光學信息chap7第七章光全息術

1、第七章 光全息術Optical Holography光波的完整記錄與再現(xiàn)Recording and Reconstruction of Light Wavefront1、全息術發(fā)展簡史 7.1 引言 Introduction 丹尼斯伽柏（Dennis Gabor，1900年1979年），英國匈牙利裔物理學家，1971年諾貝爾物理獎獲得者，全息攝影技術的發(fā)明者1948年 Dennis Gabor 提出 “波前重現(xiàn)” 理論 目的：改善電子顯微鏡的分辨率 效果：因光源(汞燈)相干性差，效果不明顯Dr. Dennis Gabor signs a copy of the Museum of Hologr

2、aphys inaugural exhibition catalogue, Through The Looking Glass, during his historic visit to the museum on March 17, 1977. (Photo by Paul D. Barefoot) 1960年 激光器 問世， 提供 理想的相干光源 為全息技術的發(fā)展創(chuàng)造了條件 紅寶石 Laser 梅曼（英），美國休斯飛機制造公司 氦氖 Laser 霍曼（伊朗），美國貝爾實驗室1962年 離軸全息圖 問世 Leith 和 Upatnieks （美） 加速了全息術的發(fā)展 40多年來，全息科學和技

3、術得到飛速發(fā)展，應用領域幾乎無所不及。5.1 引言 Introduction 1、全息術發(fā)展簡史1964年 氬離子激光器 Ar+ Laser 問世 提供了短波長連續(xù)可見光 擴展了全息技術的應用范圍 同年，蘇聯(lián)科學家 Denisyuk 發(fā)明了白光反射全息圖This pioneer image was produced in 1964 by Emmett Leith and Juris Upatnieks at the University of Michigan only four years after the invention of the laser Leith and Upatniek

4、s preparing to shoot a laser transmission hologram using the off-axis technique borrowed from their work in the development of side-reading radar. (Photo by Fritz Goro for Life Magazine, 1967)Russian scientist Yuri N. Denisyuk, State Optical Institute in Leningrad, USSR, signing a copy of his book,

5、Fundamentals of Holography. (Photo by Dr. Stephen Benton, 1979)Introduction to laser light激光簡介1 Light is most easily thought of its being trains of waves, which like water waves and sound waves. 4 In comparison to red light, green light has a shorter wavelength6 Most light, though, like the light fr

6、om a flashlight, is disorganized or incoherent. 9 This means the light is a single color and monochromic. 11 Together these properties result in a highly uniform and controllable beam of coherent light. 2 They also lay between two extremes called crests and troughs.3 The color of light depends on th

7、e distance between crests and its called its wavelength5 Light comes from many different sources.7 Its made of many colors generated random and traveling in many different directions8 Laser light, however, consists of only one wavelength.10 The light is also in phase. Crests and troughs are in perfe

8、ct alignment.and blue lights wavelength is shorter still.單色光波 在z = 0 平面, 復振幅分布: O (x,y)記錄此波前要求: 制作出一種薄的光學元件, 其復振幅透過率 t(x,y) = O (x,y)再現(xiàn)：用單位振幅的平面波垂直照明在z = 0 平面，透射波復振幅: U(x,y) 1. t(x,y) O(x,y) 在z = 0平面上所有的點都再現(xiàn)出初始的波 在z 0 的空間中任意位置都再現(xiàn)出初始的波。7-2 全息術原理 波前記錄與再現(xiàn) 1. 波前記錄: 將位相編碼為強度Transform Phase into Intensity

9、 制作透明片t(x,y)= O(x,y)的關鍵障礙：光學探測器只響應光強度| O(x,y)|2，而對位相argO(x,y)不敏感。位相信息不應當丟棄。為了記錄O(x,y)的位相，應當找到一種編碼方法將位相的變化轉(zhuǎn)換為強度變化。 1. 波前記錄: 全息編碼 Holographic Code 基本點：在z = 0平面, 將初始光波O（物波）與已知的參考波R疊加(混合).用照相方法記錄兩個波疊加以后干涉圖樣的強度得到復振幅透過率 t與曝光強度成正比的透明片. 物光波的振幅和位相信息以干涉條紋的形狀、疏密和強度的形式“凍結”在感光的全息干板上。這就是波前記錄的過程。Recording of a hol

