Ptychographic同調繞射顯微術 (Ptychographic Coherent Diffraction Microscopy, PCDM) 是一種較為新穎且可以不使用透鏡的顯微技術，現今，廣泛使用在PCDM的演算法是extend Ptychographic Iterative Engine (ePIE) 演算法，將X光、電子束和可見光做為發射源的成像系統已有利用ePIE重建影像。本論文建立一套氦氖雷射為發射源且發射源尺寸為可變的光學同調繞射 (Coherence Diffraction Imaging, CDI) 成像系統，並將位置校正 (position correction) 與混合態 (mixed state) 的功能加入ePIE演算法，對負片型標準解析度樣品與生物標本樣品進行觀察。具有位置校正與混合態功能的ePIE演算法成功重建兩種樣品的強度影像和相位影像，包含樣品形貌影像及發射源影像。但是在負片型標準解析度樣品中，較小發射源掃描較細條紋之高解析度區域時，ePIE無法順利重建影像，不過，發射源影像及其相位是可以被具有位置校正與混合態功能的ePIE演算法成功重建。未來，具有位置校正與混合態功能的ePIE演算法所重建之發射源相位，或許能與相位取回演算法 (Hybrid Input-Output, HIO) 結合，發展出功能更加完善的Ptychographic同調繞射顯微術。

Ptychographic Coherent Diffraction Microscopy (PCDM) is a relatively novel microscopy technique that does not require the use of lenses. Currently, the widely used algorithm in PCDM is the extended Ptychographic Iterative Engine (ePIE) algorithm. Imaging systems utilizing X-rays, electron beams, and visible light as the illumination sources have been reconstructed using ePIE. In this paper, we establish an optical Coherence Diffraction Imaging (CDI) system with a helium-neon laser as the illumination source, where the source size is adjustable. We incorporate position correction and mixed state capabilities into the ePIE algorithm to observe both negative-tone standard resolution samples and biological specimens. The ePIE algorithm with position correction and mixed state successfully reconstructs intensity and phase images of both samples, including sample morphology and source images. However, in the case of the negative-tone standard resolution sample, when scanning the high-resolution region with finer fringes using a smaller illumination source, ePIE fails to reconstruct the image smoothly. Nonetheless, the source image and its phase can still be successfully reconstructed using the ePIE algorithm with position correction and mixed state capabilities. In the future, the phase of the reconstructed source using the ePIE algorithm with position correction and mixed state capabilities may be combined with the Hybrid Input-Output (HIO) algorithm for phase retrieval. This integration could lead to the development of a more advanced PCDM technique with enhanced functionality.

F. Hüe et al, “Extended ptychography in the transmission electron microscope: possibilities and limitations”, Ultramicroscopy (2011).
J. Miao, P. Charalambous, J. Kriz, D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens“, Nature 400, 342 (1999).
U. Weierstall, Q. Chen, J.C.H. Spence, M.R. Howells, M. Isaacson, R.R. Panepucci, “Image reconstruction from electron and X-ray diffraction patterns using iterative algorithms: experiment and simulation“, Ultramicroscopy 90, 171 (2002).
J.M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L.A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities“, Science 300, 1419 (2003).
J.M. Zuo, I. Vartanyants, M. Gao, R. Zhang, L.A. Nagahara, “Atomic resolution imaging of a carbon nanotube from diffraction intensities“, Science 300, 1419 (2003).
S. Morishita, J. Yamasaki, K. Nakamura, T. Kato, N. Tanaka, “Diffractive imaging of the dumbbell structure in silicon by spherical-aberration corrected electron diffraction”, Appl. Phys. Lett. 93, 183103 (2008).
W.J. Huang, J.M. Zuo, B. Jiang, K.W. Kwon, M. Shim, “sub-ångströmresolution diffractive imaging of single nanocrystals”, Nat. Phys. 5, 129 (2009).
L.D. Caro, E. Carlino, G. Caputo, P.D. Cozzoli, C. Giannin, “Electron diffractive imaging of oxygen atoms in nanocrystals at sub- sub-ångström resolution”, Nat. Nanotechnol. 5, 360 (2010).
O. Kamimura, Y. Maehara, T. Dobashi, K. Kobayashi, R. Kitaura, H. Shinohara, H. Shioya, K. Gohara, “Low voltage electron diffractive imaging of atomic structure in single-wall carbon nanotubes”, Appl. Phys. Lett. 98 174103 (2011).
