Considering the necessity of alignment in practical applications of photolithography, distribution of complex amplitude of moire fringe patterns that are produced in superposition of two gratings is analyzed in the viewpoint of Fourier Optics and the relationship between fringes and properties of these two gratings is concluded by means of an analysis model. The rule of one-dimensional gratings (1D-gratings) is extended to other form of the gratings which have quasi-periodic repetitive structures. Especially, moire fringes generated by the two superposed 1D-gratings (used in alignment of lithography) can be expressed by an arithmetical operation of two vectors which include enough information about these 1D-gratings. Numerical analyses regarding the moire model and its application in the alignment process of lithography are carried out. Our computational analyses results show that the moire fringes of the two extended gratings can be refined as a transformed fringe pattern of two standard 1D-gratings. Finally, the results also make it out that the fringes which have magnified periods versus that of two 1D-gratings are highly sensitive to relative shift of two gratings thus might be applicable in alignment of lithography or correlated fields. (C) 2008 Optical Society of America.