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研究生：	廖佳麒 Liao, Chia-Chi
論文名稱：	寬頻光干涉應用於近場光學與光學同調斷層掃描之研究 Research on Using Interference with Broad-bandwidth Light in Near-field Optics and Mueller Optical Coherence Tomography
指導教授：	羅裕龍 Lo, Yu-Lung
學位類別：	博士 Doctor
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2013
畢業學年度：	101
語文別：	英文
論文頁數：	158
中文關鍵詞：	無孔徑式掃描近場光學顯微鏡、訊號調變、光學同調斷層掃描、異向光學材料、謬勒矩陣、基因演算法
外文關鍵詞：	Apertureless scanning near-field optical microscopy, Modulation signal analysis, Optical coherence tomography, Anisotropic optical materials, Mueller matrix, Genetic algorithm
相關次數：	點閱：154 下載：7
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　　本論文應用寬頻光低同調干涉特性，使其在無孔徑式掃描光學近場顯微技術系統中濾除大範圍的背景雜訊，並結合所發展出光學信號分析模型以推導出各種不同方法來改良信號。研究也將寬頻光干涉技術應用至光學同調斷層掃描技術進行延伸量測材料的多重光學異向參數。
　　無孔徑式近場光學顯微技術主要應用於奈米尺度之材料性質檢測，其解析度可達10奈米，是具有超高解析度檢測材料之新興技術。而對於無孔徑式掃描近場光學顯微鏡而言，如何消除背景散射光是改良系統效能的重要方向；在傳統的無孔徑式近場光學顯微技術多使用自調變或外差調變等調變技術來減弱背景干擾，本研究先提出一唯象模型來分析顯微鏡中包含近場交互作用效應與背景信號所產生的總信號。模型驗證可符合使用聲光調變器進行外差調變量測之實驗所獲得的壓克力材料(Polymethylmethacrylate, PMMA)響應頻譜，因此我們可根據此模型來判定系統中的實驗參數，進而減小背景信號的影響，以確認實驗可量得真實的近場信號。以此唯象模型為基礎，分析模型可驗證系統引入寬頻光干涉技術，利用其低同調干涉條件濾除背景雜訊，以獲得無背景雜訊之近場信號；或另一系統使用擬外差干涉技術達成無背景雜訊之近場量測。然而此兩種技術都需要昂貴儀器與繁複嚴格校正技術，因此本研究再以唯象模型為基礎，引入基因演算法，發展不需使用複雜且昂貴的系統便可精確地定義奈米材料性質，分析其材料結構、殘留應力、應變量等特性之方法。本研究可改良信號並拓展整套無孔徑近場光學顯微技術的應用面，研究成果將是探討奈米尺度下量測分析材料的一項利器，提供最新奈米級量測能力，並大幅改善量測之準確性，是支援生醫及光電材料研究強而有力之檢測技術。
　　本論文並延伸白光干涉技術於雙折射材料之檢測，研究發展出一套偏極化光學同調斷層掃描儀，利用其高解析度與色散補償獲得更多資訊，比較演算來量得線性雙折射材料各反射層的厚度、折射率、主軸方位角、相位延遲量、以及尋常光與非尋常光折射率。本研究再以此架構為基礎，將系統延伸至謬勒光學同調斷層掃描儀。此謬勒光學同調斷層掃描儀可量得待測物的謬勒矩陣，因此本研究將根據謬勒矩陣之分析，結合謬勒矩陣微分演算與謬勒矩陣分解法，提出一合成模型來解析混合材料之線性雙折射/雙衰減、旋性雙折射/雙衰減與去偏極效應。此模型相較於既存的謬勒矩陣微分演算可拓展參數量測範圍至全域量測；而相較於謬勒矩陣分解法，此模型可解決元素矩陣相乘時需特定排列條件之限制。實驗則使用偏光儀與合成模型成功解析甲殼素、葡萄糖與微米粒子之混合物中旋性雙折射/線性雙折射/去偏極效應；以及兩種磁流材料分別具有的旋性雙折射/旋性雙衰減/去偏極效應，或線性雙折射/線性雙衰減/去偏極效應之特性。實驗亦驗證合成模型對於擁有多重異向特性之真實待測物能提供較穩定的量測結果。而此理論應用於光學同調斷層掃描儀中，更可獲得待測物的深度截面資訊，更提供生物科技或工業技術上相對應之光學異向材料理想之檢測技術。

Using the low coherence of the broad-bandwidth light to improve and extend the existing optical measurement technique is discussed in this dissertation. An improvement in the signal of the apertureless scanning near-field optical microscopy (a-SNOM) by using the broad-bandwidth light is derived by the proposed phenomenological model. Also, a measurement in the materials containing multiple optically anisotropic properties by using optical coherence tomography (OCT) based on the low coherence interfreometry with broad-bandwidth light is introduced in this study.
