本博士論文主要是利用掃描式穿透電子顯微鏡進行新穎的電腦科學顯微技術開發研究，根據所育觀測的樣品形貌大小和材料特性以及最終解析度需求，應用上可分為斷層掃描技術與掃描式同調繞射光顯微技術兩者。
前者之目標樣品為百奈米級材料的三維結構，我們選用以往需染色才能清楚解析的高分子聚合物作為樣品，利用掃描式穿透電子顯微鏡的原子序對比成像原理，在厚度兩百微米的樣品以無染色的方式完成了奈米級解析度的三維重建。
後者之目標樣品為二維材料之缺陷與差排量測，有別於以往受限於顯微鏡光斑大小的解析度定義，透過疊印法(ptychography)與新世代的像素陣列偵測器分析四維度之繞射圖譜系列組，我們可以重建亞埃級解析度的樣品圖像，並藉此觀測二維材料受輻射累加時的原子級損傷結果。
本論文內容將詳細介紹上述兩者技術之原理、實驗方法與現階段實驗成果，最後也將總結兩者之異同並與其未來展望。

Based on the specimen's scale and material properties, we investigate two computational imaging techniques in scanning transmission electron microscope (STEM), electron tomography and electron ptychography.
The first approach focuses on reconstructing the three-dimensional (3D) structure at the submicron to nanometer scale. Using the z-contrast imaging through high-angle annular dark-field imaging (HAADF), we successfully achieved a nanometer-scale resolution in the 3D reconstruction of the PS-P2VP sample, which had a thickness of 200 nm, without the requirement for staining. The elimination of staining processing enables us to perform the 3D tomography of the low-z sample without suffering artificial destruction.
Next, in contrast to conventional STEM HAADF images where resolution is limited by the incident probe size and scanning interval, electron ptychography, as a scanning coherent imaging technique, defines resolution based on wavelength and diffraction angle. By using ptychography and the novel pixel-array detectors to analyze a series of 4D diffraction patterns, we can reconstruct sample images with sub-angstrom resolution. Simultaneously, this enables the observation of atomic-level damage results when 2D materials are damaged by the cumulative radiation
This thesis will introduce in detail the principles, experimental methods, and experimental results of the above two technologies, and finally, summarize the advantages and disadvantages of the two technologies and their future prospects.

1. 緒論 8
1.1穿透式電子顯微鏡發展 8
1.2顯微鏡結構介紹 9
1.2.1 電子槍 9
1.2.2 透鏡組 10
1.2.3光圈 11
1.2.4 樣品座與試片載網 11
1.2.5 偵測器 13
2. 電子顯微鏡斷層掃描 14
2.1 前言 14
2.2 原理與步驟 16
2.1.1 經驗模態分解 16
2.1.2 投影對齊 18
2.1.3 背景值校正 19
2.1.4 Radon Transform 21
2.1.5 Fourier slice theorem 22
2.1.6 傅立葉迭代演算法 23
2.1.7 Fourier shell correlation 25
2.3 結果與討論 26
2.3.1光子晶體 26
2.3.2 PS-P2VP劑量模擬 27
2.3.3 染色問題 28
2.3.4 EMD 29
2.3.5 重建結果優化 31
2.3.6 數學模型比較 32
2.3.7 尺度比較 34
3. 電子掃描式同調繞射顯微術 35
3.1 前言 35
3.2 原理與步驟 39
3.2.1 繞射與傅立葉轉換 39
3.2.2 相位問題 41
3.2.3 解析度 42
3.2.4 相位恢復演算法Hybrid input-output 43
3.2.5 相位恢復演算法ptychographic iterative engine 44
3.2.6 座標修正position correction PIE 45
3.2.7 混合多模態光斑假設multi-mode PIE 47
3.3 結果與討論 49
3.3.1 Dr. Probe軟體 49
3.3.2 模擬實驗與測試結果 52
3.3.3 針對低訊噪比的繞射圖所進行的引導式最佳化ptychography 56
3.3.4 200kV加速電壓下量測二維材料的輻射損傷 65
4.結論 73
5.參考文獻 74

[1] M. Knoll, E. Ruska, Das elektronenmikroskop, Zeitschrift für physik, 78 (1932) 318-339.
[2] G. Binnig, H. Rohrer, Scanning tunneling microscopy—from birth to adolescence, reviews of modern physics, 59 (1987) 615.
[3] D. Cressey, E. Callaway, Cryo-electron microscopy wins chemistry Nobel, Nature, 550 (2017).
