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In coherent x-ray diffractive imaging, the oversampled far-field diffraction pattern for phase retrieval iterative algorithm is used in order to reconstruct the information about the real space. The support constraint is one of the most important steps of the 3D phase retrieval process. Here we use a small nonperiodic 2D digital image as an object for studying the algorithm of pursuing support constraint automatically and noise correction for different types of noises in the diffraction pattern. We find an efficient method of noise correction while the traditional methods do not work well in the high noise condition. The result shows that this method can be used to reduce the effect effectively for the reconstruction. We also study the 3D reconstruction for the electron density distribution of Au nano-particles. We achieve a good reconstruction separately with and without noise effect in the diffraction pattern and we find that the signal-to-noise ratio should be bigger than 27 for successful 3D reconstruction.
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Keywords:
- coherent x-ray diffractive imaging /
- oversampling /
- 3D phase retrieval /
- microscopy
[1] Xie H L, Hu W, Luo H X, Du G H, Deng B, Chen R C, Xue Y L, Shi S M, Xiao T Q 2008 Acta Phys. Sin. 57 7044 (in Chinese) [谢红兰, 胡雯, 罗红心, 杜国浩, 邓彪, 陈荣昌, 薛艳玲, 师绍猛, 肖体乔 2008 57 7044]
[2] Liu L X, Du G H, Hu W, Xie H L, Xiao T Q 2007 Acta Phys. Sin. 56 4556 (in Chinese) [刘丽想, 杜国浩, 胡雯, 谢红兰, 肖体乔 2007 56 4556]
[3] Shi S M, Chen R C, Xue Y L, Ren Y Q, Du G H, Deng B, Xie H L, Xiao T Q 2008 Acta Phys. Sin. 57 6319 (in Chinese) [师绍猛, 陈荣昌, 薛艳玲, 任玉琦, 杜国浩, 邓彪, 谢红兰, 肖体乔 2008 57 6319]
[4] Xue Y L, Xiao T Q, Wu L H, Chen C, Guo R Y, Du G H, Xie H L, Deng B, Ren Y Q, Xu H J 2010 Acta Phys. Sin. 59 5496 (in Chinese) [薛艳玲, 肖体乔, 吴立宏, 陈灿, 郭荣怡, 杜国浩, 谢红兰, 邓彪, 任玉琦, 徐洪杰 2010 59 5496]
[5] Marchesini S, Chapman H N, Hau-Riege S P, London R A, Szoke A 2003 Opt. Express 11 2344
[6] Schroer C G, Boye P, Feldkamp M J, Patommel J, Schropp A, Schwab A, Stephan S, Burghammer, Schöder S, Riekel C 2008 Phys. Rev. Lett. 101 090801
[7] Sayre D 1952 Acta Cryst. 5 843
[8] Sayre D, Schlenker M 1980 Lecture Notes in Physics (Vol. 112) (Berlin: Springer) p229
[9] Fienup J R 1982 Appl. Opt. 21 2758
[10] Miao JW, Charalambous P, Kirz J, Sayre D 1999 Nature 400 342
[11] Miao J W, Chen C C, Song C Y, Nishino Y, Kohmura Y, Ishikawa T, Damien R J, Lee T K, Risbud S H 2006 Phys. Rev. Lett. 97 215503
[12] Chapman H N, Barty A, Marchesini S, Noy A, Cui C, Howells M R, Rosen R, He H, Spence J C H, Weierstall U, Beetz T, Jacobsen C, Shapiro D 2006 J. Opt. Soc. Am. 23 1179
[13] Abbey B, Williams G J, Pfeifer M A, Clark J N, Putkunz C T, Torrance A, McNulty I, Levin T M, Peele A G, Nugent K A 2008 Appl. Phys. Lett. 93 214101
[14] Thibault P, Elser V, Jacobsen C, Shapiro D, Sayre D 2006 Acta Cryst. 62 248
[15] Hau-Riege S P, Chapman H N, Krzywinski J, Sobierajski R, Bajt S, London R A, Bergh M, Caleman C, Nietubyc R, Juha L, Kuba J, Spiller E, Baker S, Bionta R, Tinten K S, Stojanovic N, Kjornrattanawanich B, Gullikson E, Plönjes E, Toleikis S, Tschentscher T 2007 Phys. Rev. Lett. 98 145502
[16] Chapman H N, Nugent K A 2010 Nature Photon 4 833
[17] Gerchberg R W, Saxton W O 1972 Optik 35 237
[18] Abrahams J P, Leslie A W G 1996 Acta Crystallogr. D52 30
[19] Elser V 2003 J. Opt. Soc. Am. A 20 40
[20] Luke D R 2005 Inverse Probl. 21 37
[21] Chen C C, Miao J W, Wang C W, Lee T K 2007 Phys. Rev. B 76 064113
[22] Marchesini S, He H, Chapman H N, Hau-Riege S P, Noy A, Howells M R, Weierstall U, Spence J C H 2003 Phys. Rev. B 68 140101
[23] Zhou G Z, Tong Y J, Chen C, Ren Y Q, Wang Y D, Xiao T Q 2011 Acta Phys. Sin. 60 028701 (in Chinese) [周光照, 佟亚军, 陈灿, 任玉琦, 王玉丹, 肖体乔 2011 60 028701]
