Phase Retrieval and Reconstruction of Coherent Diffraction Imaging

KANG Xu; LIU Jin

doi:10.11858/gywlxb.20190761

Volume 33 Issue 3

Jun 2019

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Chinese Journal of High Pressure Physics > 2019 > 33(3): 030105.

KANG Xu, LIU Jin. Phase Retrieval and Reconstruction of Coherent Diffraction Imaging[J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030105. doi: 10.11858/gywlxb.20190761

Citation:

KANG Xu, LIU Jin. Phase Retrieval and Reconstruction of Coherent Diffraction Imaging[J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030105. doi: 10.11858/gywlxb.20190761

KANG Xu, LIU Jin. Phase Retrieval and Reconstruction of Coherent Diffraction Imaging[J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030105. doi: 10.11858/gywlxb.20190761

Citation:

KANG Xu, LIU Jin. Phase Retrieval and Reconstruction of Coherent Diffraction Imaging[J]. Chinese Journal of High Pressure Physics, 2019, 33(3): 030105. doi: 10.11858/gywlxb.20190761

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Phase Retrieval and Reconstruction of Coherent Diffraction Imaging

doi: 10.11858/gywlxb.20190761

KANG Xu,
LIU Jin^{*
,
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Institute of Fluid Physics, CAEP, Mianyang 621999, China

Received Date: 18 Apr 2019
Rev Recd Date: 14 May 2019

Abstract

Abstract

The coherent diffraction imaging (CDI) is an ultra-high resolution imaging technique that is sensitive to the density of the material. Compared to the surface-sensitive imaging methods with ultra-high resolution, the CDI is able to probe the interior of the sample by taking advantages of hard X-rays. According to the imaging layout, the space resolution of CDI is variable and can reach up to an atomic scale. This feature depends on the iterative phase retrieval method that almost becomes the signature of CDI. Based on oversampling a sample in a detected image, the phase and intensity of X-ray beam can be retrieved simultaneously by iterative calculations with constraints, and then are used to reconstruct the sample. Meanwhile, the three-dimensional reconstruction could be realized by combining image orientating and merging techniques. Here we present the imaging theory, phase retrieval and reconstruction methods of the CDI technique, and its diagnostic ability in a variety of reconstruction situations by experimental and simulation examples, to hopefully provide a systematic introduction of its development.
- coherent diffraction imaging,
- phase retrieval,
- two-dimensional reconstruction,
- three-dimensional reconstruction

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References(31)