[4] M. Von Ardenne, Das Elektronen-Rastermikroskop: Theoretische Grundlagen, Zeitschrift für Physik, 109 (1938) 553-572.
[5] A.V. Crewe, M. Isaacson, D. Johnson, A simple scanning electron microscope, Review of Scientific Instruments, 40 (1969) 241-246.
[6] P. Batson, A. Domenicucci, E. Lemoine, Atomic resolution electronic structure in device development, Microscopy and Microanalysis, 3 (1997) 645-646.
[7] N. Dellby, L. Krivanek, D. Nellist, E. Batson, R. Lupini, Progress in aberration-corrected scanning transmission electron microscopy, Microscopy, 50 (2001) 177-185.
[8] C. Kisielowski, B. Freitag, M. Bischoff, H. Van Lin, S. Lazar, G. Knippels, P. Tiemeijer, M. van der Stam, S. von Harrach, M. Stekelenburg, Detection of single atoms and buried defects in three dimensions by aberration-corrected electron microscope with 0.5-Å information limit, Microscopy and Microanalysis, 14 (2008) 469-477.
[9] P. Roberts, J. Chapman, A. MacLeod, A CCD-based image recording system for the CTEM, Ultramicroscopy, 8 (1982) 385-396.
[10] H. Tietz, Design and characterization of 64 megapixel fiber optic coupled CMOS detector for transmission electron microscopy, Microscopy and Microanalysis, 14 (2008) 804-805.
[11] M.W. Tate, P. Purohit, D. Chamberlain, K.X. Nguyen, R. Hovden, C.S. Chang, P. Deb, E. Turgut, J.T. Heron, D.G. Schlom, High dynamic range pixel array detector for scanning transmission electron microscopy, Microscopy and Microanalysis, 22 (2016) 237-249.
[12] Y. Jiang, Z. Chen, Y. Han, P. Deb, H. Gao, S. Xie, P. Purohit, M.W. Tate, J. Park, S.M. Gruner, Electron ptychography of 2D materials to deep sub-ångström resolution, Nature, 559 (2018) 343-349.
[13] B. Plotkin-Swing, G.J. Corbin, S. De Carlo, N. Dellby, C. Hoermann, M.V. Hoffman, T.C. Lovejoy, C.E. Meyer, A. Mittelberger, R. Pantelic, Hybrid pixel direct detector for electron energy loss spectroscopy, Ultramicroscopy, 217 (2020) 113067.
[14] L. Deng, Y. Gong, X. Lu, Y. Lin, Z. Ma, M. Xie, STELA: A real-time scene text detector with learned anchor, IEEE Access, 7 (2019) 153400-153407.
[15] A. Pakzad, R. dos Reis, The Performance of Detectors for Diffraction-Based Studies in (S) TEM, Microscopy and Microanalysis, 28 (2022) 3192-3193.
[16] A.A. Murthy, P.M. Das, S.M. Ribet, C. Kopas, J. Lee, M.J. Reagor, L. Zhou, M.J. Kramer, M.C. Hersam, M. Checchin, Potential nanoscale sources of decoherence in niobium based transmon qubit architectures, Fermi National Accelerator Lab.(FNAL), Batavia, IL (United States), 2022.
[17] M.M. Woolfson, M.M. Woolfson, An introduction to X-ray crystallography, Cambridge University Press1997.
[18] M. Smyth, J. Martin, x Ray crystallography, Molecular Pathology, 53 (2000) 8.
[19] F. Hosokawa, H. Sawada, Y. Kondo, K. Takayanagi, K. Suenaga, Development of Cs and Cc correctors for transmission electron microscopy, Microscopy, 62 (2013) 23-41.
[20] A. Kak, M. Slaney, Principles of Computerized Tomographic Imaging. O’Malley RE ed, SIAM, IEEE Press, New York, DOI (1988).
[21] J. Trampert, J.J. Leveque, Simultaneous iterative reconstruction technique: Physical interpretation based on the generalized least squares solution, Journal of Geophysical Research: Solid Earth, 95 (1990) 12553-12559.
[22] S. Singh, M.K. Kalra, J. Hsieh, P.E. Licato, S. Do, H.H. Pien, M.A. Blake, Abdominal CT: comparison of adaptive statistical iterative and filtered back projection reconstruction techniques, Radiology, 257 (2010) 373-383.
[23] R. Gordon, R. Bender, G.T. Herman, Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography, Journal of theoretical Biology, 29 (1970) 471-481.
[24] M. Scott, C.-C. Chen, M. Mecklenburg, C. Zhu, R. Xu, P. Ercius, U. Dahmen, B. Regan, J. Miao, Electron tomography at 2.4-ångström resolution, Nature, 483 (2012) 444-447.
