基于S-R分解理论的变形激光频谱测量法  

Deformation Analysis of Laser Spectra Based on S_R Decomposition Theorem

作　　者：姜耀东[1] 安里千[1] 刘艳华[1] 陈至达[1] 

机构地区：[1]中国矿业大学,北京100083

出　　处：《应用数学和力学》1999年第11期1107-1114,共8页Applied Mathematics and Mechanics

基　　金：中国矿业大学"211 工程"项目

摘　　要：在傅立叶频谱分析器中，当激光正射前焦面的图象时，其后焦面上形成一个个衍射斑，即傅立叶频谱；前焦面上的图象发生变形时后焦面上的频谱亦发生改变，通过分析频谱的这种改变量就可以获得图象变形信息·　以现代光学中的Ｆｒａｕｎｈｏｆｅｒ 衍射理论和有限变形的Ｓ＿Ｒ 分解理论为基础，论述了用激光频谱来分析测量有限应变和转动的数学力学基础、测量原理和方法以及计算机识别与处理技术。In the Fourier spectral analyzer, the Fourier spectra or the Fraunhofer diffraction pattern of an image is formed on the back focal plane when a laser beam is directed on the image lying on the front focal plane. If the image is deformed, its Forier spectra are also subjected to change. Therefore the change of the Fourier spectra provides a particular beautiful in sight into the deformation of that image. Through proposing the corresponding relationship between the image and its spectra, and analyzing the change of Fourier spectra, the deformation of the image can be obtained. Based on Fourier optical theory and S_R decomposition theorem of finite deformation, this paper presents a state of the art deformation measurement technique using laser spectral analysis. It discusses theoretical foundation of this new technique related to mathematics and optics, experimental principle and the technique of automatic recognizing and processing of the deformed spectral image. The paper is as a special commemoration and memorial to the death anniversary of professor Chen Zhida(1927～1998),who initially proposed the above academic idea in early 80s.

关 键 词：有限变形 应变测量 激光频谱 变形 S-R分解 

分 类 号：O33[理学—一般力学与力学基础] O344.3[理学—力学]