本研究主要為改良斷層相位顯微鏡 (Tomographic Phase Microscopy, TPM)，其做法為在新架構中增設反射鏡及離軸全像架構，在保留傳統TPM功能外，亦同時降低系統複雜度以及掃描時間。本系統利用離軸數位全像概念先獲取樣本不同方向的相位投影，再利用相位展開 (Phase Unwrapping, PhU)演算法，將包裹相位展開成連續相位分佈，最後透過濾波反投影 (Filtered-Back Projection, FBP)演算法，重建物體的三維折射率分佈。
本研究可分為模擬以及實驗兩部分。在模擬方面，主要將各種影像還原演算法建立於重建流程中，用於處理實驗所擷取的原始數據；在實驗部份，先是建構了鏡像輔助TPM系統，而後利用已知粒徑與折射率的小球作為樣本並取得小球的三維折射率分佈來驗證新架構與演算法，亦將本系統應用於細胞三維折射率分佈的量測。最後比較半角度與全角度範圍的小球重建影像相似度。

The main purpose of this study is to improve tomographic phase microscopy (TPM). The method is to increase mirror and off-axis holographic structure in the novel system. Not only saving functions of the traditional TPM, but also reducing system complexity and scanning time. The first, the system uses the concept of off-axis digital holography to obtain phase projections of sample in different directions, and the wrapped phase will be unwrapped to successive phase distribution by phase unwrapping algorithm. Finally, the three-dimensional refractive index distribution of the reconstructed object by filtered backprojection (FBP)algorithm.
There are simulation and experiment in the study. In the simulation, the various algorithms about image reconstruction will be established in the reconstruction process for processing the raw data captured by the experiment. In the experiment, the first is the construction of mirror-assisted TPM system. Then using beads of the known diameter and refractive index as a sample to obtain three-dimensional refractive index distribution of the beads for verifying the novel system and algorithms. The system will also be applied to measure the three-dimensional refractive index distribution of cell.

1.A. C. Kak and M. Slaney, Principles of computerized tomographic imaging (Siam, 1988), Vol. 33.
2.W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, "Tomographic phase microscopy," Nature methods 4, 717-719 (2007).
3.C. Haisch, "Optical tomography," Annual Review of Analytical Chemistry 5, 57-77 (2012).
4.D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, "Optical coherence tomography," Science 254, 1178-1181 (1991).
5.T. A. Holly, B. G. Abbott, M. Al-Mallah, D. A. Calnon, M. C. Cohen, M. R. Freeman, R. C. Hendel, D. Jain, S. M. Leonard, and R. N. CNMT, "Single photon-emission computed tomography," Journal of nuclear cardiology 17, 941-973 (2010).
6.J. M. Ollinger and J. A. Fessler, "Positron-emission tomography," Signal Processing Magazine, IEEE 14, 43-55 (1997).
7.W. C. Röntgen, "On a new kind of rays," Science 3, 227-231 (1896).
8.J. Radon, "On determination of functions by their integral values along certain multiplicities," Ber. der Sachische Akademie der Wissenschaften Leipzig,(Germany) 69, 262-277 (1917).
9.A. M. Cormack, "Representation of a function by its line integrals, with some radiological applications," Journal of Applied Physics 34, 2722-2727 (1963).
10.G. N. Hounsfield, "Computerized transverse axial scanning (tomography): Part 1. Description of system," British Journal of Radiology 46, 1016-1022 (1973).
11.K. Lim, P. Treitz, M. Wulder, B. St-Onge, and M. Flood, "LiDAR remote sensing of forest structure," Progress in physical geography 27, 88-106 (2003).
12.J. Sharpe, U. Ahlgren, P. Perry, B. Hill, A. Ross, J. Hecksher-Sørensen, R. Baldock, and D. Davidson, "Optical projection tomography as a tool for 3D microscopy and gene expression studies," Science 296, 541-545 (2002).
13.A. Bassi, L. Fieramonti, C. D’Andrea, M. Mione, and G. Valentini, "In vivo label-free three-dimensional imaging of zebrafish vasculature with optical projection tomography," Journal of biomedical optics 16, 100502-100502-100503 (2011).
14.F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, "Cell refractive index tomography by digital holographic microscopy," Opt. Lett. 31, 178-180 (2006).
15.P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, "Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy," Opt. Lett. 30, 468-470 (2005).
