斷層攝影術乃是當代科學發展中的一個重要技術，而本文將利用斷層攝影術於不同角度下獲取鉑釕奈米原子顆粒的二維影像投影片，並利用一種三維影像重組技術：等斜率斷層掃描重組出立體影像，而後將重組後的三維影像做單原子層厚度的切片，以觀察其內部結構，並將這些切片進行原子追蹤得到原子座標，分類出鉑釕不同原子位置，以觀察其內部共存之奈米結構。

Tomography is a breakthrough technique in scientific development nowadays. In this thesis, we take two-dimensional images of tomography in different angles as projections. Using equally sloped tomography algorithm (EST) to get the three-dimensional reconstruction of the Pt(Platinum)Ru(Ruthenium) nanoparticle. Divide the reconstruction into several slices with the single atomic layer thickness. Afterward, we search for the coordinates of atoms from these slices. Classifying these coordinates into Pt(Platinum) and Ru(Ruthenium) to observe the internal nanostructure.

論文審定書 i
誌謝 ii
摘要 iii
英文摘要 iv
目錄 v
圖目錄 vi
表目錄 viii
第一章 導論 1
1-1前言 1
1-2實驗動機 2
第二章 實驗原理 4
2-1斷層攝影術數學原理 4
2-2傅立葉切片定理 5
2-3等斜率斷層掃描(equally sloped tomography, EST) 8
2-4二維投影校準(alignment)以及反投影校準 12
2-5維納濾波器(Wiener filter) 16
第三章 三維影像重組結果 20
第四章 追蹤原子位置 28
4-1追蹤原子點座標位置 28
4-2鉑釕原子分類 37
第五章 結論 42
參考資料 43

M. C. Scott, Chien-Chun Chen, Matthew Mecklenburg, Chun Zhu, Rui Xu, Peter
Ercius, Ulrich Dahmen, B. C. Regan & Jianwei Miao, Electron tomography at 2.4-
ångström resolution, Nature 483, 444–447 (2012)
L.E. Sutton (ed.), Table of interatomic distances and configuration in molecules and ions, Supplement 1956-1959, Special publication No. 18, Chemical Society, London, UK, (1965)
吳俊瑋, 區塊式濾波反投影演算法設計與 FPGA 實作 (I), 國立交通大學資訊科學與工程研究所碩士論文(2006)
J. Miao, Friedrich Förster & O. Levi, Equally Sloped Tomography with
Oversampling Reconstruction, Phys. Rev. B. 72, 052103 (2005)
A. Averbuch, R.R. Coifman, D.L. Donoho, M. Elad, M. Israeli, Fast and accurate
Polar Fourier transform, Appl. Comput. Harmon. Anal. 21, 145–167 (2006)
Bailey, D. H. & Swarztrauber, P. N. The fractional Fourier transform and applications. SIAM Rev. 33, 389–404 (1991)
Chien-Chun Chen, Chun Zhu, Edward R. White, Chin-Yi Chiu, M. C. Scott, B. C.
Regan, Laurence D. Marks, Yu Huang & Jianwei Miao, Three-dimensional
imaging of dislocations in a nanoparticle at atomic resolution, Nature 496, 74–77
(2013)
R. Xu, C.-C. Chen, L. Wu, M. C. Scott, W. Theis, C. Ophus, M. Bartels, Y. Yang, H. Ramezani-Dakhel, M. R. Sawaya, H. Heinz, L. D. Marks, P. Ercius and J. Miao , “Three-Dimensional Coordinates of Individual Atoms in Materials Revealed by Electron Tomography”, Nat. Mater. 14, 1099-1103 (2015)
B. D. A. Levin, E. Padgett, C.-C. Chen, M. C. Scott, R. Xu, W. Theis, Y. Jiang, Y. Yang, C. Ophus, H. Zhang, D.-H. Ha, D. Wang, Y. Yu, H. D. Abruña, R. D. Robinson, P. Ercius, L. F. Kourkoutis, J. Miao, D.A. Muller and R. Hovden, "Nanomaterial datasets to advance tomography in scanning transmission electron microscopy", Sci. Data 3, 160041 (2016)
Jiang, H. et al. Quantitative 3D imaging of whole, unstained cells by using Xray diffraction microscopy. Proc. Natl. Acad. Sci. USA 107, 11234–11239 (2010)
J. A. Rodriguez, R. Xu, C.-C. Chen, Z. Huang, H. Jiang, A. L. Chen, K. S. Raines, A. Pryor, Jr., D, Nam, L. Wiegart, C. Song, A. Madsen, Y. Chushkin, F. Zontone, P. J. Bradley and J. Miao, “Three-dimensional Coherent X-ray Diffractive Imaging of Whole, Frozen-Hydrated Cells”, IUCrJ 2, 575–583 (2015)
Fahimian, B. P., Mao, Y., Cloetens, P., & Miao, J. Low dose X-ray phasecontrast and absorption CT using equally-sloped tomograph. Phys. Med. Bio. 55, 5383-5400 (2010)
J. Miao, C. -C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D.
Ramunno-Johnson, T.K. Lee & S.H. Risbud, Three-Dimensional GaN-Ga2O3
Core Shell Structure Revealed by X-ray Diffraction Microscopy, Phys. Rev. Lett.
97, 215503 (2006).
H. Jiang, C. Song, C.-C. Chen, R. Xu, K. S. Raines, B. P. Fahimian, C.-H.Lu, T.
K. Lee, A. Nakashima, J. Urano, T. Ishikawa, F. Tamanoi, & J. Miao, Quantitative
3D Imaging of Whole, Unstained Cells by Using X-ray Diffraction Microscopy,
Proc. Natl. Acad. Sci. USA 107, 11234-11239 (2010).
B. P. Fahimian, Y. Mao, P. Cloetens, & J. Miao, Low Dose X-ray Phase-Contrast
and Absorption CT Using Equally-Sloped Tomograph, Phys. Med. Bio. 55, 5383-
5400 (2010)
Y. Zhao, E. Brun, P. Coan, Z. Huang, A. Sztrokay, P. C. Diemoz, S. Liebhardt, A.
Mittone, S. Gasilov, J. Miao & A. Bravin, High resolution, low dose phase
contrast x-ray tomography for 3D diagnosis of human breast cancers, Proc. Natl.
58 Acad. Sci. USA 109, 18290-18294 (2012)
Norbert Wiener (1949), Extrapolation, Interpolation, and Smoothing of Stationary Time Series, New York: Wiley, ISBN 0-262-73005-7
吳宗翰, 利用總體經驗分析提取奈米材料的三維原子座標Determination of 3D Atomic Coordinates by Using EEMD, 國立中山大學物理系碩士論文(2016)
Y. Yang, C. –C. Chen, M. C. Scott, C. Ophus, R. Xu, A. P. Jr, L. Wu, F. Sun, W. Theis, J. Zhou, M. Eisenbach, P. R. C. Kent, R. F. Sabirianov, H. Zeng, P. Ercius and J. Miao, "Deciphering 3D structure and material properties at the single-atom level",Nature 542, 15-79 (2017)