10、ogram全息圖拍攝Recording of a hologram全息圖拍攝In holographic laboratory, the laser and the object sit on the massive table that isolates them from vibration of the environment. This setup is used to make the basic laser transmission hologram, the type gained by Dennis Gabor and developed by Emmett Leith. Us

11、ing a piece of ground glass to show the laser light, lets follow this path. The light leaves a laser and hits a partially specular mirror called a beam splitter, which splitters the laser beam in two. One beam, called the object beam, is directed to the space shuttle. A lens expands the beam to cove

12、r the shuttle with light. This light reflects off the shuttle onto the film holder, which would be loaded with unexposed films. The other beam, called the reference beam, is directed by mirrors and expanded with a lens to shine directly on the film holder. From above, the table looks like this. Now

13、we are ready to shoot the hologram. The laser light is blocked, the room is darken, and the film holder is loaded with film, which is exposed by the laser light from the shuttle. Principle of hologram recording全息圖的拍攝原理During exposure the object beam, whose crests are indicated by lines, strikes the

14、space shuttle, The light reflecting from the low of space shuttle is shown for simplicity At the same time, the uniform and featureless wave-front of reference beam arrived at the emulsion. At the areas with wave crests from the object, and reference beam meet, and it is greater than the other areas

15、 of intersection. This phenomenon called interference results in an interference pattern of bright and dim regions on the film. The bright regions exposed film forming microscopic planes. which reflects its characteristics pattern of light or wave-front to the film. the brightness or intensity of li

16、ght energy combines,1. 波前記錄: 數(shù)學模型 Mathematical Model 設物波和參考波到達H上的復振幅分別為: O ( x , y ) = O 0 ( x , y ) exp jfo ( x , y ) R ( x , y ) = R 0 ( x , y ) exp jfr ( x , y ) 干板記錄的是干涉場的光強分布，曝光光強為 I ( x , y ) = U ( x , y )U * ( x , y ) =O2 +R2 + OR* + O*R 干涉場光振幅應是兩者的相干疊加，H 上的總光場 U ( x , y ) = O ( x , y ) + R (

17、 x , y ) xy全息干板H上設置x , y坐標，Complex Amplitude Transmittance of a Hologram 全息圖的復振幅透過率復雜的余弦條紋調(diào)制度1令Ir和Io分別為參考波和物波在z = 0平面的強度，經(jīng)線性處理后，底片的透過率函數(shù)tH 與曝光光強成正比 tH ( x , y ) I ( x , y ) tH ( x , y ) =|O2 +R2 + OR* + O*R 這就是全息照片，又稱全息圖 (Hologram)。 tH( x, y ) = Ir + Io + 2 (IrIo)1/2cosfr ( x , y ) - fo ( x , y ) 全息

18、圖的復振幅透過率又可寫為：Reconstruction of holograms全息圖再現(xiàn)The developed hologram looks much like a photographic negative. The hologram itself seems to contain no image at all. But if the reference beam shines on the hologram at a correct angle, a replica of the light originally reflected by the space shuttle is

19、played back. This is caused by an effect known as diffraction. Principle of hologram reconstruction 全息圖的再現(xiàn)原理When the reference beam shines on the emulsion, the exposed planes in the emulsion behave like tiny prisms changing the direction or diffracting some of the light. This diffracted light is the

20、 duplicate of the wave-front reflected by the shuttle during exposure. When you look at the hologram, what you see is the same wave-frontBecause the light is transmitted by the hologram during viewing, it is called a transmission hologram. qqqqqqqqqqqqqqqqqqq that you would see if you would look at