A-SNOM enables the surface properties of optically scattering materials to be measured with an ultra-high resolution. However, the detection signal is inevitably contaminated by the background noise. This noise must be eliminated if the properties of the measured sample are to be reliably determined. Modulation methods such as homodyne and heterodyne detections are employed in a-SNOM in order to eliminate serious background noises from scattering fields. Usually, the frequency-modulated detection signal in a-SNOM is generally analyzed using a simple dipole-interaction model based only on the near-field interaction. However, the simulated a-SNOM spectra obtained using such models are in poor agreement with the experimental results since the effects of background noise are ignored. Accordingly, this study proposes a new phenomenological model for analyzing the a-SNOM detection signal in which the effects of both the dipole-interaction field and the background noise are taken into account. It is shown that the simulated a-SNOM spectrum for polymethylmethacrylate (PMMA) sample in the standard acousto-optic modulator (AOM) based heterodyne detection configuration is in good agreement with the experimental results. Additionally, the literature contains various configurations capable of directly obtaining a background-free detection signal of a-SNOM (the a-SNOM configuration with the broad-bandwidth light source and a pseudo-heterodyne a-SNOM configuration), but these methods generally requires the use of a complex experimental setup and the strict calibration. Accordingly, the present study provides the robust phenomenological model with a genetic algorithm for inversely extracting material properties without using a background-free signal from a complex experimental setup. Finally, the properties of SiC crystal in different structures are successfully and inversely extracted by only using the first and second orders of modulation signals as multiple objective functions in cure-fitting genetic algorithm.
A new polarization-sensitive optical coherence tomography (PS-OCT) system is proposed for obtaining simultaneous measurements of the thickness, mean group refractive index, apparent phase retardation, and optical axis orientation of a linear birefringent material. This study extends the proposed OCT system to a Mueller OCT to extract linear birefringence (LB), linear dichroism (LD) parameters properties in the optically anisotropic material. The full 4×4 Mueller matrix of the sample is able to be measured by the Mueller OCT. Hence, based on the analysis of the Mueller matrix, a hybrid model comprising the differential Mueller matrix formalism and the Mueller matrix decomposition method is proposed for extracting the linear birefringence (LB), linear dichroism (LD), circular birefringence (CB), circular dichroism (CD), and depolarization properties (Dep) of turbid optical samples. In contrast to the differential-based Mueller matrix method, the proposed hybrid model provides full-range measurements of all the anisotropic properties of the optical sample. Furthermore, compared to the decomposition-based Mueller matrix method, the proposed model is insensitive to the multiplication order of the constituent basis matrices. The validity of the proposed method is confirmed by extracting the anisotropic properties of a compound chitosan-glucose-microsphere sample with LB/CB/Dep properties and two ferrofluidic samples with CB/CD/Dep and LB/LD/Dep properties by Stokes polarimetry, respectively. The results presented in this study confirm that the proposed model has significant potential for extracting the optical parameters of real-world samples characterized by either single or multiple anisotropic properties. As such, inclusive of the ability to get in-depth cross-sectional images of the sample by OCT, the proposed Mueller OCT combining the hybrid model provides an ideal solution for biological and industrial application in which a precise knowledge of the optical properties of an anisotropic material is required.

