数字全息原理及应用的研究
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摘要
数字全息是一种全新的获取光学信息的方法,它是传统的全息术和数字技术相结合的产物。随着计算机技术和高分辨率图像传感器的飞速发展,数字全息技术的优势正在越来越明显地显示出来,其应用范围已涉及三维形貌测量、形变测量、粒子场测试、显微和防伪等许多领域。本文的研究目的是深入探讨数字全息记录和再现的原理,改进和完善数字全息再现算法,扩展数字全息技术的应用领域,为数字全息的实用化提供理论指导和实践经验。本文的主要研究内容和成果为:
对数字全息图的记录过程建立了数学模型,以此数学模型为基础,对离轴数字全息和同轴相移数字全息的采样条件进行了探讨。对两种常用的离轴全息光路——菲涅耳离轴数字全息和离轴无透镜傅里叶变换数字全息进行了深入的理论研究,在菲涅耳近似的前提下,导出了它们的频谱分离条件、采样条件、最小记录距离、离轴参考光对再现像的影响和系统的空间带宽积。
研究了数字再现的核心问题——衍射计算。以衍射理论和离散时间信号理论为工具,设计出两种新的采样参数可以灵活设定的再现算法——任意采样的菲涅耳变换法和离散线性卷积法,这两种算法是传统的菲涅耳变换算法和卷积法的改进和完善。
用理论推导和计算机模拟两种方法深入地研究了数字全息的点扩散函数。通过点扩散函数分析了不同再现算法在各种情况下的表现,定量地得到了CCD采样和积分效应对再现像的影响。为数字全息系统的设计提供了依据。
对数字全息在三维形貌测量和显微领域的应用进行了实验研究。提出了两种新的扩大数字全息视场的方法——预成像法和基于精密旋转的图像拼接法,并将它们用于大尺寸物体的三维形貌测量,利用离轴菲涅耳数字全息成功地测量了一块香皂和一个人嘴石膏模型的三维形貌,使数字全息三维形貌测量可用于几十厘米的大尺寸物体。利用预放大数字全息显微检测了一个微透镜阵列的面型缺陷。用Matlab6.5的图形用户界面开发工具(GUIDE)开发了一套数字全息软件,可用于数字全息显微、三维形貌测量、位移和形变测量的数据处理和结果显示。
Digital holography is a brand new method of obtaining optical information. It is a combination of the traditional optical holography and digital technique. With the fast development of computer science and high resolution image sensor, the advantage of digital holography is becoming more and more obvious, its application area has already included many domains like surface shape measurement, deformation measurement, particle field testing, microscopy and anti-counterfeiting. The purpose of this research is to discuss the principle of hologram recording and numerical reconstruction in detail, improve the reconstruction algorithm, expand the application area of digital holography and provide theoretical guidance and practical experience for its application. The main research work and achievements of the paper is:
A mathematical model is built to describe the recording of digital holography. Based on this model, the sampling conditions for off-line digital holography and in-line phase shifting digital holography are investigated. A profound theoretical study is made on two off-line architectures that are often used—fresnel off-line digital holography and lensless fourier transform off-line digital holography, their frequency separation condition, sampling condition, minimum recording distance, influence of the off-line reference wave, space-bandwidth product of the system are derived under the condition of fresnel approximate
The core problem of numerical reconstruction—diffraction computing is studied. Using diffraction theory and discrete time signal theory as a tool, two novel reconstruction algorithms—fresnel transform algorithm with arbitrary sampling and Discrete linear convolution algorithm are designed. These new algorithms can be seen as an improvement and perfection to the traditional fresnel transform algorithm and convolution algorithm.
The point spread function of digital holography is thoroughly studied by both theoretical derivation and computer simulation. The performance of different reconstruction algorithms under different conditions is analyzed through the point spread function. The influence of CCD integral effect to the reconstructed image is found. The study of point spread function provides an important reference for the design of digital holography system.
