相移数字全息显微的理论与实验研究
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摘要
数字全息显微是近年来逐步发展起来的一种新型显微成像技术，是目前光学领域中一个活跃的研究热点。它利用CCD等光电记录器件代替传统光学全息干板来记录被测样品的显微全息图并存入计算机，然后通过相应的数字算法模拟实际光学衍射过程，在计算机中数值再现被测样品的三维形貌，以实现显微测量。该技术融合了光学干涉显微和数字图像技术，具有全场、无接触、快速、三维实时测量等许多独特的优势，已经广泛应用于生物医学观察、振动分析、形变检测、粒子场分析、微纳器件检测等诸多领域。
普通的离轴数字全息显微虽然可以有效地消除衍射再现过程中零级像和孪生像的干扰，但由于目前光电记录器件的分辨率限制，使得离轴数字全息显微的分辨率受到一定的影响，不利于数字全息显微技术的实际应用。为了提高数字全息显微的分辨率，同轴相移数字全息显微随之诞生。通过在记录过程中改变参考光相对于物光的相位来记录多幅相移全息图，然后利用相应的数值算法再现记录面上物光场的复振幅分布。相比离轴数字全息显微，同轴相移数字全息显微通过相移操作，在同轴记录的情况下解决全息再现时零级和孪生像的干扰问题，提高CCD空间带宽积的利用率，改善再现质量，提高显微观测的分辨率。围绕构建可实用的高稳定数字全息显微装置，本论文以相移数字全息显微技术为主要研究内容，主要完成了以下研究工作：
1、综述了数字全息技术和数字全息显微技术的产生和发展历程。分析了相移数字全息显微的特点并介绍了该领域的国内外研究发展现状。详细介绍了相移数字全息显微技术中的一些基础知识，如相移的概念、相移的实现方法、数字全息图的记录与再现方法以及相移算法等等，为后面的研究提供理论支持。
2、基于偏振相移的原理分别搭建了分步相移和同步相移数字全息显微装置，并对两种相移装置的结构特点、适用范围和性能特点进行了实验研究和对比分析。系统地分析了显微记录过程中聚光镜和物镜等透镜产生附加相位的原因和相移误差对再现结果的影响。分别提出了一种基于最小二乘椭球面拟合的方法和基于衍射相位统计分布的实际相移量获取方法，消除附加相位和相移误差的影响，提高测量精度。
3、结合空间分光技术和点衍射干涉技术，分别搭建了基于分光棱镜和光栅衍射的物参共路相移数字全息显微装置。通过分光棱镜或光栅在空间分光，然后利用针孔滤波产生参考光使得物光和参考光沿着相同的路径传播。物参共路的结构使得外界环境的干扰在记录时被有效消除，提高了数字全息显微装置的稳定性和实用性。
4、基于彩色CCD的特点和双波长成像特性，搭建了轻载频双波长数字全息显微装置。通过单次曝光可同时获得两幅不同波长的正交载频全息图并按比例相减消除零级项，实现了轻载频全息图记录并提高最终成像质量。同时，利用两个波长的“差频”产生大小为Λ12=λ1λ2/|λ1-λ2|的长“合成波长”，实现对样品的无包裹测量，为运动物体或动态过程的观测提供一种实时高精度观测手段。
5、分别提出了双波长衍射差异自动聚焦法和单波长双离轴照明自动聚焦法。通过寻找不同波长或不同传播方向上再现像之间的最小像差位置，实现了全息图数字再现过程中的自动聚焦，使得再现像最清晰，从而消除误判，提高测量精度。这两种自动聚焦算法除了吸收型样品和双折射型样品外均适用，应用范围广。
Digital Holographic Microscopy (DHM) is a recently well developed microscopictechnique, and has been becoming a hot research spot in optic science. DHM uses acharge coupled device (CCD) camera, intead of the traditional hologram recordingmedium, to store the hologram in computer digitally, and then simulate the opticaldiffraction process with corresponding algorithms for reconstruction of the originalobject field to realize three-dimensional microscopic imaging and measurement of thespecimen. DHM combines the characteristics of optical interferometic technology andmodern digital image processing technology, and has the features of whole-field,nondestructive, high-speed, real-time3D measurement. It has been widely used inbiomedical diagnosis, vibration analysis, deformation detection, particle field analysis,micro-/nano device inspection, and so on.
