In this paper, the interference phenomenon in an optical system with three gratings in series arrangement is proposed and analysed in terms of the partial coherence theory and the ambiguity function. As a result, the fringe intensity distribution is derived as a joint convolution-correlation integral of three equivalent functions of gratings. The conditions on the distances and the period ratios between gratings are studied. With the change of the slit width, the Talbot effect, the partially coherent effect and the Lau effect can be observed in sequence. The profile of partially coherent fringes varies with the relative shift of any grating. Finally, experimental verifications for theoretical predictions are given.