圆孔夫琅禾费衍射图样的三维特性分析

THREE DIMENSIONAL ANALYSIS OF FRAUNHOFER DIFFRACTION IN A CIRCULAR APERTURE

基于菲涅耳-基尔霍夫衍射积分公式,在远场傍轴条件下,推导了圆孔夫琅禾费衍射场三维分布的积分表达式,并使用可视化科学计算软件Matlab进行了数值积分,得到了圆孔夫琅禾费衍射图样的三维光强分布数据。展示了焦平面、离焦平面和轴向切面上的二维光强分布图,分析了衍射图样的横向、轴向和离焦光强分布特性,拓展了对圆孔夫琅禾费衍射图样的理解。使用数值计算求解光电场三维分布的方法,无需复杂的特殊函数,利于在大学物理教学中推广。

Based on the Fresnel-Kirchhoff diffraction integral formula,this paper deduces the integral expression of Fraunhofer diffraction field created by circular aperture under the farfield and paraxial condition.The three-dimensional intensity distribution of the diffraction pattern is obtained by using MATLAB software for numerical calculation.The two-dimensional intensity distributions of the focus,defocus and axial plane are presented.The horizontal and axial distribution characteristics of intensity are analyzed.A more comprehensive description of Fraunhofer diffraction by circular aperture is obtained.It does not require sophisticated special functions to solve the three-dimensional distribution of electric fields by using numerical calculation,which is conductive to be popularized in college physics teaching.