第十二章--光的干涉和干涉系统-《工程光学(第3版)》课件.ppt

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1、第十二章第十二章 光的干涉和干涉系统光的干涉和干涉系统 121 光波的干涉条件光波的干涉条件一、干涉现象一、干涉现象1、什么是干涉现象（Interference）2、相干光波（Coherent wave）和相干光源 （Coherent light source）能够产生干涉的光波，叫相干光波；其光源称为相干光源。1干涉现象（Interference）4在两个光波叠加的区域形成稳定的光强分布的现象，称为光的干涉现象干涉现象The term Interference refers to the phenomenon that waves,under certain conditions,inten

2、sify or weaken each other.2干涉现象实例（Interference Examples）3二、干涉条件二、干涉条件一般情况下，4干涉条件（必要条件）：干涉条件（必要条件）：补充条件：补充条件：叠加光波的光程差不超过波列的长度如：氦氖激光的波列长度可达107 km。白光为几个波长。6当两光波振动方向有一定夹角时，即只有两个振动的平行分量能够产生干涉，而其垂直分量将在观察面上形成背景光，对干涉条纹的清晰程度产生影响。一般夹角值小时，这种影响可以忽略。712122 2 杨氏干涉实验杨氏干涉实验（Youngs double-slit experiment）一、干涉图样的计算一、

3、干涉图样的计算1、P点的干涉条纹强度光强 I 的强弱取决于光程差83、干涉条纹（Interference fringes）及其意义x对于接收屏上相同的x值，光强I相等。条纹垂直于x轴。10用光程差表示：结论：1、干涉条纹代表着光程差的等值线。2、相邻两个干涉条纹之间其光程差变化量为一个波长l，位相差变化2p。在同一条纹上的任意一点到两个光源的光程差是恒定的。114、干涉条纹的间隔定义：两条相干光线的夹角为相干光束的会聚角，用w表示。m+113干涉条纹间隔与波长的关系x0白条纹白条纹白光条纹15二、两个点源在空间形成的干涉场二、两个点源在空间形成的干涉场16Key words1.Path dif

4、ference2.Phase difference3.The order of interference4.The light distribution5.A maximum amount of light(maxima)6.A minimum amount of light(minima)18本课内容回顾本课内容回顾6、干涉条纹间隔与波长：多色光的干涉7、两个点源在空间形成的干涉场：等光程差面2、P点的干涉条纹强度：3、光程差的计算：4、干涉条纹的意义：光程差的等值线。5、干涉条纹的间隔：1、干涉现象和干涉条件19Homework(12-1&2)1.Light passes through

5、two narrow slits of d=0.8mm.On screen 1.6m away the distance between the two second-order maxima is 5mm.What is the wavelength of the light?2021Thomas Young(1773-1829)4A British physician and physicist.He could read at age 2,at 6 began studying Latin,and at 13 had also mastered Greek,Hebrew,Italian

6、and French.At 19 he entered medical school,correctly explained the accommodation of the eye and was elected Fellow of the Royal Society.In 1796,he graduated from the University of Gottingen Medical School,opened a practice in London,and 5 years later became professor of Natural Philosophy at the Roy

7、al Institution.That same year,1801,he read the first of several papers presenting the wave theory of light and the principle of interference,much to the opposition of Newtons followers.Young made noteworthy contributions also to acoustics,atmospheric refraction,elasticity,fluid dynamics and color vi

8、sion.22Interference fringesaxialZeroth-order maximumFirst-order minimumFirst-order maximum24123 干涉条纹的可见度干涉条纹的可见度 the visibility(contrast)of interference fringesK表征了干涉场中某处干涉条纹亮暗反差的程度。可见度可见度(Visibility,Contrast)定义：定义：25式（11-14）26二、二、光源宽度光源宽度 的影响和的影响和空间相干性空间相干性相干性（Coherence）相干性与干涉（Coherence&interferenc

