The Fourier principles of moiré fringes produced by the square aperture planar microlens array and micrographics array are studied. The square aperture planar microlens array is regarded as orthometric 2D grid lines. The analytic formula of Fourier transform for 2D moiré fringes of the square aperture planar microlens array is derived based on the principle of Fourier transform of 1D grating moiré fringe. Moreover, the low frequency (1, -1) moiré fringe is analyzed in detail. The period and synchronization of moiré fringe with different angles are studied as key point. The experiments are carried out by using the 2D grid templates and micrographics arrays with different structural parameters. The results show that the experimental values agree well with the theoretical values, which provides theoretical basis for the application and research of the square aperture planar microlens array.