中文摘要...2
Abstract...4
Table of Contents...6
List of Figures...9
List of Tables...12
Chapter 1 Introduction...13
1.1 Apertureless Scanning Near-field Optical Microscopy...13
1.2 Optical Coherence Tomography...16
1.3 Analysis of the Mueller Matrix...21
1.4 Destination and Motivation of the Research...23
1.4.1 For apertureless near-field scanning optical microscopy...23
1.4.2 For optical coherence tomography...24
1.4.3 For analysis of the Mueller matrix...24
Chapter 2 Basic Theories...26
2.1 Basic Theories of Apertureless Scanning Near-field Optical Microscopy...26
2.1.1 Near-field optics theories...26
2.1.2 Scanning near-field optical microscopy...28
2.1.3 Apertureless scanning near-field scanning optical microscopy...29
2.2 Basic Theories of Optical Coherence Tomography...31
2.2.1 OCT based on low coherence interferometry...31
2.2.2 Polarization sensitive OCT...35
2.3 Basic Theories of Optically Anisotropic Properties and Mueller Matrix Analysis...42
2.3.1 Linear birefringence (LB) materials...42
2.3.2 Circular birefringence (CB) materials...47
2.3.3 Linear dichroism (LD) materials...49
2.3.4 Circular dichroism (CD) materials...50
2.3.5 Stokes vectors and Mueller matrix...51
2.3.6 Mueller matrices of LB, CB, LD, and CD...52
Chapter 3 Methodology in Apertureless Scanning Near-field Optical Microscopy...54
3.1 Phenomenological Model of A-SNOM...54
3.2 Demonstration of the Robustness in the Phenomenological Model...58
3.2.1 Application of the phenomenological model to the acousto-optic modulator based heterodyne a-SNOM detection...59
3.2.2 Application of phenomenological model to pseudo-heterodyne detection...65
3.2.3 Application of the phenomenological model to the a-SNOM detection by using the broad-bandwidth light source...71
3.3 Elimination of Background Noise in General A-SNOM Detection Signal...77
3.4 Application of Phenomenological Model to Residual Stress and Strain Measurement...82
3.5 Extraction of Unknown Factors in Phenomenological Model Using Genetic Algorithms...85
3.5.1 Example of extracting properties of materials by using genetic algorithms in a general AOM-based heterodyne a-SNOM...89
Chapter 4 Methodology in Mueller Matrix Analysis...93
4.1 Mueller-Stokes Parameter Measurement Method...93
4.2 Differential Mueller Matrix...94
4.3 Hybrid Mueller Matrix Model...99
4.3.1 LB/CB/Dep composite sample...99
4.3.2 CB/CD/Dep composite sample...102
4.3.3 LB/LD/Dep composite sample...104
4.3.4 LB/CB/LD/CD/Dep composite sample...105
4.4 Simulation Results...106
4.4.1 LB/CB/Dep composite sample...107
4.4.2 CB/CD/Dep composite sample...108
4.4.3 LB/LD/Dep composite sample...109
4.4.4 LB/CB/LD/CD/Dep composite sample...111
4.5 Experimental Measurement of Anisotropic Parameters of Turbid Media...112
4.5.1 Composite chitosan-glucose-microsphere sample...114
4.5.2 Ferrofluidic samples with CB/CD/Dep and LB/LD/Dep properties...116
4.6 Appendix of Macroscopic Mueller Matrix of LB/LD...120
Chapter 5 Methodology in Mueller Optical Coherence...122
5.1 Mueller OCT to Measure Mueller Matrix...122
5.2 Analytical Hybrid Model for Mueller Matrix Containing LB and LD...125
5.2.1 Differential matrix formulation...125
5.2.2 Hybrid model for Mueller OCT system...127
5.3 Signal Process by Hilbert Transform...130
5.4 Simulation Results...133
5.5 Experiments on Mueller OCT...135
5.5.1 Measurement System and Devices...135
5.5.2 Measurement in Quarter wave plate...139
Chapter 6 Conclusions and Discussions...144
6.1 Conclusions of A-SNOM...144
6.1.1 Phenomenological model of a-SNOM...144
6.1.2 Eliminate background in a-SNOM to obtain exact measurement...146
6.2 Conclusions of Analysis in the Mueller Matrix...147
6.3 Conclusions of Mueller OCT...148
6.4 Future Works...148
Reference...150
List of Publications...158
List of Figures
Fig. 1.1 Schematic of typical SNOM set-up...14
Fig. 1.2 Schematic of conventional apertureless near-field optical microscopy...14
Fig. 1.3 Schematic of the OCT scanner...17
Fig. 1.4 Schematic diagram of the birefringence-sensitive optical coherence-domain interferometer...19
Fig. 1.5 Stroboscopic ultrahigh-resolution full-field optical coherence tomography...19
Fig. 1.6 New OCT structure with no high-precision scanning stage and stage controller...20
Fig. 1.7 Schematic of the polarization-sensitive OCT system for measuring the Mueller matrix...21
Fig. 2.1 Quasi-electrostatic theory model of a-SNOM represents the probe tip by a sphere, and the interaction with the sample by an image dipole...30
Fig. 2.2 The basic structure of the low coherence interferometer...32
Fig. 2.3 Schematic diagram of the PS-OCT system...36
Fig. 2.4 The refractive index ellipsoid of the uniaxial crystal...44
Fig. 2.5 (A) Positive uniaxial crystal ; (B) Negative uniaxial Crystal...45
Fig. 2.6 The two axes of the birefringent material...46
Fig. 2.7 (a) The superposition of right- and left-circularly state at z = 0 (b) The superposition of right- and left-circularly state at z = d (nL＞nR)...48
