  Fresnel diffraction calculation on an arbitrary shape surface is proposed.
This method is capable of calculating Fresnel diffraction from a source surface
with an arbitrary shape to a planar destination surface. Although such
calculation can be readily calculated by the direct integral of a diffraction
calculation, the calculation cost is proportional to $O(N^2)$ in one
dimensional or $O(N^4)$ in two dimensional cases, where $N$ is the number of
sampling points. However, the calculation cost of the proposed method is $O(N
\log N)$ in one dimensional or $O(N^2 \log N)$ in two dimensional cases using
non-uniform fast Fourier transform.
