基于快速傅里叶变换的瑞利-索末菲衍射公式数值积分方法。

Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula.

作者信息

Shen Fabin, Wang Anbo

机构信息

Center for Photonics Technology, Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA.

出版信息

Appl Opt. 2006 Feb 20;45(6):1102-10. doi: 10.1364/ao.45.001102.

DOI:10.1364/ao.45.001102

PMID:16523770

Abstract

The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical accuracy and on computational complexity are discussed for the FFT-DI and the FFT-based angular spectrum (FFT-AS) methods. The performance of the FFT-DI method is verified by numerical simulation and compared with that of the FFT-AS method.

摘要

研究了瑞利 - 索末菲衍射积分的数值计算。提出了一种基于快速傅里叶变换（FFT）的直接积分（FFT - DI）方法的实现方式，并使用辛普森法则来提高计算精度。针对FFT - DI方法和基于FFT的角谱（FFT - AS）方法，讨论了采样间隔、计算窗口大小及其对数值精度和计算复杂度的影响。通过数值模拟验证了FFT - DI方法的性能，并与FFT - AS方法的性能进行了比较。