摘要
通过应用复指数函数与Bessel函数的展开关系和将径向对称的光瞳函数展开成方位角的Fourier级数的方法,可以将衍射受限光学成像系统的点扩散函数的二维Fourier变换的计算转换为一维Fourier变换和一维Hankel变换的计算。并借助MATLAB软件在计算机上实现了编程计算。与二维Fourier变换计算方法相比,一维计算可以方便而清晰地获得像平面上任一确定方向的点扩散强度分布。与Fortran、Basic和C等编程计算语言相比,应用MATLAB语言编程计算,程序语言简洁,且大大降低了使用者对数学基础和计算机语言知识的要求,是进行科学与工程研究的高效工具。
The computation of two-dimensional Fourier transform for point spread function of diffraction limited pupil can be transformed to the computation of one-dimensional Fourier and Hankel transform by use of the relationship between exponential function and Bessel function and property of an expansion of a optical symmetrical pupil function into azimuthal Fourier series. The detailed numerical procedure based on one-dimensional digital algorithm is completed on MATLAB. In comparison with the classic two-dimensional Fourier transform algorithm, the one-dimensional method of Fourier and Hankel transform can obtain intensity samples along arbitrary radial direction at the image plane. And compared with Fortran, Basic and C language etc., the MATLAB program has advantages of succinct language, great reductions of demand of mathematic basis and computer language, and it is a efficient tool for scientific and engineering research.
出处
《红外与激光工程》
EI
CSCD
北大核心
2004年第4期405-408,共4页
Infrared and Laser Engineering
基金
武器装备预研基金资助项目(51401020104HK0106)
关键词
点扩散函数
一维计算
HANKEL变换
MATLAB软件
Algorithms
Bessel functions
Computational methods
Computer programming languages
Computer software
Fourier transforms
