  Scalar diffraction calculations such as the angular spectrum method (ASM) and
Fresnel diffraction, are widely used in the research fields of optics, X-rays,
electron beams, and ultrasonics. It is possible to accelerate the calculation
using fast Fourier transform (FFT); unfortunately, acceleration of the
calculation of non-uniform sampled planes is limited due to the property of the
FFT that imposes uniform sampling. In addition, it gives rise to wasteful
sampling data if we calculate a plane having locally low and high spatial
frequencies. In this paper, we developed non-uniform sampled ASM and Fresnel
diffraction to improve the problem using the non-uniform FFT.