The application of digital holography in three dimensional surface shape measurement and microscopy is studied by experiments. Two novel methods of enlarging the field-of-view in digital holography are proposed and used in 3-D surface measurement of big objects. The 3-D surface shape of a soap and a gesso mouth model is successfully measured by fresnel off-line digital holography, the result indicates that digital holographic 3-D surface shape measurement can be used to objects as big as tens of centimeters. The defects on a microlens array are detected by pre-magnification digital holographic microscopy. A software for digital holography is developed using Graphical User Interface Development Environment (GUIDE) in Matlab6.5. This software can be used in data processing and result visualization in digital holographic microscopy and 3-D surface shape measurement.
对数字全息图的记录过程建立了数学模型,以此数学模型为基础,对离轴数字全息和同轴相移数字全息的采样条件进行了探讨。对两种常用的离轴全息光路——菲涅耳离轴数字全息和离轴无透镜傅里叶变换数字全息进行了深入的理论研究,在菲涅耳近似的前提下,导出了它们的频谱分离条件、采样条件、最小记录距离、离轴参考光对再现像的影响和系统的空间带宽积。
研究了数字再现的核心问题——衍射计算。以衍射理论和离散时间信号理论为工具,设计出两种新的采样参数可以灵活设定的再现算法——任意采样的菲涅耳变换法和离散线性卷积法,这两种算法是传统的菲涅耳变换算法和卷积法的改进和完善。
用理论推导和计算机模拟两种方法深入地研究了数字全息的点扩散函数。通过点扩散函数分析了不同再现算法在各种情况下的表现,定量地得到了CCD采样和积分效应对再现像的影响。为数字全息系统的设计提供了依据。
对数字全息在三维形貌测量和显微领域的应用进行了实验研究。提出了两种新的扩大数字全息视场的方法——预成像法和基于精密旋转的图像拼接法,并将它们用于大尺寸物体的三维形貌测量,利用离轴菲涅耳数字全息成功地测量了一块香皂和一个人嘴石膏模型的三维形貌,使数字全息三维形貌测量可用于几十厘米的大尺寸物体。利用预放大数字全息显微检测了一个微透镜阵列的面型缺陷。用Matlab6.5的图形用户界面开发工具(GUIDE)开发了一套数字全息软件,可用于数字全息显微、三维形貌测量、位移和形变测量的数据处理和结果显示。
Digital holography is a brand new method of obtaining optical information. It is a combination of the traditional optical holography and digital technique. With the fast development of computer science and high resolution image sensor, the advantage of digital holography is becoming more and more obvious, its application area has already included many domains like surface shape measurement, deformation measurement, particle field testing, microscopy and anti-counterfeiting. The purpose of this research is to discuss the principle of hologram recording and numerical reconstruction in detail, improve the reconstruction algorithm, expand the application area of digital holography and provide theoretical guidance and practical experience for its application. The main research work and achievements of the paper is:
A mathematical model is built to describe the recording of digital holography. Based on this model, the sampling conditions for off-line digital holography and in-line phase shifting digital holography are investigated. A profound theoretical study is made on two off-line architectures that are often used—fresnel off-line digital holography and lensless fourier transform off-line digital holography, their frequency separation condition, sampling condition, minimum recording distance, influence of the off-line reference wave, space-bandwidth product of the system are derived under the condition of fresnel approximate
The core problem of numerical reconstruction—diffraction computing is studied. Using diffraction theory and discrete time signal theory as a tool, two novel reconstruction algorithms—fresnel transform algorithm with arbitrary sampling and Discrete linear convolution algorithm are designed. These new algorithms can be seen as an improvement and perfection to the traditional fresnel transform algorithm and convolution algorithm.
The point spread function of digital holography is thoroughly studied by both theoretical derivation and computer simulation. The performance of different reconstruction algorithms under different conditions is analyzed through the point spread function. The influence of CCD integral effect to the reconstructed image is found. The study of point spread function provides an important reference for the design of digital holography system.
The application of digital holography in three dimensional surface shape measurement and microscopy is studied by experiments. Two novel methods of enlarging the field-of-view in digital holography are proposed and used in 3-D surface measurement of big objects. The 3-D surface shape of a soap and a gesso mouth model is successfully measured by fresnel off-line digital holography, the result indicates that digital holographic 3-D surface shape measurement can be used to objects as big as tens of centimeters. The defects on a microlens array are detected by pre-magnification digital holographic microscopy. A software for digital holography is developed using Graphical User Interface Development Environment (GUIDE) in Matlab6.5. This software can be used in data processing and result visualization in digital holographic microscopy and 3-D surface shape measurement.
