In this paper, the fundamental principle of precision displacement measurement with a doubly blazed grating is analyzed in detail by means of Fourier Optics. The mathematical expressions about the amplitude and the intensity of diffracted light are derived, and the measurement formula is presented. At the same time it is indicated that moire fringes are nearly perfect two-beam interference fringes with superb contrast. These conclusions are consistent with the theoretical and experimental results given by Post D, and helpful to further development of the measurement principle.