformation relationship in the presence of integrated attitude error of the detection light, and the deflection of the grating period direction is the key source of the geometric measurement error of the system. To preliminarily determine the measurement performance index of a certain system, a method that can quickly determine the original resolution of displacement measurement is given in this paper. Since the frequency shift theory in this paper starts from the underlying logic of physics, the relevant conclusions are universal, which not only guides the principle analysis of all grating interference systems, but also has an important reference for the analysis of geometric measurement errors in various advanced systems.