[24] Jiang H D, Song C Y, Chen C C, Xu R, Raines K S, Benjamin P F, Lu C H, Lee T K, Nakashima A, Urano J, Ishikawa T, Tamanoi F, Miao J W 2010 PNAS 107 11234
[25] Barty A, Marchesini S, Chapman H N, Cui C, Howells M R, Shapiro D A, Minor A M, Spence J C H, Weierstall U, Ilavsky J, Noy A, Hau-Riege S P, Artyukhin A B, Baumann T, Willey T, Stolken J 2008 Phys. Rev. Lett. 101 055501
[26] Raines K S, Sara S, Richard L S, Jiang H D, Jose A R, Benjamin P F, Henry C K, Du J C, Miao J W 2009 Nature 463 214
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[1] Xie H L, Hu W, Luo H X, Du G H, Deng B, Chen R C, Xue Y L, Shi S M, Xiao T Q 2008 Acta Phys. Sin. 57 7044 (in Chinese) [谢红兰, 胡雯, 罗红心, 杜国浩, 邓彪, 陈荣昌, 薛艳玲, 师绍猛, 肖体乔 2008 57 7044]
[2] Liu L X, Du G H, Hu W, Xie H L, Xiao T Q 2007 Acta Phys. Sin. 56 4556 (in Chinese) [刘丽想, 杜国浩, 胡雯, 谢红兰, 肖体乔 2007 56 4556]
[3] Shi S M, Chen R C, Xue Y L, Ren Y Q, Du G H, Deng B, Xie H L, Xiao T Q 2008 Acta Phys. Sin. 57 6319 (in Chinese) [师绍猛, 陈荣昌, 薛艳玲, 任玉琦, 杜国浩, 邓彪, 谢红兰, 肖体乔 2008 57 6319]
[4] Xue Y L, Xiao T Q, Wu L H, Chen C, Guo R Y, Du G H, Xie H L, Deng B, Ren Y Q, Xu H J 2010 Acta Phys. Sin. 59 5496 (in Chinese) [薛艳玲, 肖体乔, 吴立宏, 陈灿, 郭荣怡, 杜国浩, 谢红兰, 邓彪, 任玉琦, 徐洪杰 2010 59 5496]
[5] Marchesini S, Chapman H N, Hau-Riege S P, London R A, Szoke A 2003 Opt. Express 11 2344
[6] Schroer C G, Boye P, Feldkamp M J, Patommel J, Schropp A, Schwab A, Stephan S, Burghammer, Schöder S, Riekel C 2008 Phys. Rev. Lett. 101 090801
[7] Sayre D 1952 Acta Cryst. 5 843
[8] Sayre D, Schlenker M 1980 Lecture Notes in Physics (Vol. 112) (Berlin: Springer) p229
[9] Fienup J R 1982 Appl. Opt. 21 2758
[10] Miao JW, Charalambous P, Kirz J, Sayre D 1999 Nature 400 342
[11] Miao J W, Chen C C, Song C Y, Nishino Y, Kohmura Y, Ishikawa T, Damien R J, Lee T K, Risbud S H 2006 Phys. Rev. Lett. 97 215503
[12] Chapman H N, Barty A, Marchesini S, Noy A, Cui C, Howells M R, Rosen R, He H, Spence J C H, Weierstall U, Beetz T, Jacobsen C, Shapiro D 2006 J. Opt. Soc. Am. 23 1179
[13] Abbey B, Williams G J, Pfeifer M A, Clark J N, Putkunz C T, Torrance A, McNulty I, Levin T M, Peele A G, Nugent K A 2008 Appl. Phys. Lett. 93 214101
[14] Thibault P, Elser V, Jacobsen C, Shapiro D, Sayre D 2006 Acta Cryst. 62 248
[15] Hau-Riege S P, Chapman H N, Krzywinski J, Sobierajski R, Bajt S, London R A, Bergh M, Caleman C, Nietubyc R, Juha L, Kuba J, Spiller E, Baker S, Bionta R, Tinten K S, Stojanovic N, Kjornrattanawanich B, Gullikson E, Plönjes E, Toleikis S, Tschentscher T 2007 Phys. Rev. Lett. 98 145502
[16] Chapman H N, Nugent K A 2010 Nature Photon 4 833
[17] Gerchberg R W, Saxton W O 1972 Optik 35 237
[18] Abrahams J P, Leslie A W G 1996 Acta Crystallogr. D52 30
[19] Elser V 2003 J. Opt. Soc. Am. A 20 40
[20] Luke D R 2005 Inverse Probl. 21 37
[21] Chen C C, Miao J W, Wang C W, Lee T K 2007 Phys. Rev. B 76 064113
[22] Marchesini S, He H, Chapman H N, Hau-Riege S P, Noy A, Howells M R, Weierstall U, Spence J C H 2003 Phys. Rev. B 68 140101
[23] Zhou G Z, Tong Y J, Chen C, Ren Y Q, Wang Y D, Xiao T Q 2011 Acta Phys. Sin. 60 028701 (in Chinese) [周光照, 佟亚军, 陈灿, 任玉琦, 王玉丹, 肖体乔 2011 60 028701]
[24] Jiang H D, Song C Y, Chen C C, Xu R, Raines K S, Benjamin P F, Lu C H, Lee T K, Nakashima A, Urano J, Ishikawa T, Tamanoi F, Miao J W 2010 PNAS 107 11234
[25] Barty A, Marchesini S, Chapman H N, Cui C, Howells M R, Shapiro D A, Minor A M, Spence J C H, Weierstall U, Ilavsky J, Noy A, Hau-Riege S P, Artyukhin A B, Baumann T, Willey T, Stolken J 2008 Phys. Rev. Lett. 101 055501
[26] Raines K S, Sara S, Richard L S, Jiang H D, Jose A R, Benjamin P F, Henry C K, Du J C, Miao J W 2009 Nature 463 214
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