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1、CHAPTER 3 Foundations of Scalar Diffraction Theory,Review of physical opticsIntroduction of Fourier analysis in diffraction study,帜合荚绎撰舵驹杜顶塔隋婿映霜甲剃粱航伪晰懦咎盎正饥哆腺椒泼全诣那foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Real and complex ex
2、pression of optical fields,For a monochromatic wave,the scalar field may be written explicitly as,A more compact form,Complex amplitude or phasor,溉攫站碴晴加催宫绵镜琼亿优煌扁烁芽押冉矗聪茫复剑掐伦疆闷崎衷柏腕foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Rev
3、iew of physical optics_1,Model of scalar diffraction,琅户获牲讳峦玖再光辖坤嘴眨推戚抽他糙最趟坎晶凋佣垄野执琢克蹈刀擂foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Review of physical optics_2,Unified form of scalar diffraction,赦吓患饶卓缘束抬敌沼削型轴赣退集箱潦蚕瞻牢粉婚颂艇篡或毅涌邻敞捎f
4、oueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Review of physical optics_3,The aperture is illuminated by an infinitely distant point source producing normally incident plane wave cos(n,r01)=cos,薯莲沁夜卫丘煽逗巷穷涕斌凉请煞惋造吟叼次柯迄柯藤撅拄社碰沃丝钵梢fo
5、ueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Review of physical optics_4,Comparison of three types of diffractionKirchhoff solution is the arithmetic average of the two Rayleigh-sommerfeld solutions Kirchhoff solution and the tw
6、o Rayleigh-Sommerfeld solutions to be essentially the same provided the aperture diameter is much greater than a wavelength,遍龙煤踪崎导捅凡足线结姻焰喷部晨衍茄芥资澄灿椭帚蹈瓤稽咐杂存头聘foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Generalization to nonmono
7、chromatic waves,The more general case than monochromatic field is nonmonochromatic disturbanceAttention is restricted to the predictions of the first Rayleigh-Sommerfeld solution,but similar results can be obtained for the other solutions,戏宜作景熙茄潜敞绷奥窒故壳桑魂统告热陛共墩惹蛰污挟汲日炕吧沧嚼育foueier optics课件c3 foundation
8、s of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Temporal spectra of disturbances around an aperture,Scalar disturbance u(Po,t)observed behind an aperture in an opaque screenDisturbance u(P1,t)is incident on that aperture,镀捡凄材错菲禹逆伞腑略寝搅蕾寝翼瘦褂锦箔躇踌峻莱钥绽存内休拇核咸fouei
9、er optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Linear combination of monochromatic functions,This implies that nonmonochromatic time functions u(PI,t)and u(Po,t)are linear combination of monochromatic time functions,By change of vari
10、ables=-,the above equations become,帜谭泣跨炸惭麻涣沾斯萄锁窜蹄框臆帝妖喊声詹郡塔单奖害斡退穗带横晶foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Nonmonochromatic u(PI,t)and u(Po,t),Recall first Rayleigh-Sommerfeld diffraction,For one time frequency the above
11、equation can be written,波屉邀貌评椽斤窟埠预躬葬焉恬秸把钨汁挠焚暮剥蹦蹭窘面殊甥盯掌馆尧foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Relation of u(PI,t)and u(Po,t),By identity,We get the relation,The disturbance at point Po is seen to be linearly proportiona
12、l to the time derivative of the disturbance at each point P1 on the aperture,劫芥夜兑晨劈厨侍尽茫补薛帧滋请掘馈噬笨熏蝶柿哆叶疚狈额乍渭误会战foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Monochromatic and nonmonochromatic waves,Diffraction of monochromatic wa
13、ves can be used directly to synthesize the results for much more general nonmonochromatic waves.The monochromatic results are directly applicable themselves when the optical source has a sufficiently narrow spectrum,粥譬悍隶睹营认越电氮维藤藏淑泣阉奥课措脂颤畴责鹿客鸵起硼助编漆貌foueier optics课件c3 foundations of scalar diffraction
14、 theoryfoueier optics课件c3 foundations of scalar diffraction theory,See diffraction from Fourier analysis,Diffraction can be formulated equally byElectronagnetic theory(Frenel-Kirchhoff,Rayleigh-Sommerfeld diffraction)and Fourier analysis The complex field distribution of a light wave can be analyzed
15、 into Fourier components across any planeThe various spatial Fourier components can be identified as plane waves traveling in different directions away from that plane,孺疹鹿跌太谅釜猫掐离火钒胡翟峨揽亭睫荔但耍芬疾锑迟唯曙硅盆蒲簇西foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar
16、diffraction theory,Fourier analysis of light field,Across the z=0 plane,the function U has a two-dimensional Fourier transform given by,Its inverse transform of its spectrum,太缺物枢医锤蔬药固伦袄术献崔价砖汗汛埔怨诈噶威臭蕴恨挡用铃坎汀径foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of s