9、e）xIxI281、光源宽度 对条纹可见度的影响(扩展光源)Pr1r2OS1S2SS0 x1r2rSdxcdblDl1l2x2931讨论：1）光源的临界宽度：条纹可见度为0时的光源宽度2）光源的允许宽度：能够清晰地观察到干涉条纹时，允许的光源宽度(K=0.9)322、空间相干性（Spatial Coherence)1S20 xebcLDxS120若通过光波场横向两点横向两点的光在空间相遇时能够发生干涉，则称通过空间两点的光具有相干性。334当光源是点光源时，所考察的任意两点S1和S2的光场都是空间相干的，当光源是扩展光识时，光场平面上具有空间相干性的各点的范围与光源的大小成反比。对于一定的光波

10、长和干涉装置，当光源宽度b较大，且满足时，通过S1和S2两点的光将不发生干涉，因而这两点的光场没有空间相干性。我们从另一个角度考察光的空间相干性范围。对一定的光源宽度b，通常称光通过S1和S2恰好不发生干涉时所对应的这两点的距离为横向相干宽度，以么表示，34调节d的大小，观察什么时间条纹消失，此时测量d，就可以计算出星体角直径。35三、三、光源非单色性光源非单色性 的影响和的影响和时间相干性时间相干性1、光源非单色性 对条纹可见度的影响3637讨论：相干长度(coherence length)：对于光谱宽度为（或k）的光源能够产生干涉的最大光程差。382、时间相干性(Temporal Cohe

11、rence)时间相干性：若同一光源在相干时间内发出的光经过不同的路径在空间相遇时，能够产生干涉，则称光具有时间相干性。相干时间 t：光通过相干长度所需的时间。公式：39Partial Coherence&contrastIt is incorrect to think of light as either coherent or incoherent.Light can have different degrees of coherence,which introduced the concept of partial coherence.Complete coherence is merel

12、y a theoretical limit.40Partial Coherence&contrastAssume that two wavetrains of light,each of finite length s,overlap to their full extent.Such complete overlap will result in distinct maxima and minima of the highest degree of contrast.But even if the wavetrains overlap only in part,interference is

13、 possible.Although the degree of contrast of the fringes is less,depending on the degree of overlap.41本课内容回顾本课内容回顾2、振幅比与可见度的关系：3、光源宽度与可见度的关系4、光源单色性与可见度的关系5、名词解释：空间相干性、时间相干性、相干长度、相干时间、干涉孔径角1、可见度的定义42Homework1.比较说明空间相干性和时间相干性的联系和区别。43VisibilityIt can be defined as K=(Imax-Imin)/(Imax+Imin)where Imax a

14、nd Imin are the intensities at the maxima and minima of the fringe pattern.44ContrastIt can be defined as the ratio of the difference between maximum areance Emax,and mimimum areance,Emin,to the sum of such areances:K=(Emax-Emin)/(Emax+Emin)The amount of power incident per unit area is called areanc

15、e(illuminance).45CoherenceThe property of light necessary to produce interference is called coherence.46Coherence&InterferenceCoherence is a property of light.Interference is the process of interaction.Coherence means that two or more waves in a radiation field are in a fixed and predictable phase r

16、elationship to each other.We distinguish two classes of coherence,spatial coherence and temporal coherence.47Spatial CoherenceSpatial coherence or,more precisely transverse spatial coherence refers to the phase relationship between waves traveling side by side,at a certain distance from one another.

17、The farther apart the two waves,and the less coherent the light will be.48Coherence LengthThe length of a wavetrain,s,is called coherence length.49Temporal CoherenceTemporal coherence or,longitudinal spatial coherence(often called monochromaticity)applies to waves traveling the same path.It refers t

18、o the constancy,and predictability,of phase as a function of time.50分光性质：振幅分割两个干涉的点源：两个反射面对S点的象S1和S2 12124 4 平板的双光束干涉平板的双光束干涉511.条纹定域：能够得到清晰干涉条纹的区域。一、干涉条纹的定域2.平板干涉的优点，取 ，用面光源。非定域条纹：非定域条纹：在空间任何区域都能得到的干涉条纹。定域条纹：定域条纹：只在空间某些确定的区域产生的干涉条纹。52二、平行平板(Plane-Parallel Plates)干涉（等倾干涉 Interference of equal inclin