引文
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[3]Thomas M.Kreis,Mike Adams,Werner P.O.Juptner.Methods of digital holography:A Comparison.Proc.SPIE 1997,3098,224-233
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[5]Thomas M.Kreis.Frequency analysis of digital holography.Opt.Eng,2002,41(4):771-778
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[9]刘诚,李良钰,李银柱等.无直透光和共轭像的数字全息.光子学报,2002,22(4):427-431
[10]Thomas M.Kreis,Werner P.O.Juptner.Suppression of the dc term in digital holography.Opt.Eng,1997,36:2357-2360
[11]国承山,王伟田,李健等.全息数字再现中零级衍射斑的消除.光子学报,1998,18(8):1073-1076
[12]Ichirou Yamaguchi,Tong Zhang.Phase-shifting digital holography.Opt.Lett,1997,22(16):1268-1270
[13]王华英,王大勇,谢建军.用极值频率法分析数字全息的记录条件.光子学报,2007,36(4):645-649
[14]王华英,王大勇,谢建军等.数字离轴无透镜傅里叶变换全息重建方法研究.激光技术,2007,31(2):288-294
[15]王华英,王大勇,谢建军.显微数字全息中物光波前重建方法研究和比较.光子学报,2007,36(6):1023-1027
[16]范琦,赵健林,向强等.改善数字全息显微术分辨率的几种方法.电子·激光,2005,16(2):226-230
[17]向强.光纤数字全息术及其应用研究.硕士学位论文.西比工业大学(2004)
[18]Fucai Zhang,I.Yamaguchi,L.Yaroslavsky.Systematic approach for the design of reconstruction algorithm in digital holography.Proc.SPIE,2005,Vol.5642:261-270
[19]Jose L.Valin,Edison Goncalves,Francisco Palacios,et al.Methodology for analysis of displacement using digital holography.Optics and Lasers in Engineering,43(2005):99-111
[20]Dieter Dirksen,H.Droste,B.Kemper,et al.Lensless Fourier holography for digital holographic interferometry on biological samples.Optics and Lasers in Engineering,36(2001):241-249
[21]Giancarlo Pedrini,Philipp Froning,Hans J.Tiziani,et al.Shape measurement of microscopic structures using digital holograms.Opt.Commun.164(1999):257-268
[22]Ichirou Yamaguchi,Jun-ichi Kato,Sohgo Ohta.Surface shape measurement by phase-shifting digital holography.Optical Review,2001,8(2):85-89
[23]M.Adams,T.Kreis,W.Juptner,Particle analysis with digital holography.Proc.SPIE 2000,4101,314-319
[24]T.Kreis,M.Adams,W.Juptner,digital in-line holography ha particlemeasurement.Proc.SPIE 1999,3744,54-64
[25]M.Adams,T.Kreis,W.Juptner,Particle measurement with digital holography.Proc.SPIE 1999,3823,38-43
[26]M.Adams,T.Kreis,W.Juptner,Particle size and position measurement with digital holography.Proc.SPIE 1997,3096,234-239
[27]Shigeru Murata,Norifumi Yasuda.Potential of digital holography in particle measurement.Optics & Laser Technology,32(2000):567-574
[28]H.J.Kreuzer,N.Pomerleau,K.Blagrave,et al.Digital in-line holography with numerical reconstruction.Proc.SPIE 1999,3744,65-74
[29]H.J.Kreuzer,M.H.Jericho,Wenbo Xu.Digital in-line holography with numerical reconstruction:three dimensional particle tracking.Proc.SPIE 2001,4401,234-244
[30]S.L.Pu,D.Allano,B.Patte-Rouland,et al.Particle field characterization by digital in-line holography:3D location and sizing.Experiments in fluids,(2005)39:1-9
[31]吕且妮.数字全息技术及其在粒子场中的应用研究.博士学位论文.天津大学(2003)
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