References

[1]	CHAO W, HARTENECK B D, LIDDLE J A, et al. Soft X-ray microscopy at a spatial resolution better than 15 nm [J]. Nature, 2005, 435(7046): 1210. doi: 10.1038/nature03719
[2]	BARBER J L, BARNES C W, SANDBERG R L, et al. Diffractive imaging at large fresnel number: challenge of dynamic mesoscale imaging with hard X-rays [J]. Physical Review B, 2014, 89(18): 184105. doi: 10.1103/PhysRevB.89.184105
[3]	XIAO X H, SHEN Q. Wave propagation and phase retrieval in fresnel diffraction by a distorted-object approach [J]. Physical Review B, 2005, 72(3): 033103. doi: 10.1103/PhysRevB.72.033103
[4]	MIAO J W, AMONETTE J E, NISHINO Y, et al. Direct determination of the absolute electron density of nanostructured and disordered materials at sub-10-nm resolution [J]. Physical Review B, 200, 68(1): 012201.
[5]	SAYER D. Some implications of a theorem due to shannon [J]. Acta Crystallographica, 1952, 5: 843.
[6]	GERCHBERG R W, SAXTON W O. A practical algorithm for the determination of phase from image and diffraction plane pictures [J]. Optik, 1972, 35: 237.
[7]	FIENUP J R. Phase retrieval algorithm: a comparison [J]. Applied Optics, 1982, 21: 2758. doi: 10.1364/AO.21.002758
[8]	ELSER V. Phase retrieval by iterated projections [J]. Journal of the Optical Society of America, 2003, 20(1): 40. doi: 10.1364/JOSAA.20.000040
[9]	CHEN C C, MIAO J, WANG C W, et al. Application of optimization technique to noncrystalline X-ray diffraction microscopy: guided hybrid input-output method [J]. Physical Review B, 2007, 76(6): 064113. doi: 10.1103/PhysRevB.76.064113
[10]	LUKE D R. Relaxed averaged alternating reflections for diffraction imaging [J]. Inverse Problems, 2005, 21: 37. doi: 10.1088/0266-5611/21/1/004
[11]	MARCHESINI S, HE H, CHAPMAN H N, et al. X-ray image reconstruction from a diffraction pattern alone [J]. Physical Review B, 2003, 68: 140101. doi: 10.1103/PhysRevB.68.140101
[12]	MIAO J, SYAER D, CHAPMAN H N. Phase retrieval from the magnitude of the fourier transforms of nonperiodic objects [J]. Josa A, 1998, 15: 1662. doi: 10.1364/JOSAA.15.001662
[13]	周光照, 佟亚军, 陈灿, 等. 相干X射线衍射成像的数字模拟研究 [J]. 物理学报, 2011, 60(2): 028701. ZHOU G Z, TONG Y J, CHEN C, et al. Digital simulation for coherent X-ray diffractive imaging [J]. Acta Physica Sinica, 2011, 60(2): 028701.
[14]	VARTANYANTS I A, ROBINSON I K. Partial coherence effects on the imaging of small crystals using coherent X-ray diffraction [J]. Journal of Physics: Condensed Matter, 2001, 13(47): 10593. doi: 10.1088/0953-8984/13/47/305
[15]	MIAO J W, CHARALAMBOUS P, KIRZ J, et al. Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens [J]. Nature, 1999, 400: 342. doi: 10.1038/22498
[16]	MIAO J W, NISHINO Y, KOHNURA Y, et al. Quantitative image reconstruction of GaN quantum dots from oversampled diffraction intensities alone [J]. Physical Review Letters, 2005, 95(8): 085503. doi: 10.1103/PhysRevLett.95.085503
[17]	NISHINO Y, TAKAHASHI Y, IMAMOTO N, et al. Three-dimensional visualization of a human chromosome using coherent X-ray diffraction [J]. Physical Review Letters, 2009, 102(1): 018101. doi: 10.1103/PhysRevLett.102.018101
[18]	EKEBERG T, SVENDA M, ABERGEL C, et al. Three-dimensional reconstruction of the giant mimivirus particle with an X-ray free-electron laser [J]. Physical Review Letters, 2015, 114(9): 098102. doi: 10.1103/PhysRevLett.114.098102
[19]	DUANE N T, ELSER V. Reconstruction algorithm for single-particle diffraction imaging experiments [J]. Physical Review E, 2009, 80(2): 026705. doi: 10.1103/PhysRevE.80.026705
[20]	MIAO J W, CHEN C C, SONG C, et al. Three-dimensional GaN-Ga₂O₃ core shell structure revealed by X-ray diffraction microscopy [J]. Physical Review Letters, 2006, 97(21): 215503. doi: 10.1103/PhysRevLett.97.215503
[21]	TAKAHASHI Y, NISHINO Y, TSUTSUMI R, et al. High-resolution projection image reconstruction of thick objects by hard X-ray diffraction microscopy [J]. Physical Review B, 2010, 82(21): 214102. doi: 10.1103/PhysRevB.82.214102
[22]	THIBAULT P, DIEROLF M, MENZEL A, et al. High-resolution scanning X-ray diffraction microscopy [J]. Science, 2008, 321(5887): 379. doi: 10.1126/science.1158573
[23]	RODENBURG J M, HURST A C, CULLIS A G, et al. Hard-X-ray lensless imaging of extended objects [J]. Physical Review Letters, 2007, 98(3): 034801. doi: 10.1103/PhysRevLett.98.034801
[24]	KLAUS G, PIERRE T, SEBASTIAN K, et al. Quantitative biological imaging by ptychographic X-ray diffraction microscopy [J]. Proceedings of the National Academy of Sciences of the United States of America, 2010, 107(2): 529. doi: 10.1073/pnas.0905846107
[25]	DIEROLF M, MENZEL A, THIBAULT P, et al. Ptychographic X-ray computed tomography at the nanoscale [J]. Nature, 2010, 467(7314): 436. doi: 10.1038/nature09419
[26]	ROBINSON I K, VARTANYANTS I A, WILLIAMS G J, et al. Reconstruction of the shapes of gold nanocrystals using coherent X-ray diffraction [J]. Physical Review Letters, 2001, 87(19): 195505. doi: 10.1103/PhysRevLett.87.195505
[27]	WILLIAMS G J, PFEIFER M A, VARTANYANTS I A, et al. Three-dimensional imaging of microstructure in Au nanocrystals [J]. Physical Review Letters, 2003, 90(17): 175501. doi: 10.1103/PhysRevLett.90.175501
[28]	PFEIFER M A, WILLIAMS G J, VARTANYANTS I A, et al. Three-dimensional mapping of a deformation field inside a nanocrystal [J]. Nature, 2006, 442(7098): 63. doi: 10.1038/nature04867
[29]	NEWTON M C, LEAKE S J, HARDER R, et al. Three-dimensional imaging of strain in a single ZnO nanorod [J]. Nature Materials, 2010, 9(2): 279.
[30]	HARDER R, ROBINSON I. Coherent X-ray diffraction imaging of strain at the nanoscale [J]. Nature Materials, 2009, 8(4): 291. doi: 10.1038/nmat2400
[31]	GANG X, OUSSAMA M, MANFRED R, et al. Coherent X-ray diffraction imaging and characterization of strain in silicon-on-insulator nanostructures [J]. Advanced Materials, 2014, 26(46): 7747. doi: 10.1002/adma.v26.46

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