19、ation）1.光程差计算nn53nn phase changeNo phase change54Since the interval between the two surfaces may be an actual plate or film,or it may be a gap between plates.We have four possibilities,as the following.No No No No 552.平板干涉装置 注意：采用扩展光源，条纹域在无穷远。条纹成象在透镜的焦平面上。563、条纹分析(Fringes of equal inclination)l（光程差与

20、条纹级数）中心lomnh=+22（最大干涉级在中心。时最大，）光程差在q021 5758中央条纹宽，边缘条纹窄。（5）反射光条纹和透射光条纹互补59二、楔形平板干涉（等厚干涉 Interference of equal thickness）SPb)SPa)图图11-16用扩展光源时楔行平板产生的定域条纹用扩展光源时楔行平板产生的定域条纹a)定域面在板上方定域面在板上方b)定域面在板内定域面在板内c)定域面在板下方定域面在板下方SPc)60图图11-18 楔形平板的干涉楔形平板的干涉2ACSPB=01 n nnnnn2、光程差计算61垂直入射时，光程差是厚度 h 的函数，在同一厚度的位置形成同一

21、级条纹。62等厚干涉等厚干涉1、劈尖干涉、劈尖干涉 （空气隙劈尖）（空气隙劈尖）明暗条件：明暗条件：若若 i=0,并注意到并注意到 n=1di棱边棱边d等厚条纹等厚条纹63（1）劈尖愈厚处劈尖愈厚处 条纹级别条纹级别（2）棱边处棱边处 d=0 ,对应着对应着（3）相邻两明（暗）纹间相邻两明（暗）纹间对应的厚度差为对应的厚度差为 d 愈高。愈高。暗纹暗纹讨论：讨论：ddkdk+1 1 2 3 4 564由上式看出由上式看出 越小越小,越大越大,使条纹愈清晰。使条纹愈清晰。dLdkdk+1（4）明（暗）纹间距明（暗）纹间距 L:L sin =d=展示：展示：波长变化对劈尖干涉条纹的影响波长变化对劈

22、尖干涉条纹的影响65（1）对于折射率均匀的楔形平板，条纹平行于楔棱66h(2)67（3）（4）a68例、例、如何判断两个直径相差很小的滚珠的大小如何判断两个直径相差很小的滚珠的大小？（测量工具：两块平板玻璃）（测量工具：两块平板玻璃）说明说明 ：1珠小珠小说明说明 ：1珠大珠大若发现等厚条纹间隔变密若发现等厚条纹间隔变密在靠近在靠近“1”那那 端轻轻压一下端轻轻压一下 若发现等厚条纹间隔变宽若发现等厚条纹间隔变宽69复色光入射得彩色条纹复色光入射得彩色条纹70若在一平晶上放置一R很大的平凸透镜，则两面之间形成的空气契能实现等厚干涉。称为牛顿环牛顿环。71白光入射的牛顿环照片白光入射的牛顿环照片

23、72Home Work(3-4)1.An oil film(n=1.47,thickness 0.12m)rests on a pool of water.If light strikes the film at an angle of 60o,what is the wavelength reflected in the first order?2.When examining the surface of a polished workpiece in thallium light(535nm),some scratch marks are seen where the fringes a

24、re distorted by 4/10 the distance between fringes.How deep are the scratches?73 一、典型干涉系统一、典型干涉系统1、斐索(Fizeau)干涉仪：等厚干涉型的干涉仪L3GL2PQL1激光平面干涉仪激光平面干涉仪a74fizeau75球面干涉仪PLQDh R1R2PQ76小结：基本特点：（1）属于等厚干涉（2）干涉光束，一个来自标准反射面，一个来自被测面。重点掌握：（1）光程差与厚度的关系。（2）厚度变化与条纹弯曲方向的关系。（3）干涉面间距变化与条纹移动的关系。条纹分析：772、迈克尔逊干涉仪（The Michels