Although the common off-axis DHM can totally eliminate the affection of zeroorder and twin images in real-time measurement process, the low resolution ofreconstructed image is the major drawback of off-axis DHM, due to the limitedresolution of current CCDs. In order to improve the DHM's resolution, in-linePhase-Shifting Digital Holographic Microscopy (PSDHM) has been invented. Bychanging the phase of the reference wave with respect to the object wave, multiplephase-shifted holograms are captured during the recording process. Then the complexamplitude of the object field is reconstructed by using corresponding algorithms,which can eliminate zero order and twin images effectively. Compared with theoff-axis DHM, in-line PSDHM makes full use of CCD's space bandwidth, thus theresolution of the reconstructed image is improved. Aimed at constructing a highlystable DHM setup for practical application, this thesis focused on PSDHM, andaccomplished the following main contents:
1. The history and progress of digital holography (DH) and DHM are reviewed.The characteristic of PSDHM and its development are introduced andanalyzed comprehensively. The basic knowledges of PSDHM are introduced,including the concept of phase-shifting, the methods to realize thephase-shifting, recording and reconstruction of digital holograms, phase-shifting algorithms, and so on. All these knowledges are the theoreticalbasis for the next research.
2. Based on the principle of polarization phase-shifting, step-by-stepphase-shifting DHM and parallel phase-shifting DHM have been built up,respectively, and the configuration, performance and application scope ofthem are discussed and compared. The physical formation of phase aberrationintroduced by condenser lens and microscope objective and the effect ofphase-shifting error are theoretically analyzed. In order to eliminate theadditional phase aberration and phase-shifting errors to improve the accuracyof measurement, a fitting method based on least square ellipsoidal model anda simple algorithm based on the statistical property of object wave for blindextraction of real phase-shift have been proposed.3. Two kinds of common-path PSDHM have been built up by combining the
spatial beam splitting technique and the point-diffraction interferometry. Withbeamsplitters or gratings to split the light beam in space, the reference wave isreproduced by a pinhole filter to ensure the object wave and the referencewave to share the same path. The common-path configuration makes thedistributions of the two beams counteracted by each other in recordingprocess, and improves DHM's stability and practicability.
4. A dual-wavelength DHM with a slightly off-axis configuration has beenproposed based on the imaging characteristic of color CCD anddual-wavelength illumination. To realize the slightly off-axis recording andimprove the resolution of image, two single wavelength holograms withorthogonal spatial carrier frequencies can be extracted from the recordedcolor hologram with one exposure, and the dc term can be suppressed bysubtracting one from the other in property. Meanwhile, the real-timeunwrapped phase measurement is achieved by a synthetic wavelengthΛ12=λ1λ2/|λ1-λ2|, which is produced by beat frequency of two wavelengths λ1and λ2, which provides a useful measuring tool for moving object or dynamicprocess detection.
5. Two kinds of autofocusing schemes are proposed, which are based on thediffraction difference of dual-wavelength and two-angle off-axis illuminations of single wavelength, respectively. The image plane can be automaticallydetermined in the reconstructing process by seeking the minimal difference ofreconstructed images of two wavelengths or in different illuminationdirections. Both of algorithms can realize autofocusing exactly, and areapplicable to specimens without chromatic absorption and birefringence.
普通的离轴数字全息显微虽然可以有效地消除衍射再现过程中零级像和孪生像的干扰，但由于目前光电记录器件的分辨率限制，使得离轴数字全息显微的分辨率受到一定的影响，不利于数字全息显微技术的实际应用。为了提高数字全息显微的分辨率，同轴相移数字全息显微随之诞生。通过在记录过程中改变参考光相对于物光的相位来记录多幅相移全息图，然后利用相应的数值算法再现记录面上物光场的复振幅分布。相比离轴数字全息显微，同轴相移数字全息显微通过相移操作，在同轴记录的情况下解决全息再现时零级和孪生像的干扰问题，提高CCD空间带宽积的利用率，改善再现质量，提高显微观测的分辨率。围绕构建可实用的高稳定数字全息显微装置，本论文以相移数字全息显微技术为主要研究内容，主要完成了以下研究工作：
1、综述了数字全息技术和数字全息显微技术的产生和发展历程。分析了相移数字全息显微的特点并介绍了该领域的国内外研究发展现状。详细介绍了相移数字全息显微技术中的一些基础知识，如相移的概念、相移的实现方法、数字全息图的记录与再现方法以及相移算法等等，为后面的研究提供理论支持。
2、基于偏振相移的原理分别搭建了分步相移和同步相移数字全息显微装置，并对两种相移装置的结构特点、适用范围和性能特点进行了实验研究和对比分析。系统地分析了显微记录过程中聚光镜和物镜等透镜产生附加相位的原因和相移误差对再现结果的影响。分别提出了一种基于最小二乘椭球面拟合的方法和基于衍射相位统计分布的实际相移量获取方法，消除附加相位和相移误差的影响，提高测量精度。
3、结合空间分光技术和点衍射干涉技术，分别搭建了基于分光棱镜和光栅衍射的物参共路相移数字全息显微装置。通过分光棱镜或光栅在空间分光，然后利用针孔滤波产生参考光使得物光和参考光沿着相同的路径传播。物参共路的结构使得外界环境的干扰在记录时被有效消除，提高了数字全息显微装置的稳定性和实用性。
4、基于彩色CCD的特点和双波长成像特性，搭建了轻载频双波长数字全息显微装置。通过单次曝光可同时获得两幅不同波长的正交载频全息图并按比例相减消除零级项，实现了轻载频全息图记录并提高最终成像质量。同时，利用两个波长的“差频”产生大小为Λ12=λ1λ2/|λ1-λ2|的长“合成波长”，实现对样品的无包裹测量，为运动物体或动态过程的观测提供一种实时高精度观测手段。