Fig. 2.8 Origin of the circular dichroism effect...50
Fig. 2.9 Schematic diagram of Stokes parameter method...52
Fig. 3.1 View of near-field region...54
Fig. 3.2 Schematic illustration of AOM-based heterodyne a-SNOM...59
Fig. 3.3 Comparison of simulated and experimental modulated AOM-based heterodyne detection signals for PMMA sample...64
Fig. 3.4 Schematic illustration of pseudo-heterodyne detection configuration...65
Fig. 3.5 Comparison of simulated and experimental detection signal in pseudo-heterodyne configuration...70
Fig. 3.6 Schematic illustration of a-SNOM configuration based on broad-bandwidth light source...72
Fig. 3.7 Comparison of simulation results and experimental results for background-free detection signal in homodyne configuration described...76
Fig. 3.8 Simulated a-SNOM spectra for various experimental configurations (the tip-sample interaction is modeled using Eq. (3.2))...79
Fig. 3.9 Simulated a-SNOM spectra for various experimental configurations (the tip-sample interaction is modeled using Eq. (2.11))...82
Fig. 3.10 Simulated a-SNOM spectra for SiC sample with regions of residual stress...84
Fig. 3.11 Flow chart of genetic algorithms used to determine unknown factors in phenomenological model...89
Fig. 3.12 (a) So-called experimental intensity spectra corresponding to 1st and 2nd order harmonic modulation signals from a standard sample (6H-SiC); (b) so-called experimental intensity spectra corresponding to 6H-SiC, 4H-SiC and 3C-SiC simulated by 2nd order harmonic modulation detections; (c) the extracted background-free signals corresponding to 6H-SiC, 4H-SiC and 3C-SiC in 2nd order harmonic modulation detections...92
Fig. 4.1 Schematic illustration of experimental Mueller-Stokes measurement system...93
Fig. 4.2 Schematic illustration of composite sample with LB, CB and Dep properties...99
Fig. 4.3 Schematic illustration of composite sample with CB, CD and Dep properties...102
Fig. 4.4 Schematic illustration of composite sample with LB/LD and Dep properties...104
Fig. 4.5 Flow chart of a modified algorithm based on using the differential calculation method and the hybrid model...106
Fig. 4.6 Extracted values of α, β and γ for LB/CB/Dep sample using hybrid model, differential calculation method and decomposition method...108
Fig. 4.7 Extracted values of γ and R for CB/CD/Dep sample using hybrid model, differential calculation method and decomposition method...109
Fig 4.8 Extracted values of α, β, θd, and D for LB/LD/Dep composite sample using hybrid model (GA), differential calculation method and decomposition method...110
Fig. 4.9 Extracted values of α, β, γ, θd, D, and R for LB/CB/LD/CD/Dep sample using differential calculation method, and exactly β and γ are modified by the hybrid model...112
Fig. 4.10 Schematic illustration of experimental measurement system...113
Fig. 4.11 Experimental results for LB/CB/Dep properties of chitosan/glucose solutions with various chitosan concentrations...115
Fig. 4.12 Experimental results for LB/CB/Dep properties of chitosan/glucose solutions with various glucose concentrations...116
Fig. 4.13 Transmission electron microscopy image of the Fe3O4 nanoparticles...117
Fig.4.14 Ferrofluidic samples with (a) CB and CD properties, and (b) LB and LD properties...118
Fig. 4.15 Experimental results for CB/CD/Dep properties of ferrofluidic sample with Fe3O4 concentration of 0.01 M...119
Fig. 4.16 Experimental results for LB/LD/Dep properties of ferrofluidic sample with Fe3O4 concentration of 0.025 M...120
Fig. 5.1 Schematic illustration of proposed Mueller OCT system...123
Fig. 5.2 Schematic diagram of the model of the measurement on the sample containing LB/LD in OCT system...128
Fig. 5.3 The signal processing block diagram of solving the amplitude and phase of interferometric signals...133
Fig. 5.4 Simulated results for α, β, θd, and D of a LB/LD sample measured by the Mueller OCT and solved by hybrid model in GAs...135
Fig. 5.5 The experimental structure...139
Fig. 5.6 Comparison of theoretical and experimental results for optical axis orientation angle of LB...142
Fig. 5.7 Comparison of theoretical and experimental results for phase retardation of LB...142
Fig. 5.8 Comparison of theoretical and experimental results for orientation angle of LD...143
Fig. 5.9 Comparison of theoretical and experimental results for linear dichroism...143
List of Tables
Table 2.1 Symbols, ranges and definitions of effective parameters of turbid media with hybrid properties...53
Table 3.1 Dielectric constants of AFM tip and sample...70
Table 3.2 Known and unknown factors in phenomenological model of a-SNOM...88
Table 5.1 Specifications of system...137
Table 5.2 Specification of the stage controller...137
Table 5.3 Specification of the motorized stage...138
Table 5.4 Specification of the variable wave-plate...138
Table 5.5 Calibration value of the variable wave plate for the desired polarization...140
                                    

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