  This work theoretically investigates wide-spectrum and high-resolution
diffraction optical elements (DOE) 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
diffraction fields can be improved and that the stability of optical elements
within broad spectrums is significantly enhanced. Practical concern on largely
increasing the number of grating layers are efficiency of the optical designs
in theory and the manufacture of stacks of ultra-thin grating films.
