Abstract

The sample size must be less than the diffraction-limited focal spot size of the incident beam in single-shot coherent X-ray diffraction imaging (CXDI) based on a diffract-before-destruction scheme using X-ray free electron lasers (XFELs). This is currently a major limitation preventing its wider applications. We here propose multiple defocused CXDI, in which isolated objects are sequentially illuminated with a divergent beam larger than the objects and the coherent diffraction pattern of each object is recorded. This method can simultaneously reconstruct both objects and a probe from the coherent X-ray diffraction patterns without any a priori knowledge. We performed a computer simulation of the prposed method and then successfully demonstrated it in a proof-of-principle experiment at SPring-8. The prposed method allows us to not only observe broad samples but also characterize focused XFEL beams.

© 2016 Optical Society of America

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  30. K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Katayama, K. Ogawa, H. Ohashi, H. Kimura, S. Takahashi, K. Takeshita, H. Tomizawa, S. Goto, T. Ishikawa, and M. Yabashi, “Beamline, experimental stations and photon beam diagnostics for the hard x-ray free electron laser of SACLA,” New J. Phys. 15, 083035 (2013).
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2016 (1)

N. Burdet, K. Shimomura, M. Hirose, A. Suzuki, and Y. Takahashi, “Efficient use of coherent X-rays in ptychography: Towards high-resolution and high-throughput observation of weak-phase objects,” Appl. Phys. Lett. 108, 071103 (2016).
[Crossref]

2015 (2)

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, Y. Ping, D. G. Hicks, M. A. Beckwith, G. W. Collins, A. Higginbotham, J. S. Wark, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, and C. G. Schroer, “Imaging shock waves in diamond with both high temporal and spatial resolution at an XFEL,” Sci. Rep. 5, 11089 (2015).
[Crossref] [PubMed]

2014 (4)

P. Thibault, M. Guizar-Sicairos, and A. Menzel, “Coherent imaging at the diffraction limit,” J. Synchrotron Rad. 21, 1011–1018 (2014).
[Crossref]

M. F. Hantke, D. Hasse, F. R. N. C. Mala, T. Ekeberg, K. John, M. Svenda, N. D. Loh, A. V. Martin, N. Timneanu, D. S. D. Larsson, G. van der Schot, G. H. Carisson, M. Ingeiman, J. Andreasson, D. Westphal, M. Liang, F. Stellato, D. P. DePonte, R. Hartmann, N. Kimmel, R. A. Kirian, M. M. Seibert, K. Mühlig, S. Schorb, K. Ferguson, C. Bostedt, S. Carron, J. D. Bozek, D. Rolles, A. Rudenko, S. Epp, H. N. Chapman, A. Barty, J. Hajdu, and I. Andersson, “High-throughput imaging of heterogeneous cell organelles with an X-ray laser,” Nat. Photonics 8, 943–949 (2014).
[Crossref]

T. Kameshima, S. Ono, T. Kudo, K. Ozaki, Y. Kirihara, K. Kobayashi, Y. Inubushi, M. Yabashi, T. Horigome, A. Holland, K. Holland, D. Burt, H. Murao, and T. Hatsui, “Development of an X-ray pixel detector with multi-port charge-coupled device for X-ray free-electron laser experiments,” Rev. Sci. Instrum. 85, 033110 (2014).
[Crossref] [PubMed]

J. N. Clark, X. Huang, R. J. Harder, and I. K. Robinson, “Dynamic imaging using ptychography,” Phys. Rev. Lett. 112, 113901 (2014).
[Crossref] [PubMed]

2013 (8)

P. Thibault and A. Menzel, “Reconstructing state mixtures from diffraction measurements,” Nature 494, 68–71 (2013).
[Crossref] [PubMed]

R. N. Wilke, M. Vassholz, and T. Salditt, “Semi-transparent central stop in high-resolution X-ray ptychography using Kirkpatrick-Baez focusing,” Acta Crystallogr. A 69, 490–497 (2013).
[Crossref]

M. Yabashi, H. Tanaka, T. Tanaka, H. Tomizawa, T. Togashi, M. Nagasono, T. Ishikawa, J. R. Harries, Y. Hikosaka, and A. Hishikawa, “Compact XFEL and AMO sciences: SACLA and SCSS,” J. Phys. B: At. Mol. Opt. Phys. 46, 164001 (2013).
[Crossref]

K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Katayama, K. Ogawa, H. Ohashi, H. Kimura, S. Takahashi, K. Takeshita, H. Tomizawa, S. Goto, T. Ishikawa, and M. Yabashi, “Beamline, experimental stations and photon beam diagnostics for the hard x-ray free electron laser of SACLA,” New J. Phys. 15, 083035 (2013).
[Crossref]

