In this paper, the principle of Fourier optics is used in treating the problem of moir6 fringe multiplication formed by two contact gratings. A continuous relationship between displacement and light intensity is obtained. The gratings may be amplitude type, phase type, or amplitude and phase type. Moire fringe multiplication under coherent illumination for both homogeneous and inhomogeneous deformation-field is considered. The resulting formulas have universal significance and agree fairly well with the experimental results obtained by D. Post.