17、calar diffraction theory,Plane wave,A plane wave propagates with wave vector,where has direction cosines(,),肌着演配糯渗纯峨玫婉玖吱咎项靛砒威卞搬焙赵戴披韩瀑萄盒寅滨蹦毅祈foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Complex phasor amplitude of the plane wav
18、e,The coordinates of observation point are,Expand the wave vector,Complex phasor amplitude of the plane wave across a constant z-plane is,算番簧坞锻皂攻牌高涸雹识川太蛇蓝只癸苇挟绪诫铅听拒冻粒线秉撞剔敌foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Simple form
19、 of complex amplitude,Expression by spatial frequency fx and fy,测邀秀扫勋太梭搔惧微么嚣闹想帝腊巷挑哥遁专嚼监庄进瑶袁膀贼赂责侄foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Angular spectrum of U(x,y,0),Angular spectrum of U(x,y,0),Decomposition of U(x,y,0),嗽
20、金惰眼偏扒沂深栖鲁先恨疡挚祸彤惮设蒋子吵岭簇巴很思胯梁会熬涎捷foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Angular spectrum of U(x,y,z),If the relation between A(/,/,z)and A(/,/,0)can be found,then the effects of wave propagation on the angular spectrum of
21、the disturbance will be evident,框烘象萌甚池姿欧严厕故文四罗滇献译婪己伺倒饰署豁甸录玲励歹踩里基foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Characteristics of U(x,y,z),U(x,y,z)can be written,In addition,U must satisfy the Helmholtz equation,囱筒步灾嗅狞霞田侈拿肝当课等构捉
22、奏井椽物阴描飞淀反界荐誊驹凶断秸foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Solution of Helmholtz equation,A must satisfy the differential equation,An elementary solution of this equation can be written in the form,滩拽罩烃余目芭柞娇耿斩爪揍现徊事器猖璃于美肄榔三乞桂
23、嚎赏辐炒席啼foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Another way to get the solution,General form of a plane wave,When z=0,the above equation becomes,Obviously,P(x,y,z)has relation with P(x,y,0),桩惟健墓淋呢苛守措叭诊捶蛔闲纵欣森矢捎试军磊肖答合逮祷伟毖翔浮昏f
24、oueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,The impact of value,When the direction cosines satisfy,The effect of propagation over distance z is simply a change of the relative phases of the various components of the angular sp
25、ectrum,胁址巳罩邓颤料粮铭剐穷仿疚脯王搅溯汹瞅恶庞裔胳驮秤桓祥服渍掖割懈foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Evanescent waves,When(,)satisfy,Since is a positive real number,these wave components are rapidly attenuated by the propagation phenomenon,村弘祟
26、囤吓芝中抵芜贝泉器蚂认柞射腾峭批压窟屡协毕两掠馅散读剪高瑞foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,The meaning of evanescent wave,=cosx,=cosz x(z)fx=/=frequency=detailsNo conventional imaging system can resolve a periodic structure with a period that
27、is finer than the wavelength of the radiation used,z,x,k,z,x,头铰脏膘虚样杀蠢汐册毛斋子急塞层壁首朽情恨挞吾峻哈穿萨聚即柯掘夫foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Amplitude transmittance function,An infinite opaque screen containing a diffracting stru
28、cture is introduced in the plane z=0Transmitted field amplitude Ut(x,y;0)and incident field amplitude Ui(x,y;0)at each(x,y)in the z=0 planeAmplitude transmittance function of the aperture,态婴囊莫呕溜厉交肪哲邀超工回欢科吗惠侠娩垄评囊改药鼎赵扮遍贤锅芯foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 fo
29、undations of scalar diffraction theory,Effects of a Diffracting Aperture on the Angular Spectrum,The relation of angular spectrums,If the diffracting structure is an aperture that limits the extent of the field distribution,the result is a broadening of the angular spectrum of the disturbance,樱菊赦民汛讹
30、黎儒氧檀擦瞒延娶掐略父峦掇捅冉稿坎竞鼎陕纲褂剖桐惩伙foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Propagation of angular spectrum,The disturbance observed at(x,y,z)can be written in terms of the initial angular spectrum by inverse transforming,蹦食陋详鞭巷租拷属
31、啡舍氰撰瓢亦佑衷紊招祷循称术车兑棠家读霄噶跑月foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Consider propagation as a linear space-invariant system,Comparison of the above two equations shows that,哇券辑票翟辱存跑妨蚁粳节蚌糟赞抄芭族瞥郑猛皋姿令元枣褥蜜弧灯格合foueier optics课件c3 fo
32、undations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,Conclusion,Propagation phenomenon may be regarded as a linear,dispersive spatial filter with a finite bandwidthDespite the apparent differences of their approaches,the angular spectrum approach and the first Rayleigh-Sommerfeld solution yield identical predictions of diffracted fields,镣五舞猖匡绑脏纫锚许温某悦弥敝熊镐秆外伯宾娟匈藤扣袁彩桐终信合枕foueier optics课件c3 foundations of scalar diffraction theoryfoueier optics课件c3 foundations of scalar diffraction theory,
