工程光學(xué)2課程工光課件12

1、1第十二章 光的衍射（Diffraction）光的衍射現(xiàn)象：光波在空間傳播遇到障礙時(shí)，其傳播方向會(huì)偏離直線傳播，彎入到障礙物的幾何陰影中，并呈現(xiàn)光強(qiáng)的不均勻分布的現(xiàn)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衍射實(shí)驗(yàn)(Diffraction experiment)：SK光的衍射是光的波動(dòng)性的主要標(biāo)志之一。Light sourceBarrierScreen7衍射現(xiàn)象的分類(Classification of light diffraction)：根據(jù)光源、衍射物（衍射屏）和衍射場(chǎng)（觀察屏）三者之間的位置確定（1）夫瑯和費(fèi)衍射(Fraunhofer diffraction)： 光源和衍射場(chǎng)都在衍射物無限遠(yuǎn)處的衍射。（2）菲涅耳衍射（ Fresnel diffraction ）： 光源和衍射場(chǎng)或二者之一到衍射物的距離比較小時(shí)的衍射。8第一節(jié) 光波的標(biāo)量衍射理論一、惠更斯菲涅耳原理1

6、、惠更斯原理 (Huygens principle)：（1）波陣面的形成，（2）波面的傳播方向。圖123 光波通過圓孔的惠更斯作圖法v9圖1 點(diǎn)光源S對(duì)P點(diǎn)的作用2、惠更斯菲涅耳原理波陣面外任一點(diǎn)光振動(dòng)應(yīng)該是波面上所有子波相干疊加的結(jié)果。10波陣面外任一點(diǎn)光振動(dòng)應(yīng)該是波面上所有子波相干疊加的結(jié)果。子波向P點(diǎn)的球面波公式子波法線方向的振幅子波振幅隨q角的變化11當(dāng)q = 0 時(shí)，K(q)=Max, q p/2 時(shí)，K(q)=0.若S發(fā)出的光源振幅為A（單位距離處）,整個(gè)波面的貢獻(xiàn)菲涅爾假設(shè)：（實(shí)驗(yàn)證明是不對(duì)的）求解此公式主要問題：C、K(q)沒有確切的表達(dá)式。12二、菲涅耳基爾霍夫衍射公式（確定

7、了C、K(q)基爾霍夫 (Kirchhoff) 從波動(dòng)方程出發(fā)，用場(chǎng)論得出了比較嚴(yán)格的衍射公式。其中，設(shè)定方向角 ( n, l ) 和 ( n, r )為S的法線與 l 和 r 的夾角。Q1314當(dāng)光線接近于正入射時(shí)15將近似條件代入得到：菲涅耳基爾霍夫衍射近似公式16三、基爾霍夫衍射公式的近似圖124 孔徑 S的衍射1、傍軸近似（兩點(diǎn)近似）(1)(2)在振幅項(xiàng)中17(3)設(shè)定孔徑函數(shù)圖124 孔徑 S的衍射進(jìn)一步的計(jì)算需要將exp( ikr )中的r表示成(x,y,z)的函數(shù)。182.菲涅耳近似（對(duì)位相項(xiàng)的近似）級(jí)數(shù)展開19稱為菲涅耳近似。得到菲涅耳衍射：203.夫瑯合費(fèi)近似繼續(xù)展開取上式前

8、三項(xiàng)21菲涅耳衍射和夫瑯合費(fèi)衍射的判別式；或者(菲涅耳衍射)(夫瑯合費(fèi)衍射)菲涅耳衍射和夫瑯和費(fèi)衍射是兩個(gè)經(jīng)常應(yīng)用的衍射計(jì)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課內(nèi)容回顧23二、菲涅耳基爾霍夫衍射公式精確計(jì)算：近似計(jì)算（設(shè)平面波入射，cos(n,l )=-1 ）24三、基爾霍夫衍射公式的近似1、菲涅耳近似（對(duì)位相項(xiàng)的近似）252、夫瑯合費(fèi)近似26Finished 121下一節(jié)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