Arbitrary shape surface Fresnel diffraction

TL;DR

This paper introduces an efficient method for Fresnel diffraction calculation on arbitrary-shaped surfaces, significantly reducing computational complexity from traditional methods by leveraging non-uniform fast Fourier transform techniques.

Contribution

The paper presents a novel approach to Fresnel diffraction calculation on arbitrary surfaces with reduced computational cost using non-uniform FFT.

Findings

Calculation cost is reduced to O(N log N) in 1D.

Calculation cost is reduced to O(N^2 log N) in 2D.

Method enables efficient diffraction simulation for complex surfaces.

Abstract

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.