An approximate algorithm for simulating Fresnel diffraction patterns without Fourier transform

Zhiyuan Zhang; Chongguang Li; Yuli Lou; Siqi Liu; Xiyuan Liang; Qinghe Song; Jinbin Gui

doi:10.1117/12.3052720

12 December 2024 An approximate algorithm for simulating Fresnel diffraction patterns without Fourier transform

Zhiyuan Zhang, Chongguang Li, Yuli Lou, Siqi Liu, Xiyuan Liang, Qinghe Song, Jinbin Gui

Proceedings Volume 13446, Sixth International Conference on Optoelectronic Science and Materials (ICOSM 2024); 134461C (2024) https://doi.org/10.1117/12.3052720
Event: 6th International Conference on Optoelectronic Science and Materials (ICOSM 2024), 2024, Hefei, China

Abstract

In the study of optical systems, accurately calculating Fresnel diffraction patterns is crucial for understanding and designing various applications, from imaging systems to laser technologies. However, existing commonly used calculation methods each have their limitations. This paper proposes an approximate algorithm for calculating Fresnel diffraction to address these shortcomings. The algorithm is based on the oscillatory characteristics of the quadratic phase exponential function in the Fresnel diffraction integral. By convolving this quadratic phase exponential function with another slowly varying function, it is found that the rapidly oscillating parts cancel each other out, having little impact on the final calculation result. Therefore, only the areas that primarily contribute to the diffraction need to be computed. The study shows that this algorithm significantly reduces the computational load while maintaining a certain level of accuracy. Compared to the direct integration method, it shows a notable improvement in calculation speed. It also maintains high accuracy compared to both the direct integration method and the Fast Fourier Transform (FFT) algorithm. Additionally, since it does not involve the frequency domain transformation used in FFT, it avoids under-sampling issues. This algorithm offers a feasible method for calculating diffraction patterns while ensuring a balance between accuracy and computational efficiency.

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Zhiyuan Zhang, Chongguang Li, Yuli Lou, Siqi Liu, Xiyuan Liang, Qinghe Song, and Jinbin Gui "An approximate algorithm for simulating Fresnel diffraction patterns without Fourier transform", Proc. SPIE 13446, Sixth International Conference on Optoelectronic Science and Materials (ICOSM 2024), 134461C (12 December 2024); https://doi.org/10.1117/12.3052720

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KEYWORDS

Diffraction

Convolution

Near field diffraction

Fourier transforms

Computation time

Computer simulations

Aliasing

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