5、分别提出了双波长衍射差异自动聚焦法和单波长双离轴照明自动聚焦法。通过寻找不同波长或不同传播方向上再现像之间的最小像差位置，实现了全息图数字再现过程中的自动聚焦，使得再现像最清晰，从而消除误判，提高测量精度。这两种自动聚焦算法除了吸收型样品和双折射型样品外均适用，应用范围广。
Digital Holographic Microscopy (DHM) is a recently well developed microscopictechnique, and has been becoming a hot research spot in optic science. DHM uses acharge coupled device (CCD) camera, intead of the traditional hologram recordingmedium, to store the hologram in computer digitally, and then simulate the opticaldiffraction process with corresponding algorithms for reconstruction of the originalobject field to realize three-dimensional microscopic imaging and measurement of thespecimen. DHM combines the characteristics of optical interferometic technology andmodern digital image processing technology, and has the features of whole-field,nondestructive, high-speed, real-time3D measurement. It has been widely used inbiomedical diagnosis, vibration analysis, deformation detection, particle field analysis,micro-/nano device inspection, and so on.
Although the common off-axis DHM can totally eliminate the affection of zeroorder and twin images in real-time measurement process, the low resolution ofreconstructed image is the major drawback of off-axis DHM, due to the limitedresolution of current CCDs. In order to improve the DHM's resolution, in-linePhase-Shifting Digital Holographic Microscopy (PSDHM) has been invented. Bychanging the phase of the reference wave with respect to the object wave, multiplephase-shifted holograms are captured during the recording process. Then the complexamplitude of the object field is reconstructed by using corresponding algorithms,which can eliminate zero order and twin images effectively. Compared with theoff-axis DHM, in-line PSDHM makes full use of CCD's space bandwidth, thus theresolution of the reconstructed image is improved. Aimed at constructing a highlystable DHM setup for practical application, this thesis focused on PSDHM, andaccomplished the following main contents:
1. The history and progress of digital holography (DH) and DHM are reviewed.The characteristic of PSDHM and its development are introduced andanalyzed comprehensively. The basic knowledges of PSDHM are introduced,including the concept of phase-shifting, the methods to realize thephase-shifting, recording and reconstruction of digital holograms, phase-shifting algorithms, and so on. All these knowledges are the theoreticalbasis for the next research.
2. Based on the principle of polarization phase-shifting, step-by-stepphase-shifting DHM and parallel phase-shifting DHM have been built up,respectively, and the configuration, performance and application scope ofthem are discussed and compared. The physical formation of phase aberrationintroduced by condenser lens and microscope objective and the effect ofphase-shifting error are theoretically analyzed. In order to eliminate theadditional phase aberration and phase-shifting errors to improve the accuracyof measurement, a fitting method based on least square ellipsoidal model anda simple algorithm based on the statistical property of object wave for blindextraction of real phase-shift have been proposed.3. Two kinds of common-path PSDHM have been built up by combining the
spatial beam splitting technique and the point-diffraction interferometry. Withbeamsplitters or gratings to split the light beam in space, the reference wave isreproduced by a pinhole filter to ensure the object wave and the referencewave to share the same path. The common-path configuration makes thedistributions of the two beams counteracted by each other in recordingprocess, and improves DHM's stability and practicability.
4. A dual-wavelength DHM with a slightly off-axis configuration has beenproposed based on the imaging characteristic of color CCD anddual-wavelength illumination. To realize the slightly off-axis recording andimprove the resolution of image, two single wavelength holograms withorthogonal spatial carrier frequencies can be extracted from the recordedcolor hologram with one exposure, and the dc term can be suppressed bysubtracting one from the other in property. Meanwhile, the real-timeunwrapped phase measurement is achieved by a synthetic wavelengthΛ12=λ1λ2/|λ1-λ2|, which is produced by beat frequency of two wavelengths λ1and λ2, which provides a useful measuring tool for moving object or dynamicprocess detection.
5. Two kinds of autofocusing schemes are proposed, which are based on thediffraction difference of dual-wavelength and two-angle off-axis illuminations of single wavelength, respectively. The image plane can be automaticallydetermined in the reconstructing process by seeking the minimal difference ofreconstructed images of two wavelengths or in different illuminationdirections. Both of algorithms can realize autofocusing exactly, and areapplicable to specimens without chromatic absorption and birefringence.
引文
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