This work theoretically investigates wide-spectrum and high-resolution diffraction optical elements that are made of stacks of low-resolution binary phase gratings, whereby the two-dimensional grids in different grating layers are arranged with specified displacements. We remodel the common kinoform algorithm for this multi-scale architecture. Numerical computations show that, by increasing the number of stacking layers, the resolution of the far-field image can be improved and also that the optical elements are more insensitive to variations of incident wavelengths at the cost of part accuracy of the image reconstructions. Practical concern focuses on largely increasing the number of grating layers and efficiency of the optical designs in theory and on the manufacture of stacks of ultra-thin grating films.