A Caltech Library Service

Diffraction integral computation using sinc approximation

Cubillos, Max and Jimenez, Edwin (2022) Diffraction integral computation using sinc approximation. Applied Numerical Mathematics, 178 . pp. 69-83. ISSN 0168-9274. doi:10.1016/j.apnum.2022.02.011.

[img] PDF - Accepted Version
See Usage Policy.

[img] PDF - Submitted Version
See Usage Policy.


Use this Persistent URL to link to this item:


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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Cubillos, Max0000-0002-7583-8305
Jimenez, Edwin0000-0001-8184-5790
Additional Information:© 2022 Published by Elsevier B.V. on behalf of IMACS. Received 9 November 2021, Revised 15 February 2022, Accepted 16 February 2022, Available online 23 February 2022. This work was supported by the Air Force Office of Scientific Research [grant number 20RDCOR016]. We thank the reviewers for their helpful comments which improved the presentation of the manuscript. Approved for public release; distribution is unlimited. AFRL Public Affairs release approval number AFRL-2021-3954. The views expressed are those of the authors and do not reflect the official guidance or position of the United States Government, the Department of Defense, or of the United States Air Force.
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)20RDCOR016
Subject Keywords:Fresnel diffraction; Rayleigh-Sommerfeld diffraction; angular spectrum method; sinc method
Record Number:CaltechAUTHORS:20220223-919276000
Persistent URL:
Official Citation:Max Cubillos, Edwin Jimenez, Diffraction integral computation using sinc approximation, Applied Numerical Mathematics, Volume 178, 2022, Pages 69-83, ISSN 0168-9274,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:113543
Deposited By: George Porter
Deposited On:24 Feb 2022 17:28
Last Modified:06 Apr 2022 18:04

Repository Staff Only: item control page