利用Mathematica研究纱窗网孔的Fraunhofer衍射

Analysis of Fraunhofer Diffraction by Rectangular Aperture Mesh Screen Using Mathematica

根据基尔霍夫衍射理论,用Mathematica软件推导出由矩形孔构成的2行×2列、4行×2列、2行×4列、4行×4列等纱窗网孔的Fraunhofer衍射相对衍射强度公式,并在此基础上归纳推广,得到由2n行×2m列矩形孔构成的纱窗网孔的Fraunhofer衍射相对衍射强度通式.绘制不同数目矩形孔构成的纱窗网孔的几种典型衍射图样及对应的相对光强三维立体图,更加真实、精确、简便地再现了不同数目矩形孔构成的纱窗网孔的Fraunhofer(夫琅禾费)衍射现象,对深刻理解不同数目矩形孔构成的纱窗网孔的Fraunhofer衍射现象具有重要意义.

Based on Kirchhoff＇s diffraction formula and by using Mathematica, we derived the formula of relative diffraction intensity of Fraunhofer diffraction by different slides with different Rectangular aper- ture matrix such as 2 rows x2 columns,4 rows x2 columns,2 rows ~4 columns,4 rows x4 columns etc. extended the formula to a generally applicable one, which is Fraunhofer diffraction by a slides with 2rows x 2m columms Rectangular aperture matrix. In order to make a better description of Fraunhofer dif- fraction, we simulated several diffraction patterns by slides with rectangular aperture and the 3-Dimension- al pattern of the relative light intensity distribution, which is meaningful on the comprehending of Fraun- hofer Diffraction by Rectangular aperture matrix.