[25] C.-C. Chen, C. Zhu, E.R. White, C.-Y. Chiu, M. Scott, B. Regan, L.D. Marks, Y. Huang, J. Miao, Three-dimensional imaging of dislocations in a nanoparticle at atomic resolution, Nature, 496 (2013) 74-77.
[26] R. Xu, C.-C. Chen, L. Wu, M. Scott, W. Theis, C. Ophus, M. Bartels, Y. Yang, H. Ramezani-Dakhel, M.R. Sawaya, Three-dimensional coordinates of individual atoms in materials revealed by electron tomography, Nature materials, 14 (2015) 1099-1103.
[27] Y. Yang, C.-C. Chen, M. Scott, C. Ophus, R. Xu, A. Pryor, L. Wu, F. Sun, W. Theis, J. Zhou, Deciphering chemical order/disorder and material properties at the single-atom level, Nature, 542 (2017) 75-79.
[28] 林義銘, 蔣酉旺, 高分子電子顯微影像技術, 化工, 64 (2017) 15-27.
[29] N.E. Huang, Z. Shen, S.R. Long, M.C. Wu, H.H. Shih, Q. Zheng, N.-C. Yen, C.C. Tung, H.H. Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proceedings of the Royal Society of London. Series A: mathematical, physical and engineering sciences, 454 (1998) 903-995.
[30] J. Miao, F. Förster, O. Levi, Equally sloped tomography with oversampling reconstruction, Physical Review B, 72 (2005) 052103.
[31] A. Pryor Jr, Y. Yang, A. Rana, M. Gallagher-Jones, J. Zhou, Y.H. Lo, G. Melinte, W. Chiu, J.A. Rodriguez, J. Miao, GENFIRE: A generalized Fourier iterative reconstruction algorithm for high-resolution 3D imaging, Scientific reports, 7 (2017) 10409.
[32] E. Armstrong, C. O'Dwyer, Artificial opal photonic crystals and inverse opal structures–fundamentals and applications from optics to energy storage, Journal of materials chemistry C, 3 (2015) 6109-6143.
[33] R.J. Macfarlane, B. Kim, B. Lee, R.A. Weitekamp, C.M. Bates, S.F. Lee, A.B. Chang, K.T. Delaney, G.H. Fredrickson, H.A. Atwater, Improving brush polymer infrared one-dimensional photonic crystals via linear polymer additives, Journal of the American Chemical Society, 136 (2014) 17374-17377.
[34] E.-L. Lin, W.-L. Hsu, Y.-W. Chiang, Trapping structural coloration by a bioinspired gyroid microstructure in solid state, ACS nano, 12 (2018) 485-493.
[35] M.A. Hayat, Principles and techniques of electron microscopy. Biological applications, Edward Arnold.1981.
[36] A.W. Miller, J.F. Robyt, Detection of dextransucrase and levansucrase on polyacrylamide gels by the periodic acid-Schiff stain: staining artifacts and their prevention, Analytical biochemistry, 156 (1986) 357-363.
[37] P. Bindhu, R. Krishnapillai, P. Thomas, P. Jayanthi, Facts in artifacts, Journal of oral and maxillofacial pathology: JOMFP, 17 (2013) 397.
[38] C.-W. Wang, S.-M. Ka, A. Chen, Robust image registration of biological microscopic images, Scientific reports, 4 (2014) 1-12.
[39] D. Sayre, Some implications of a theorem due to Shannon, Acta Crystallographica, 5 (1952) 843-843.
[40] D. Sayre, M. Schlenker, Imaging processes and coherence in physics, Springer Lecture Notes in Physics, 112 (1980) 229-235.
[41] W.-B. Yun, J. Kirz, D. Sayre, Observation of the soft X-ray diffraction pattern of a single diatom, Acta Crystallographica Section A: Foundations of Crystallography, 43 (1987) 131-133.
[42] J. Miao, D. Sayre, H. Chapman, Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects, JOSA A, 15 (1998) 1662-1669.
[43] J. Miao, P. Charalambous, J. Kirz, D. Sayre, Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens, Nature, 400 (1999) 342-344.
[44] R. Hegerl, W. Hoppe, Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primärstrahlwellenfeld, Berichte der Bunsengesellschaft für physikalische Chemie, 74 (1970) 1148-1154.
[45] J. Rodenburg, R. Bates, The theory of super-resolution electron microscopy via Wigner-distribution deconvolution, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, 339 (1992) 521-553.