O. Kamimura, T. Dobashi, K. Kawahara, T. Abe, K. Gohar, “10-kV diffractive imaging using newly developed electron diffraction microscope”, Ultramicroscopy 110 130 (2010).
M.J. Humphry, B. Kraus, A.C. Hurst, A.M. Maiden, J.M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging”, Nature Commu. 3 730 (2012).
L.N. Longchamp, T. Latychevskaia, C. Escher, H.W. Fink, “Graphene unit cell imaging by holographic coherent diffraction“, Phys. Rev. Lett.110 255501 (2013).
J. C. H. Spence, U. Weierstall, M. Howells,“Phase recovery and lensless imaging by iterative methods in optical, X-ray and electron diffraction”, Phil. Trans. R. Soc. Lond. A 360, 875 (2002)
G. J. Yu, “Ptychographical coherent diffraction microscopy for extend periodic structure” (Unpublished master’s thesis), National Chiao Tung University, Hsinchu (2014).
A. C. Hurst and J. M. Rodenburg, “ An optical demonstration of ptychographical imaging for focussed-probe illumination”, Journal of Physics: Conference Series 126, 012093 (2008)
Martin Dierolf et al., “Coherent laser scanning diffraction microscopy”, Journal of Physics: Conference Series 186, 012052 (2009).
Oliver Bunk et. al., “Influence of the overlap parameter on the convergence of the ptychographical iterative engine”, Ultramicroscopy 108, 481 (2008).
Thibault, P., et al., Probe retrieval in ptychographic coherent diffractive imaging. Ultramicroscopy, 2009. 109(4): p. 338-343.
Thibault, P., et al., High-resolution scanning x-ray diffraction microscopy. Science, 2008. 321(5887): p. 379-382.
Humphry, M., et al., Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging. Nature communications, 2012. 3: p. 730.
Rodenburg, J., et al., Hard-x-ray lensless imaging of extended objects. Physical review letters, 2007. 98(3): p. 034801.
C.Y. Lin, “Low-kilovolt Coherent Electron Diffraction Imaging Based on a Single-Atom Electron Source” (Unpublished doctoral dissertation), National Taiwan University, Taipei (2016).
http://www.microbehunter.com/phase-contrast-vs-bright-field-microscopy/.
J.C.H. Spence, U. Weierstall, M. Howells, “Coherence and sampling requirements for diffractive imaging”, Ultramicroscopy 101, 149 (2004)
W. C. Huang, “Holographic Simulations and Reconstructions of Low energy Electron Point Projection Microscopy” (Unpublished master’s thesis), National Taiwan University, Taipei (2018).
J. R. Fienup, T. R. Crimmins, and W. Holsztynski, “Reconstruction of the support of an object from the support of its autocorrelation” J. Opt. Soc.. 72, 5 (1982).
R. Hegerl, W. Hoppe, “Dynamische theorie der kristallstrukturanalyse durch elektronenbeugung im inhomogenen primärstrahlwellenfeld”, Berichte der Bunsengesellschaft für physikalische Chemie. 74, 11, 1148 (1970)
W. Hoppe, “ Diffraction in inhomogeneous primary wave fields. 1. Principle of phase determination from electron diffraction interference”, Acta Crystallogr. A 25, 495 (1969)
W. Hoppe, “Trace structure analysis, ptychography, phase tomography”, Ultramicroscopy 10, 187 (1982)
H. Faulkner, J. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm”, Physical review letters 93, 2, 023903 (2004)
J. Rodenburg, H. Faulkner, “A phase retrieval algorithm for shifting Illumination”, Applied physics letters 85, 20, 4795 (2004)
A.M. Maiden, M.J. Humphry, M.C. Sarahan, B. Kraus, J.M. Rodenburg, “An annealing algorithm to correct positioning errors in ptychography”, Ultramicroscopy, 120 (2012), pp. 64-72
Thibault, P. & Menzel, A. Reconstructing state mixtures from diffraction measurements. Nature 494, 68–71 (2013).
https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=4338
https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=6277
Rob Sumner, “Processing RAW Images in MATLAB”, Department of Electrical Engineering, UC Santa Cruz (2014).
J. R. Fienup, “ Invariant error metrics for image reconstruction” , Appl. Opt. 36, 32, 10 (1997)