25、on interferometer）特点：M1 和M2 垂直时是等倾干涉，否则为等厚干涉。掌握：（1）系统结构，（2）M1或M2垂直于光线移动时对条纹的影响。Extended sourceBeam splitter Reflective coating MirrorCompensating plate 78NN79S80迈克耳逊干涉仪的干涉条纹迈克耳逊干涉仪的干涉条纹迈克耳逊干涉仪的干涉条纹迈克耳逊干涉仪的干涉条纹M2M1M2M1M2M1M2M1与与重重 合合等等倾倾干干涉涉条条纹纹M1M281M2M1M2M1M2M1M2M1M2M1等等厚厚干干涉涉条条纹纹迈克耳逊干涉仪的干涉条纹迈克耳逊干涉

26、仪的干涉条纹迈克耳逊干涉仪的干涉条纹迈克耳逊干涉仪的干涉条纹82用迈克耳孙干涉仪测气流用迈克耳孙干涉仪测气流 迈克尔逊干涉仪833、泰曼干涉仪（Twyman interferometer）特点：在迈克尔逊干涉仪的一个光路中加入了被测光学器件Contour linesFringes of equal thickness844、马赫曾德干涉仪（Mach-Zehnder interferometer）测量光一次通过被测域It is preferred to measuring large transparent objects.8586二、其他干涉技术二、其他干涉技术1、数字波面干涉术目的：产生移动

27、的干涉条纹，用光电器件探测条纹的变化。基本原理：利用光学拍频中干涉条纹强度随时间变化的性质。外差干涉原理频率偏移器ABP87tI(x,y,t)条纹是随时间变化的量。88ABtITt892、傅里叶变换光谱仪原理：利用光源的相干长度对条纹可见度的影响，测量光源的光谱分布。相干长度：光谱宽度为的光源能够产生干涉的最大光程差设：I0(k)为随波数而变化的谱密度函数，整个光谱分布在（-，+）之间，为两光路的光程差。则：90通过移动M2，改变获得W()，再通过反傅里叶变换计算出I0(k)。W()I()设91Homework(3-5)1.Using red cadmium light,=643.8nm,Mi

28、chelson in his original experiment could still see interference fringes after he had moved one of the mirrors 25cm away from the coincidence position.How many fringes did he count?92Armand H.L.FizeauArmand H.L.Fizeau(1819-1896),French physicist,was born of a wealthy French family that enabled him to

29、 be financially independent.Instead of shunning work,however,he devoted his life to diligent scientific experiment.His most important achievement was the measurement of the speed of light in 1849.93Albert Abraham MichelsonAlbert Abraham Michelson(1852-1931)was born in Strelno,Prussia.He moved to the

30、 United States with his parents when he was 2.He graduated from,and taught at,the U.S.Naval Academy and later worked at the Case School of Applied Science,Clark University and the University of Chicago.In 1907 he was awarded the Nobel prize in physics,the first American scientist to be so honored.94

31、Michelson is best known for his precise determination of the velocity of light,for inventing the interferometer that bears his name.He also made noteworthy contributions to astronomy,spectroscopy and geophysics,was proficient in tennis and other sports,played the violin,and liked to paint landscapes

32、.95Frank TwymanHe is a manager,at Adam Hilger Ltd.,astronomical and optical instrument makers in London.The Twyman interferometer is particularly useful for the testing of optical components such as lenses,prisms and mirrors.9612-5 平行平板的多光束干涉及其应用平行平板的多光束干涉及其应用一、平行平板的多光束干涉LP1、干涉场的强度分布（1）光程差与位相差（相邻光束之

