Diffraction integral computation using sinc approximation

TL;DR

This paper introduces a sinc series approximation method for computing diffraction integrals in optics, offering super-algebraic convergence and bandwidth preservation, outperforming traditional FFT-based methods like ASM especially over long distances.

Contribution

The paper presents a novel sinc-based numerical approach for diffraction integral computation that overcomes limitations of FFT-based methods, ensuring higher accuracy and bandwidth preservation.

Findings

Sinc method achieves high-order accuracy for diffraction calculations.

The approach is independent of wavelength and propagation distance.

Numerical results confirm superior performance over ASM.

Abstract

We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The diffraction integrals are given in terms of a convolution, and our proposed numerical approach is not only super-algebraically convergent, but it also satisfies an important property of the convolution -- namely, the preservation of bandwidth. Furthermore, the accuracy of the proposed method depends only on how well the source field is approximated; it is independent of wavelength, propagation distance, and observation plane discretization. In contrast, methods based on the fast Fourier transform (FFT), such as the angular spectrum method (ASM) and its variants, approximate the optical fields in the source and observation planes using Fourier series. We will show that the ASM introduces artificial periodic boundary conditions and violates the preservation of bandwidth property, resulting in limited accuracy which decreases for longer propagation distances. The sinc-based approach avoids both of these problems. Numerical results are presented for Gaussian beam propagation and circular aperture diffraction to demonstrate the high-order accuracy of the sinc method for both short-range and long-range propagation. For comparison, we also present numerical results obtained with the angular spectrum method.