小波分析在光学信息处理中的应用* 马晶 谭立英 冉启文 用小波变换分析惠更斯-菲涅耳原理,为小波光学理论描述理论基础.运用该理论,对光学系统的空域滤波、空频域滤波现象进行分析,其中小波在空域滤波以空间可变处理为例,小波在空频域滤波以匹配滤波为例,波前滤波则以夫琅和费单缝、圆孔等为例,分析了小波变换在光学领域处理问题的可行性,初步建立了小波光学的理论框架. PACC:4200;4230 APPLICATION OF WAVELET ANALYSIS TO OPTICAL INFORMATION PROCESSING* MA JING TAN LI-YING (State Key Laboratory of Tunable Laser Technology,Harbin Institute of Technology,Harbin 150001) RAN QI-WEN (Department of Mathematics,Harbin Institute of Technology,Harbin 150001) ABSTRACT In this paper,the Huygens-Fresnel principle is restudied by means of wavelet analysis firstly,this builds the basis of the theory for wavelet optics.Then the theory of wavelet analysis is used to analyze the filtering in spatial domain and spatial frequency domain.For example,it gives the space variable processing for the filtering with wavelet in spatial domain,the match filtering for the filtering with wavelet in spatial frequency domain and a single slit and a round aperture for the wave-front filtering.The feasibility for treating the problems in optical field with wavelet transform is discussed,and the theoretical frame of wavelet optics is built. PACC:4200;4230 1 引言 小波变换是一种新的有效的分析手段.它能有效地从光学图像(信号)中提取信息,通过伸缩和平移等运算功能对光学图像进行多尺度的细化(multiscale analysis)[1].近年来,人们尝试用光学系统实现小波变换.Szu等人提出了利用二维相关器实现一维小波变换的方案[2,3].Mendlovic等人提出了一个利用 Dammann光栅的多通道系统[4],其中一个通道实现一个尺度的小波变换.Wang等人采用体全息技术,利用角度复用实现了光学 Harr小波变换,并用于图像特征提取[5].Bloch等人讨论了利用计算全息方法实现光学小波变换的方案[6].此外还有利用干涉计量仪实现光学小波变换的方案[...