21、the object itself.7-2全息術原理波前記錄與再現(xiàn) 2、波前再現(xiàn)透過H后的光場復振幅 U( x , y ) = C ( x , y )tH ( x , y ) 用照明光波 C ( x , y ) = C 0 ( x , y ) exp jfc ( x , y ) 照射全息圖 = C0(O02 + R02) expjfc(x, y)+C0O0R0expj(fofr+fc)+C0O0R0exp-j(fofrfc) 全息學基本方程U(x, y) = C0(x, y)expjfc(x, y)|O|2+|R|2 +OR*+ O*R 7-2全息術原理波前記錄與再現(xiàn) 2、波前再現(xiàn)全息學基本方

22、程:特例(1): 用原參考光再現(xiàn)，C(x, y ) = R(x, y ) 全同照明 U(x, y)=R0(O02+R02)expjfr + + U(x, y) = C0(O02 + R02) expjfc(x, y)+C0O0R0expj(fofr+fc)+C0O0R0exp-j(fofrfc) 與再現(xiàn)光相似包含物的位相信息包含物的共軛位相信息畸變了的共軛像(實像)，-1級像原始像（虛象）1級像R02O0expjfoR02O0exp-j(fo-2fr)7-2全息術原理波前記錄與再現(xiàn) 2、波前再現(xiàn)U(x,y)=R0(O02+R02)exp-jfr+R02O0expj(fo-2fr)+R02O0e

23、xp-jfo特例（2）共軛光再現(xiàn)， C( x, y ) = R* (x, y ) C0(x, y) = R0(x, y)，fc = -fr 畸變了的虛像與原物相像的實像（贗實像）7-2 全息術原理 波前記錄與再現(xiàn) U(x, y) = C0(O02 + R02) expjfc(x, y)+C0O0R0expj(fofr+fc)+C0O0R0exp-j(fofrfc) 由于光是獨立傳播的，再現(xiàn)時在全息圖上相互重疊的四項將分別沿三個不同方向傳播。這稱為離軸全息圖。7-2 全息術原理 波前記錄與再現(xiàn)例：P160, 習題 5.1 兩束夾角為 = 450的平面波在記錄平面上產(chǎn)生干涉，已知光波波長為632.

24、8nm，求對稱情況下（兩平面波的入射角相等）該平面上記錄的全息光柵的空間頻率。 HqxzORO ( x , y ) = expjkxsin(q /2)R ( x , y ) = exp-jkxsin(q /2)U(x, y) = expjkxsin(q /2) + exp-jkxsin(q /2)I(x, y)=U(x, y)U*(x, y)=|O|2+|R|2+OR*+O*R =2+2coskx.2sin(q /2)7-2 全息術原理 波前記錄與再現(xiàn)例：P160, 習題 5.1HqxzORx干涉圖樣為余弦條紋，其調(diào)制度為1，空頻為：經(jīng)線性處理后，底片的透過率函數(shù)tH 與曝光光強成正比，形成全

25、息光柵： 7-2 全息術原理 波前記錄與再現(xiàn)例：P160, 習題 5.1x其調(diào)制度為1，空頻為：經(jīng)線性處理后，底片的透過率函數(shù)tH 與曝光光強成正比，形成全息光柵： 代入 = 450，l = 632.8nm， 計算得：f =1209.5 lp/mm7-2全息術原理波前記錄與再現(xiàn) 3、全息實驗裝置 光的相干性包括時間相干性和空間相干性。要求光束的相干長度足夠長，相干面積足夠大相干光源激光器7-2全息術原理波前記錄與再現(xiàn) 3、全息實驗裝置 光學隔振平臺：必須達到相當高的穩(wěn)定度，使曝光時間內(nèi)兩臂光程差的變化量不得超過/10。光學元件：光分束器、反射鏡、擴束鏡、針孔濾波器、透鏡、散射器用于分光、折光、擴束、濾波、準直、成像、散射等等全息實驗裝置全息實驗光路的設計原則（1）等光程差原則（2）物參比適宜（3）空間頻率考慮（4）使用光學元件數(shù)量要盡可能少作業(yè) 用波長為532nm的激光制作全息光柵，要求光柵的