工程光学2课程工光课件12

1、1第十二章 光的衍射（Diffraction）光的衍射现象：光波在空间传播遇到障碍时，其传播方向会偏离直线传播，弯入到障碍物的几何阴影中，并呈现光强的不均匀分布的现象。2When light passes through a narrow slit, it spreads out more than what could be accounted for by geometric construction. This is an example of diffraction. Diffraction can be defined as any departure from the predic

2、tions of geometric optics.What is the Diffraction?3 The phenomenon that the light waves tend to bend around and e spread out when they pass near a barrier is called diffraction. Diffraction of light occurs when a light wave passes by a corner or through an opening or slit that is physically the appr

3、oximate size of, or even smaller than that lights wavelength.Diffraction4Related ConceptThe terms diffraction and scattering are often used interchangeably and are considered to be almost synonymous. Diffraction describes a specialized case of light scattering in which an object with regularly repea

4、ting features (such as a diffraction grating) produces an orderly diffraction of light in a diffraction pattern. 5In the real world most objects are very complex in shape and should be considered to be composed of many individual diffraction features that can collectively produce a random scattering

5、 of light.6衍射实验(Diffraction experiment)：SK光的衍射是光的波动性的主要标志之一。Light sourceBarrierScreen7衍射现象的分类(Classification of light diffraction)：根据光源、衍射物（衍射屏）和衍射场（观察屏）三者之间的位置确定（1）夫琅和费衍射(Fraunhofer diffraction)： 光源和衍射场都在衍射物无限远处的衍射。（2）菲涅耳衍射（ Fresnel diffraction ）： 光源和衍射场或二者之一到衍射物的距离比较小时的衍射。8第一节 光波的标量衍射理论一、惠更斯菲涅耳原理1

6、、惠更斯原理 (Huygens principle)：（1）波阵面的形成，（2）波面的传播方向。图123 光波通过圆孔的惠更斯作图法v9图1 点光源S对P点的作用2、惠更斯菲涅耳原理波阵面外任一点光振动应该是波面上所有子波相干叠加的结果。10波阵面外任一点光振动应该是波面上所有子波相干叠加的结果。子波向P点的球面波公式子波法线方向的振幅子波振幅随q角的变化11当q = 0 时，K(q)=Max, q p/2 时，K(q)=0.若S发出的光源振幅为A（单位距离处）,整个波面的贡献菲涅尔假设：（实验证明是不对的）求解此公式主要问题：C、K(q)没有确切的表达式。12二、菲涅耳基尔霍夫衍射公式（确定

7、了C、K(q)基尔霍夫 (Kirchhoff) 从波动方程出发，用场论得出了比较严格的衍射公式。其中，设定方向角 ( n, l ) 和 ( n, r )为S的法线与 l 和 r 的夹角。Q1314当光线接近于正入射时15将近似条件代入得到：菲涅耳基尔霍夫衍射近似公式16三、基尔霍夫衍射公式的近似图124 孔径 S的衍射1、傍轴近似（两点近似）(1)(2)在振幅项中17(3)设定孔径函数图124 孔径 S的衍射进一步的计算需要将exp( ikr )中的r表示成(x,y,z)的函数。182.菲涅耳近似（对位相项的近似）级数展开19称为菲涅耳近似。得到菲涅耳衍射：203.夫琅合费近似继续展开取上式前

8、三项21菲涅耳衍射和夫琅合费衍射的判别式；或者(菲涅耳衍射)(夫琅合费衍射)菲涅耳衍射和夫琅和费衍射是两个经常应用的衍射计算。22一、惠更斯菲涅耳原理1、惠更斯原理2、惠更斯菲涅耳原理本课内容回顾23二、菲涅耳基尔霍夫衍射公式精确计算：近似计算（设平面波入射，cos(n,l )=-1 ）24三、基尔霍夫衍射公式的近似1、菲涅耳近似（对位相项的近似）252、夫琅合费近似26Finished 121下一节27DefinitionFraunhofer diffraction refers to parallel, collimated light (far-field diffraction). I

9、n Fresnel diffraction, the light need not be parallel (near-field diffraction).Fresnel diffraction is more general; it includes Fraunhofer diffraction as a special case. But Fraunhofer diffraction is so much easier to discuss that it is customarily presented first.28Fraunhofer Joseph von Fraunhofer

10、(1787-1826), German. After working for a while as a lens grinder and apprentice optician, he became a partner in an optical company that made precision theodolites, professor at the University of Munich, and was knighted by King Maximilian of Bavaria. In his short life (died of tuberculosis at age 3

11、9), he produced large-aperture telescope lenses, exceptionally well corrected for spherical and chromatic aberration, ruled precision gratings and discovered their use for spectroscopy, and found that the spectrum of the sun is crossed by dark lines since named Fraunhofer lines.29Fresnel Augustin Je

12、an Fresnel (1788-1827), a nineteenth century French physicist. He studied mathematics, then civil engineering; he went into optics later. He is best known for the invention of unique compound lenses designed to produce parallel beams of light, which are still used widely in lighthouses. In the field

13、 of optics, Fresnel derived formulas to explain reflection, diffraction, interference, refraction, double refraction, and the polarization of light reflected from a transparent substance.30Huygens principleHuygens principle states that each point on a wavefront may be considered the origin of new, s

14、econdary wavelets, these form another wavefront, and so on. In this way the wave moves forward.31HuygensChristiaan Huygens (1629-1695) - Christiaan Huygens was a brilliant Dutch mathematician, physicist, and astronomer who lived during the seventeenth century, a period sometimes referred to as the Scientific Revolution. Huygens, a particularly gifted scientist, is best known for his work on the theories of centrifugal force, the wave theory of light, and the pendulum clock. His theories neatly e