Y. Takahashi, A. Suzuki, N. Zettsu, T. Oroguchi, Y. Takayama, Y. Sekiguchi, A. Kobayashi, M. Yamamoto, and M. Nakasako, “Coherent diffraction imaging analysis of shape-controlled with focused hard X-ray free-electron laser pulses,” Nano Lett. 13, 6028–6032 (2013).
[Crossref]

M. Nakasako, Y. Takayama, T. Oroguchi, Y. Sekiguchi, A. Kobayashi, K. Shirahama, M. Yamamoto, T. Hikima, K. Yonekura, S. Maki-Yonekura, Y. Kohmura, Y. Inubushi, Y. Takahashi, A. Suzuki, S. Matsunaga, Y. Inui, K. Tono, T. Kameshima, Y. Joti, and T. Hoshi, “KOTOBUKI-1 apparatus for cryogenic coherent X-ray diffraction imaging,” Rev. Sci. Instrum. 84, 093705 (2013).
[Crossref] [PubMed]

A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, D. Nilsson, F. Uhlén, U. Vogt, H. M. Hertz, and C. G. Schroer, “Full spatial characterization of a nanofocused x-ray free-electron laser beam by ptychographic imaging,” Sci. Rep. 3, 1633 (2013).
[Crossref] [PubMed]

H. Yumoto, H. Mimura, T. Koyama, S. Matsuyama, K. Tono, T. Togashi, Y. Inubushi, T. Sato, T. Tanaka, T. Kimura, H. Yokoyama, J. Kim, Y. Sano, Y. Hachisu, M. Yabashi, H. Ohashi, H. Ohmori, T. Ishikawa, and K. Yamauchi, “Focusing of X-ray free-electron laser pulses with reflective optics,” Nat. Photonics 7, 43–47 (2013).
[Crossref]

2010 (1)

M. Dierolf, P. Thibault, A. Menzel, C. M. Kewish, K. Jefimovs, I Schlichting, K. von König, O. Bunk, and F. Pfeiffer, “Ptychographic coherent diffractive imaging of weakly scattering specimens,” New J. Phys. 12, 035017 (2010).
[Crossref]

2009 (4)

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[Crossref]

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

Y. Takahashi, Y. Nishino, R. Tsutsumi, H. Kubo, H. Furukawa, H. Mimura, S. Matsuyama, N. Zettsu, E. Matsubara, T. Ishikawa, and K. Yamauchi, “High-resolution diffraction microscopy using the plane-wave field of a nearly diffraction limited focused x-ray beam,” Phys. Rev. B 80, 054103 (2009).
[Crossref]

2008 (2)

M. J. Bogan, W. H. Benner, S. Boutet, U. Rohner, M. Frank, A. Barty, M. M. Seibert, F. Maia, S. Marchesini, S. Bajt, B. Woods, V. Riot, S. P. Hau-Riege, M. Svenda, E. Marklund, E. Spiller, J. Hajdu, and H. N. Chapman, “Single particle X-ray diffractive imaging,” Nano Lett. 8, 310–316 (2008).
[Crossref]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

2007 (1)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Robinson, “Hard-X-Ray Lensless Imaging of Extended Objects,” Phys. Rev. Lett. 98, 034801 (2007).
[Crossref] [PubMed]

2006 (2)

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Peterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97, 025506 (2006).
[Crossref] [PubMed]

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Photonics 2, 101–104 (2006).

2005 (1)

K. A. Nugent, A. G. Peele, H. M. Quiney, and H. N. Chapman, “Diffraction with wavefront curvature: a path to unique phase recovery,” Acta Cryst. A 61, 373–381 (2005).
[Crossref]

2003 (2)

S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spense, “X-ray image reconstruction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
[Crossref]

J. Miao, T. Ishikawa, E. H. Anderson, and K. O. Hodgson, “Phase retrieval of diffraction patterns from noncrystalline samples using the oversampling method,” Phys. Rev. B 67, 174101 (2003).
[Crossref]

2000 (1)

R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, “Potential for biomolecular imaging with femtosecond X-ray pulses,” Nature 406, 752–757 (2000).
[Crossref] [PubMed]

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[Crossref]

1982 (1)

Abbey, B.

D. J. Vine, G. J. Williams, B. Abbey, M. A. Pfeifer, J. N. Clark, M. D. de Jonge, I. McNulty, A. G. Peele, and K. A. Nugent, “Ptychographic Fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[Crossref]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
[Crossref]

Anderson, E. H.

J. Miao, T. Ishikawa, E. H. Anderson, and K. O. Hodgson, “Phase retrieval of diffraction patterns from noncrystalline samples using the oversampling method,” Phys. Rev. B 67, 174101 (2003).
[Crossref]

Andersson, I.

