基于任意正多边形孔径的菲涅尔衍射
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摘要
在基尔霍夫衍射公式的基础上,通过模拟仿真研究了任意正多边形小孔的菲涅尔衍射规律.首先利用Matlab中的for循环给出衍射平面的球面波复振幅分布,再利用函数graythresh和im2bw读取Photoshop绘制的小孔图像得到孔径函数;然后通过函数fft2对点扩散函数和衍射平面的复振幅分布与孔径函数的乘积进行傅里叶变换;最后利用函数ifft2对输出频谱做傅里叶逆变换,从而得到衍射条纹分布.研究结果表明:在正多边形各边的垂直方向上,衍射条纹清晰;在各角的方位上,衍射呈条带分布(正多边形边数为奇数时为亮条带,正多边形边数为偶数时为暗条带),正多边形的边数越多,衍射条纹越密集.
On the basis of Kirchhoff diffraction formula,the Fresnel diffraction law of any regular polygon small hole is studied by simulation.Firstly,the spherical wave complex amplitude distribution of the diffraction plane is given by using the For loop in Matlab,and then the aperture function is obtained by using the function Graythresh and IM2BW to read the small hole image drawn by Photoshop,and then the product of complex amplitude distribution and aperture function of the point diffusion function and the diffraction plane is Fourier transform through the function fft2,and finally the diffraction stripe distribution is obtained by using the function ifft2 to make Fourier inverse transformation to the output spectrum.The results show that the diffraction stripes are clear in the vertical direction of each edge of the regular polygon,and in the azimuth of each angle,the diffraction shows a strip distribution(bright strip when the polygon edge is odd,dark strip when the polygon edge is even).Moreover,the more the number of sides of the regular polygon,the denser the diffraction fringes.
On the basis of Kirchhoff diffraction formula,the Fresnel diffraction law of any regular polygon small hole is studied by simulation.Firstly,the spherical wave complex amplitude distribution of the diffraction plane is given by using the For loop in Matlab,and then the aperture function is obtained by using the function Graythresh and IM2BW to read the small hole image drawn by Photoshop,and then the product of complex amplitude distribution and aperture function of the point diffusion function and the diffraction plane is Fourier transform through the function fft2,and finally the diffraction stripe distribution is obtained by using the function ifft2 to make Fourier inverse transformation to the output spectrum.The results show that the diffraction stripes are clear in the vertical direction of each edge of the regular polygon,and in the azimuth of each angle,the diffraction shows a strip distribution(bright strip when the polygon edge is odd,dark strip when the polygon edge is even).Moreover,the more the number of sides of the regular polygon,the denser the diffraction fringes.
引文
[1]李仲怡.基于菲涅尔衍射的光谱望远镜研究[D].长春:长春理工大学,2016.
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[11]宋易知.任意正多边形小孔夫琅禾费衍射成像探讨[J].物理实验,2017,37(11):48-51.
[12]Jeffrey A D,Don M C.Simulation of Anderson localization in a random fiber using a fast Fresnel diffraction algorithm[J].Optical Engineering,2016,55(6):066122.
[13]Qian H,Lin W,Qi X.Numerical simulation of Fresnel and Fraunhofer diffractions of monochromatic and white light[J].Optical Engineering,2016,55(8):084104.
[14]苏显渝,李继陶,曹益平,等.信息光学[M].2版.北京:科学出版社,2011:23-46.
[2]郑耀辉,阮萍,曹尚.空间薄膜衍射望远镜展开结构设计与分析[J].红外与激光工程,2016,45(1):0118004.
[3]王若秋,张志宇,国成立,等.用于空间望远镜的大口径高衍射效率薄膜菲涅尔衍射元件[J].红外与激光工程,2017,46(9):1-8.
[4]罗晓贺,惠梅.基于菲涅尔衍射的圆孔直径测量[J].激光与红外,2018,48(3):380-383.
[5]孙向阳.圆孔衍射与像分辨本领的Matlab仿真分析[J].湖北工业大学学报,2004,19(5):47-49.
[6]王竞争,刘显龙,殷文金,等.基于Matlab的光的干涉和衍射现象的模拟研究[J].延边大学学报(自然科学版),2009,35(4):319-322.
[7]成海英,陈冬冬,张亚.基于Matlab的圆孔衍射实验模拟[J].盐城工学院学报(自然科学版),2011,24(2):11-13.
[8]王永祥.矩孔菲涅尔衍射的光强分布[J].量子电子学学报,2010,27(3):265-269.
[9]郝忠秀,赵亚军,李立功,等.基于Matlab的矩孔夫琅和费衍射场模拟计算[J].河北大学学报(自然科学版),2009,29(3):266-269.
[10]刘有菊,杨庆辞.“E”字孔的夫琅禾费衍射场[J].保山学院学报,2017,36(2):19-21.
[11]宋易知.任意正多边形小孔夫琅禾费衍射成像探讨[J].物理实验,2017,37(11):48-51.
[12]Jeffrey A D,Don M C.Simulation of Anderson localization in a random fiber using a fast Fresnel diffraction algorithm[J].Optical Engineering,2016,55(6):066122.
[13]Qian H,Lin W,Qi X.Numerical simulation of Fresnel and Fraunhofer diffractions of monochromatic and white light[J].Optical Engineering,2016,55(8):084104.
[14]苏显渝,李继陶,曹益平,等.信息光学[M].2版.北京:科学出版社,2011:23-46.