The operation of diffraction-limited misfocused correlator is analysed in terms of a model of off-axis optical Fourier-transformation system and the theory of Fresnel diffraction. It is proven that correlation still remains but between the intensity transmittance of the first transparency and the intensity diffraction pattern, of the second. The diffraction correlator can be modified as an interferometer, a general theory is deduced for it. The interferometry using two Ronchi gratings is discussed in detail, that yields lateral shearing interferogram, some corresponding experiment results are also given.It can be seen that the diffraction correlator is the setup of Lau effect for any plane objects and for any observating distance. Thus its application for interferometry is just as the interferometer directly based on the Lau effect.