[46] J. Rodenburg, B. McCallum, P. Nellist, Experimental tests on double-resolution coherent imaging via STEM, Ultramicroscopy, 48 (1993) 304-314.
[47] J.M. Rodenburg, H.M. Faulkner, A phase retrieval algorithm for shifting illumination, Applied physics letters, 85 (2004) 4795-4797.
[48] J.M. Rodenburg, A. Hurst, A.G. Cullis, B.R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, I. Johnson, Hard-x-ray lensless imaging of extended objects, Physical review letters, 98 (2007) 034801.
[49] P. Thibault, M. Dierolf, O. Bunk, A. Menzel, F. Pfeiffer, Probe retrieval in ptychographic coherent diffractive imaging, Ultramicroscopy, 109 (2009) 338-343.
[50] A. Maiden, M. Humphry, M. Sarahan, B. Kraus, J. Rodenburg, An annealing algorithm to correct positioning errors in ptychography, Ultramicroscopy, 120 (2012) 64-72.
[51] P. Thibault, A. Menzel, Reconstructing state mixtures from diffraction measurements, Nature, 494 (2013) 68-71.
[52] P. Nellist, B. McCallum, J.M. Rodenburg, Resolution beyond the'information limit'in transmission electron microscopy, nature, 374 (1995) 630-632.
[53] J. Rodenburg, A. Hurst, A. Cullis, Transmission microscopy without lenses for objects of unlimited size, Ultramicroscopy, 107 (2007) 227-231.
[54] A.M. Maiden, J.M. Rodenburg, An improved ptychographical phase retrieval algorithm for diffractive imaging, Ultramicroscopy, 109 (2009) 1256-1262.
[55] J. Spence, J. Zuo, Large dynamic range, parallel detection system for electron diffraction and imaging, Review of Scientific Instruments, 59 (1988) 2102-2105.
[56] Z. Chen, Y. Jiang, Y.-T. Shao, M.E. Holtz, M. Odstrčil, M. Guizar-Sicairos, I. Hanke, S. Ganschow, D.G. Schlom, D.A. Muller, Electron ptychography achieves atomic-resolution limits set by lattice vibrations, Science, 372 (2021) 826-831.
[57] J. Miao, D. Sayre, On possible extensions of X-ray crystallography through diffraction-pattern oversampling, Acta Crystallographica Section A: Foundations of Crystallography, 56 (2000) 596-605.
[58] C.-C. Chen, J. Miao, C. Wang, T. Lee, Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method, Physical Review B, 76 (2007) 064113.
[59] K. Kim, M. Yankowitz, B. Fallahazad, S. Kang, H.C. Movva, S. Huang, S. Larentis, C.M. Corbet, T. Taniguchi, K. Watanabe, van der Waals heterostructures with high accuracy rotational alignment, Nano letters, 16 (2016) 1989-1995.
[60] J. Choi, W.-T. Hsu, L.-S. Lu, L. Sun, H.-Y. Cheng, M.-H. Lee, J. Quan, K. Tran, C.-Y. Wang, M. Staab, Moiré potential impedes interlayer exciton diffusion in van der Waals heterostructures, Science advances, 6 (2020) eaba8866.
[61] M.J. Peet, R. Henderson, C.J. Russo, The energy dependence of contrast and damage in electron cryomicroscopy of biological molecules, Ultramicroscopy, 203 (2019) 125-131.
[62] Q. Chen, C. Dwyer, G. Sheng, C. Zhu, X. Li, C. Zheng, Y. Zhu, Imaging beam‐sensitive materials by electron microscopy, Advanced Materials, 32 (2020) 1907619.
[63] M. Ilett, M. S'ari, H. Freeman, Z. Aslam, N. Koniuch, M. Afzali, J. Cattle, R. Hooley, T. Roncal-Herrero, S.M. Collins, Analysis of complex, beam-sensitive materials by transmission electron microscopy and associated techniques, Philosophical Transactions of the Royal Society A, 378 (2020) 20190601.
[64] H.-P. Komsa, S. Kurasch, O. Lehtinen, U. Kaiser, A.V. Krasheninnikov, From point to extended defects in two-dimensional MoS 2: Evolution of atomic structure under electron irradiation, Physical Review B, 88 (2013) 035301.
[65] K.L. Tai, C.W. Huang, R.F. Cai, G.M. Huang, Y.T. Tseng, J. Chen, W.W. Wu, Atomic‐scale fabrication of in‐plane heterojunctions of few‐layer MoS2 via in situ scanning transmission electron microscopy, Small, 16 (2020) 1905516.