33、间）9798（3）反射光的和振幅与光强分布99（4）透射光的光强分布100101102103104105二、法布里泊罗干涉仪（Fabry-Perot interferometer）（一）仪器结构（干涉仪和标准具etalon）2dcos=m106书中237页图11-37107（二）用作光谱线超精细结构的研究1、测量原理设光源中含有两条谱线：1和2，2=1+则：标准具在中心附近对应的干涉级为m2和m1。对应于条纹的位移e于是有：1082.自由光谱的范围（能测量的最大波长差）2的(m-1)级条纹1的m级条纹自由光谱范围类似于卡尺的最大量程。109当1和2差值非常小的时，它们产生的干涉条纹将非常靠近，

34、如果两个条纹合成的结果被视为一个条纹，则两个波长就不能被分辨。思路：波长能否被分辨，取决于条纹能否被分辨。瑞利判据瑞利判据：两个波长的亮条纹只有当它们合强度中央的极小值低于两边的极大值的0.81时，两个条纹才能被分开。3.分辨极限和分辨本领（Resolvance of the interferometer）110G1点epdpd+=mm2 ,221在G2G1dd+FIFIIii)2(sin1)2(sin12212任意点的光强分布121112G11212113三、干涉滤色片（Interference filters）利用多光束干涉原理制成的一种从白光中过滤出波段较窄的单色光的装置。1、滤色片的中

35、心的波长（透射比最大的波长）114其中对应同一种波长，如=5.46x10-7m，m1，m2，m3对应的h1，h2，h3分别称为1，2，3级滤波片。1152、透射波长半宽度：透射比为峰值透射比一半时对应的波长差。已知，条纹的位相半宽度思路：寻找出波长与位相的关系已知表示的是1和2的干涉圆环刚好相差一个波长差，对应的位置变化是2。因此：有：1163、峰值透过比117滤光片按其结构可分为两类：4 吸收滤光片，它是利用物质对光波的选择性吸收进行滤光的。例如，红、绿玻璃以及各种有色液体等，具体滤光性能可参看有关手册；4 干涉滤光片，它是利用多光束干涉原理实现滤光的。4前者由于使用的物质有限，不能制造出在

36、任意波长处、具有所希望带宽的滤光片。4后者从原理上讲，可以制成在任何中心波长处、有任意带宽的滤光片。118ComplementarityInterference filters can also be made for reflection.Such filters are called dichroic mirrors;they reflect certain wavelengths and transmit others.Heat reflectors or hot mirrors reflect infrared(which on absorption converts into hea

37、t)and transmit the visible;cold mirrors,used in movie projectors,transmit infrared and reflect the visible.119Antireflection CoatingsPart of the light passing through a boundary is lost due to reflection.n1n2The reflectivity r,at a boundary between two media and at normal incidence is 120Effective W

38、ayThe effective way is by interference,applying a suitable coating to the surface.The reflections can be made cancel if the two reflected waves are out of phase by 180o,and in same amplitude.n2n1n0Thin film121For n0=1n2n1n0Thin film122For m=1n2n1n0Thin filmThe thickness of the film123Homework(3-6)1.

39、Determine the least separation of two spectrum lines,near 500nm,that can be resolved by an etalon that is 10mm long(deep)and has a reflectance of 90 percent.124Fabry&PerotMarie Paul Auguste Charles Fabry(1867-1945),French Physicist.While at the University of Marseilles,He taught medical students,lat

40、er became director of the French Institute and professor of physics.Besides his work on electricity,spectroscopy,atmospheric ozone,and astrophysics,Fabry today is best known for the instrument he developed together with Jean Baptiste Gaspard Gustave Alfred Perot(1863-1925),which he referred to as“th

41、is interferometer whose name I have the honor to bear myself.”.125Interference filterColor filters are based either on absorption or on interference.Both types are characterized by three parameters:the wavelength of maximum transmission or peak wavelength,max,in nm;the efficiency or peak transmittance,Tmax,in units of relative power transmitted;and the spectral purity or halfwidth,HW,that is the width of the passband at the level of one-half the peak transmittance,in nm.126127HWTmaxmax128