  Numerical simulation of Fresnel diffraction with fast Fourier transform (FFT)
is widely used in optics, especially computer holography. Fresnel diffraction
with FFT cannot set different sampling rates between source and destination
planes, while shifted-Fresnel diffraction can set different rates. However, an
aliasing error may be incurred in shifted-Fresnel diffraction in a short
propagation distance, and the aliasing conditions have not been investigated.
In this paper, we investigate the aliasing conditions of shifted-Fresnel
diffraction and improve its properties based on the conditions.
