大学物理 ›› 2019, Vol. 38 ›› Issue (2): 9-16.doi: 10.16854 /j.cnki.1000-0712.180362

• 教学讨论 • 上一篇    下一篇

菲涅尔衍射积分的单次傅里叶变换算法

崔文乐,韩利琪,霍晓敏,杨丽君,张素恒   

  1. 河北大学物理科学与技术学院,河北保定071002
  • 收稿日期:2018-06-14 修回日期:2018-08-29 出版日期:2019-02-20 发布日期:2019-03-28
  • 通讯作者: 张素恒,E-mail: hbushz@ 163.com
  • 作者简介:崔文乐( 1994—) ,女,河北沧州人,硕士研究生,主要从事衍射计算与计算全息方面的研究.
  • 基金资助:
    河北省教育厅自然科学基金项目( QN2014086) ; 河北省自然科学基金项目( A2015201046) ; 河北大学实验室开放项目( SY201638)

    资助

Single Fourier transform method for the Fresnel diffraction integration

CUI Wen-le,HAN Li-qi,HUO Xiao-min,YANG Li-jun,ZHANG Su-heng   

  1. College of Physics Science and Technology,Hebei University,Baoding,Hebei 071002,China
  • Received:2018-06-14 Revised:2018-08-29 Online:2019-02-20 Published:2019-03-28

摘要: 单次傅里叶变换算法是一种常用的计算菲涅尔衍射积分的数值算法. 在单次傅里叶变换算法中,二次相位因子的

采样和计算窗口尺寸会严重影响计算精度. 本文利用局域空间频率的概念,结合采样定理,给出了二次相位因子的理想采样

间隔和计算窗口尺寸的选取方法. 然后将数值仿真结果分别与理论解析解和实验结果进行对比,验证了理想采样间隔和计算

窗口尺寸选择方法的有效性.

关键词: 菲涅尔衍射积分, 单次傅里叶变换算法, 局域空间频率, 理想采样间隔

Abstract: The single Fourier transform method is a common approach for numerical calculating the Fresnel

diffraction integration. In the single Fourier transform method,the sampling of quadratic phase factor and the size of

the calculation window can seriously affect the calculation accuracy. Based on the concept of local spatial frequency

and the sampling theorem,this paper gives the ideal sampling interval of quadratic phase factor and the selection

method of the size of the calculation window. Then the numerical simulation results are compared with the

theoretical analytical solutions and experimental results,respectively,to verify the effectiveness of the ideal

sampling interval and the selection method of the size of the calculation window.

Key words: Fresnel diffraction integration, single Fourier transform method, local spatial frequency, ideal sampling interval