Nonuniform sampled scalar diffraction calculation using nonuniform fast Fourier transform

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 nonuniform 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 Letter, we developed nonuniform sampled ASM and Fresnel diffraction to improve the problem using the nonuniform FFT. c 2013 Optical Society of America