16.H. Schreiber and J. H. Bruning, "Phase shifting interferometry," Optical Shop Testing, Third Edition, 547-666 (2006).
17.F. Charrière, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. Mitchell, P. Marquet, and B. Rappaz, "Living specimen tomography by digital holographic microscopy: morphometry of testate amoeba," Opt. Express 14, 7005-7013 (2006).
18.E. Wolf, "Three-dimensional structure determination of semi-transparent objects from holographic data," Optics Communications 1, 153-156 (1969).
19.V. Lauer, "New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope," Journal of Microscopy 205, 165-176 (2002).
20.S. W. Hell and J. Wichmann, "Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy," Opt. Lett. 19, 780-782 (1994).
21.M. G. Gustafsson, "Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution," Proceedings of the National Academy of Sciences of the United States of America 102, 13081-13086 (2005).
22.D. Gabor, "A new microscopic principle," Nature 161, 777-778 (1948).
23.J. W. Goodman, "Digital image formation from electronically detected holograms," in Computerized Imaging Techniques, (International Society for Optics and Photonics, 1967), 176-181.
24.E. N. Leith and J. Upatnieks, "Reconstructed wavefronts and communication theory," JOSA 52, 1123-1128 (1962).
25.M. Takeda, H. Ina, and S. Kobayashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," JosA 72, 156-160 (1982).
26.陳彥霖, "調控式平行相位展開法參數自動搜尋並結合區塊接合技術進行形貌不連續相位圖之相位展開研究," (2008).
27.R. Cusack, J. Huntley, and H. Goldrein, "Improved noise-immune phase-unwrapping algorithm," Applied Optics 34, 781-789 (1995).
28.D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping: theory, algorithms, and software (Wiley New York, 1998).
29.W. W. Macy Jr, "Two-dimensional fringe-pattern analysis," Applied Optics 22, 3898-3901 (1983).
30.B. Gutmann and H. Weber, "Phase unwrapping with the branch-cut method: role of phase-field direction," Applied Optics 39, 4802-4816 (2000).
31.L. An, Q.-S. Xiang, and S. Chavez, "A fast implementation of the minimum spanning tree method for phase unwrapping," Medical Imaging, IEEE Transactions on 19, 805-808 (2000).
32.D. C. Ghiglia, G. A. Mastin, and L. A. Romero, "Cellular-automata method for phase unwrapping," JOSA A 4, 267-280 (1987).
33.D. C. Ghiglia and L. A. Romero, "Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods," JOSA A 11, 107-117 (1994).
34.R. M. Goldstein, H. A. Zebker, and C. L. Werner, "Satellite radar interferometry: Two‐dimensional phase unwrapping," Radio Science 23, 713-720 (1988).
35.A. Buckingham, R. Disch, and D. Dunmur, "Matrix formulation of the reconstruction of phase values from phase differences," Physica 23, 825-837 (1957).
36.R. Gordon, R. Bender, and G. T. Herman, "Algebraic reconstruction techniques (ART) for three-dimensional electron microscopy and X-ray photography," Journal of theoretical Biology 29, 471-481 (1970).
37.S. Kaczmarz, "Angenäherte auflösung von systemen linearer gleichungen," Bulletin International de l’Academie Polonaise des Sciences et des Lettres 35, 355-357 (1937).
38.C. Fang-Yen, W. Choi, Y. Sung, C. J. Holbrow, R. R. Dasari, and M. S. Feld, "Video-rate tomographic phase microscopy," Journal of biomedical optics 16, 011005-011005-011005 (2011).
39.V. Barthes and G. Vasseur, "An inverse problem for electromagnetic prospection," in Applied Inverse Problems (Springer, 1978), pp. 325-329.
40.M. Slaney, A. C. Kak, and L. E. Larsen, "Limitations of imaging with first-order diffraction tomography," Microwave Theory and Techniques, IEEE Transactions on 32, 860-874 (1984).
41.J. W. Su, W. C. Hsu, C. Y. Chou, C. H. Chang, and K. B. Sung, "Digital holographic microtomography for high‐resolution refractive index mapping of live cells," Journal of Biophotonics (2012).
42.N. A. Campbell, B. Williamson, and R. J. Heyden, "Biology: Exploring Life," Boston, Massachusetts: Pearson Prentice Hall.: ISBN 0-13-250882-6 (2006).