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Phase retrieval is one of the most important steps for coherent X-ray diffractive imaging (CXDI), Which uses the oversampled far-field diffraction pattern for phase retrieval iterative algorithm in order to achieve the lost phase information. Here we used a small nonperiodic 2D digital image as the object for studying the effect of the oversampling ratio and obtained the optimum oversampling ratio of 3—7 when the iteration times was 1000. We also added random noise to the diffraction pattern to examine the applicability of this approach to real data. We found the reconstruction failed when the signal to noise ratio is less than 10. As the reconstruction process may fail when the twin image or stochastic shift appears in the reconstructed image simultaneously, we explained why these phenomena come into being, and found methods to overcome the difficulty effectively.
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Keywords:
- coherent X-ray diffractive imaging /
- oversampling /
- phase retrieval algorithms /
- microscopy
[1] 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 物理学报 56 4556]
[2] 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 物理学报 57 6319]
[3] 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 物理学报 59 5496] 〖4] 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 物理学报 57 7044]
[4] Marchesini S, Chapman H N, Hau-Riege S P, London R A, Szoke A 2003 Opt. Express. 11 2344
[5] Miao J W, Ishikawa T, Shen Q, Earnest T 2008 Annu. Rev. Phys. Chem. 59 387
[6] Sayre D 1952 Acta Cryst. 5 843
[7] Sayre D, Schlenker M 1980 Lectare Notes in physics (vol.112)(Berlin:Springer) p229
[8] Fienup J R 1982 Appl. Opt. 21 2758
[9] Miao J W, Charalambous P, Kirz J, Sayre D 1999 Nature 400 342
[10] 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
[11] 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
[12] 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
[13] Thibault P, Elser V, Jacobsen C, Shapiro D, Sayre D 2006 Acta Cryst. 62 248
[14] Hau-Riege S P, London R A, Szoke A 2004 Phys. Rev. E 69 051906
[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, Plnjes E, Toleikis S, Tschentscher T 2007 Phys. Rev. Lett. 98 145502
[16] 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
[17] Gerchberg R W, Saxton W O 1972 Optik 35 237
[18] Henke B L, Gullikson E M, Davis J C 1993 At. Data Nucl. Data Tables 54 181
[19] Miao J W, Sayre D, Chapman H N 1998 J. Opt. Soc. Am. A 15 1662
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[1] 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 物理学报 56 4556]
[2] 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 物理学报 57 6319]
[3] 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 物理学报 59 5496] 〖4] 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 物理学报 57 7044]
[4] Marchesini S, Chapman H N, Hau-Riege S P, London R A, Szoke A 2003 Opt. Express. 11 2344
[5] Miao J W, Ishikawa T, Shen Q, Earnest T 2008 Annu. Rev. Phys. Chem. 59 387
[6] Sayre D 1952 Acta Cryst. 5 843
[7] Sayre D, Schlenker M 1980 Lectare Notes in physics (vol.112)(Berlin:Springer) p229
[8] Fienup J R 1982 Appl. Opt. 21 2758
[9] Miao J W, Charalambous P, Kirz J, Sayre D 1999 Nature 400 342
[10] 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
[11] 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
[12] 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
[13] Thibault P, Elser V, Jacobsen C, Shapiro D, Sayre D 2006 Acta Cryst. 62 248
[14] Hau-Riege S P, London R A, Szoke A 2004 Phys. Rev. E 69 051906
[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, Plnjes E, Toleikis S, Tschentscher T 2007 Phys. Rev. Lett. 98 145502
[16] 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
[17] Gerchberg R W, Saxton W O 1972 Optik 35 237
[18] Henke B L, Gullikson E M, Davis J C 1993 At. Data Nucl. Data Tables 54 181
[19] Miao J W, Sayre D, Chapman H N 1998 J. Opt. Soc. Am. A 15 1662
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