摘要光的衍射现象是光的波动性的重要表现。早期建立的几何光学认为，光是沿直线传播的，因而几何光学不能够解释光的衍射现象。在光学的长期发展过程中，人们逐渐意识到，只有波动光学才能解释光的衍射现象。第一个成功地运用波动光学解释光的衍射现象的人是法国物理学家菲涅尔。菲涅尔发展了惠更斯在十七世纪提出的惠更斯原理，认为波面外一点的光振动是波面上所有子波在该点相干叠加的结果。现在称之为惠更斯-菲涅尔原理。随后，德国物理学家基尔霍夫又进一步完善了菲涅尔的理论，提出了基尔霍夫衍射公式。本文应用基尔霍夫衍射公式，在近似条件下计算了两种孔径的夫琅和费衍射，并利用MATLAB的绘图功能对计算结果做了进一步的讨论。58216
Diffraction of light is a phenomenon which shows that light has wave properties. Early established geometrical optics thinks that light travels along a straight line, and thus it can not explain the diffraction of light. With the development of optics over a long period, people gradually realized that only wave optics could explain the phenomenon of light diffraction. The first man who used wave optics to successfully explain the phenomenon of light diffraction is the French physicist Fresnel. Fresnel developed the Huygens principle which was proposed by Huygens in the seventeenth century. He thought that the outer surface of the light wave vibrations are the result of the wave surface at that point all the sub-wave coherent superposition, which is now called Huygens - Fresnel principle. Subsequently, the German physicist Kirchhoff further improved the Fresnel's theory, and proposed the Kirchhoff diffraction formula. In this paper, the Kirchhoff diffraction formula under similar conditions has been used to calculate the Fraunhofer diffraction through two different apertures, and we make further discussion by use of MATLAB graphics functions according to the result of calculations.
毕业论文关键词：惠更斯-菲涅尔原理；衍射；矩孔；圆孔
Keyword：Huggens-Fresnel principle; Diffraction; Rectangular aperture; Circular aperture
目 录
1 光的衍射现象 4
2 惠更斯-菲涅耳原理 5
3 菲涅耳-基尔霍夫衍射公式 6
4 基尔霍夫衍射公式的近似 7
5 夫琅和费衍射公式 10
5.1 矩孔衍射 11
5.2 单缝衍射 11
5.3 圆孔衍射 12
5.4 多缝衍射 12
6 模拟图像 13
7 分析与结论 18
参考文献 21
致谢 21
1 光的衍射现象
光的衍射现象是光具有波动性的有利证据。早期建立的几何光学把光的直线传播作为其基本定律，因而不能对光的衍射现象做出合理的解释。要对这种现象做出解释，只有依靠于波动光学。菲涅耳是历史上第一个成功运用波动光学解释光的衍射现象的人。他的伟大之处在于，用干涉理论补充了惠更斯在十七世纪提出的惠更斯原理。结合了干涉理论的惠更斯原理，现在人们习惯上称之为惠更斯-菲涅耳原理。正是运用这一原理，菲涅耳突破了前人的局限，比较成功地解释了光的衍射现象。随后，麦克斯韦在总结前人经验的基础上，创造性地建立了较为完善的电磁理论。于是人们开始意识到，光是一种电磁波。既然已经知道光是电磁波，那么，就可以运用处理电磁场边值问题的方法，来讨论光通过各种孔径的衍射问题。但是，这仅仅是从理论上而言，具体操作起来往往会带来大量复杂的运算。为了简化问题，在实际中经常采用的衍射理论都是一些近似解法。 夫琅和费衍射的计算及MATLAB模拟:http://www.youerw.com/wuli/lunwen_50608.html