Comparison of fast Fourier transform based algorithms for free space propagation

In this paper we compare different free space propagation algorithms based on fast Fourier transform (FFT). They are used to calculate 1D and 2D difiaction patterns in near field and far field as well. Four algorithms are considered: angular spectrum propagation, direct integral formulation, fractional Fourier transform using single FFT (S_FFT) and fractional Fourier transform using two FFT (D_FFT). We compare these algorithms and discuss their advantages and drawbacks for one and two-dimensional objects.