快速傅里叶变换
光学
物理
衍射
变换矩阵
基质(化学分析)
采样(信号处理)
离散傅里叶变换(通用)
计算机科学
数学
角谱法
算法
傅里叶变换
数学分析
傅里叶分析
分数阶傅立叶变换
材料科学
探测器
运动学
经典力学
复合材料
作者
Zhao Wang,Chenlu Wei,Yuan Chen,Chenliang Chang,Jun Ma,Rihong Zhu
出处
期刊:Optics Letters
[The Optical Society]
日期:2020-10-23
卷期号:45 (21): 5937-5937
被引量:13
摘要
Fast Fourier transform (FFT) is the most commonly used mathematical method in numerical calculation, and the FFT-based angular spectrum method (ASM) is also used widely in diffraction calculation. However, the frequency and spatial sampling rules in FFT limit the effective propagation distance and the observation window range of ASM. A novel method for calculating the angular spectrum based on the matrix product is proposed in this Letter. This method realizes the fast calculation of discrete Fourier transform (DFT) based on the matrix product, in which the sampling matrix is orthogonally decomposed into two vectors. Instead of FFT, angular spectrum diffraction calculation is carried out based on the matrix product, which is named the matrix product ASM. The method in this Letter uses a simple mathematical transformation to achieve maximum compression of the sampling interval in the frequency domain, which significantly increases the effective propagation distance of the angular spectrum. Additionally, the size of the observation window can be enlarged to obtain a wider calculation range by changing the spatial sampling of the output plane.
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