Non-uniform sampled scalar diffraction calculation using non-uniform fast Fourier transform

TL;DR

This paper introduces a novel approach to scalar diffraction calculations that leverages non-uniform FFT to efficiently handle non-uniform sampling, overcoming limitations of traditional FFT-based methods.

Contribution

It develops non-uniform sampled ASM and Fresnel diffraction methods, enabling more efficient and accurate calculations for non-uniformly sampled planes in optics and related fields.

Findings

Improved calculation efficiency for non-uniform sampling.

Reduced computational waste by avoiding uniform sampling constraints.

Enhanced accuracy in scalar diffraction simulations.

Abstract

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.