The field distributions of Lau fringes for two different gratings are theoretically and experimentally investigated. The majority of the methods that are used to deduce the intensity distribution function of the Lau effect are rather complicated, among these, the method based on the cross-spectral density function is relatively easy. The process of deducing the intensity distribution function of Lau fringes generated by double identical gratings is studied based on the method, and the method is tried to be applied in a more general situation, two different gratings. The feasibility of the method in the situation of two gratings with the same grating constant but different duty ratios is discussed, and the simplified intensity distribution functions of two cases, in which the arranged positions of the two gratings are swapped, are achieved. The theoretical predictions are well demonstrated by the experimental results. Thus, the partially coherent theory based on the cross- spectral density function also works in the situation with two gratings of the same grating constant and different duty ratios.