M. F. Hantke, D. Hasse, F. R. N. C. Mala, T. Ekeberg, K. John, M. Svenda, N. D. Loh, A. V. Martin, N. Timneanu, D. S. D. Larsson, G. van der Schot, G. H. Carisson, M. Ingeiman, J. Andreasson, D. Westphal, M. Liang, F. Stellato, D. P. DePonte, R. Hartmann, N. Kimmel, R. A. Kirian, M. M. Seibert, K. Mühlig, S. Schorb, K. Ferguson, C. Bostedt, S. Carron, J. D. Bozek, D. Rolles, A. Rudenko, S. Epp, H. N. Chapman, A. Barty, J. Hajdu, and I. Andersson, “High-throughput imaging of heterogeneous cell organelles with an X-ray laser,” Nat. Photonics 8, 943–949 (2014).
[Crossref]

Andreasson, J.

M. F. Hantke, D. Hasse, F. R. N. C. Mala, T. Ekeberg, K. John, M. Svenda, N. D. Loh, A. V. Martin, N. Timneanu, D. S. D. Larsson, G. van der Schot, G. H. Carisson, M. Ingeiman, J. Andreasson, D. Westphal, M. Liang, F. Stellato, D. P. DePonte, R. Hartmann, N. Kimmel, R. A. Kirian, M. M. Seibert, K. Mühlig, S. Schorb, K. Ferguson, C. Bostedt, S. Carron, J. D. Bozek, D. Rolles, A. Rudenko, S. Epp, H. N. Chapman, A. Barty, J. Hajdu, and I. Andersson, “High-throughput imaging of heterogeneous cell organelles with an X-ray laser,” Nat. Photonics 8, 943–949 (2014).
[Crossref]

Arnold, B.

A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, Y. Ping, D. G. Hicks, M. A. Beckwith, G. W. Collins, A. Higginbotham, J. S. Wark, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, and C. G. Schroer, “Imaging shock waves in diamond with both high temporal and spatial resolution at an XFEL,” Sci. Rep. 5, 11089 (2015).
[Crossref] [PubMed]

A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, D. Nilsson, F. Uhlén, U. Vogt, H. M. Hertz, and C. G. Schroer, “Full spatial characterization of a nanofocused x-ray free-electron laser beam by ptychographic imaging,” Sci. Rep. 3, 1633 (2013).
[Crossref] [PubMed]

Bajt, S.

M. J. Bogan, W. H. Benner, S. Boutet, U. Rohner, M. Frank, A. Barty, M. M. Seibert, F. Maia, S. Marchesini, S. Bajt, B. Woods, V. Riot, S. P. Hau-Riege, M. Svenda, E. Marklund, E. Spiller, J. Hajdu, and H. N. Chapman, “Single particle X-ray diffractive imaging,” Nano Lett. 8, 310–316 (2008).
[Crossref]

Barty, A.

M. F. Hantke, D. Hasse, F. R. N. C. Mala, T. Ekeberg, K. John, M. Svenda, N. D. Loh, A. V. Martin, N. Timneanu, D. S. D. Larsson, G. van der Schot, G. H. Carisson, M. Ingeiman, J. Andreasson, D. Westphal, M. Liang, F. Stellato, D. P. DePonte, R. Hartmann, N. Kimmel, R. A. Kirian, M. M. Seibert, K. Mühlig, S. Schorb, K. Ferguson, C. Bostedt, S. Carron, J. D. Bozek, D. Rolles, A. Rudenko, S. Epp, H. N. Chapman, A. Barty, J. Hajdu, and I. Andersson, “High-throughput imaging of heterogeneous cell organelles with an X-ray laser,” Nat. Photonics 8, 943–949 (2014).
[Crossref]

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Sci. Rep. (2)

A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, D. Nilsson, F. Uhlén, U. Vogt, H. M. Hertz, and C. G. Schroer, “Full spatial characterization of a nanofocused x-ray free-electron laser beam by ptychographic imaging,” Sci. Rep. 3, 1633 (2013).
[Crossref] [PubMed]

A. Schropp, R. Hoppe, V. Meier, J. Patommel, F. Seiboth, Y. Ping, D. G. Hicks, M. A. Beckwith, G. W. Collins, A. Higginbotham, J. S. Wark, H. J. Lee, B. Nagler, E. C. Galtier, B. Arnold, U. Zastrau, J. B. Hastings, and C. G. Schroer, “Imaging shock waves in diamond with both high temporal and spatial resolution at an XFEL,” Sci. Rep. 5, 11089 (2015).
[Crossref] [PubMed]

Science (1)

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: Diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

Ultramicroscopy (2)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref] [PubMed]

P. Thibault, M. Dierolf, O. Bunk, A. Menzel, and F. Pfeiffer, “Probe retrieval in ptychographic coherent diffractive imaging,” Ultramicroscopy 109, 338–343 (2009).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Schematic drawing of multiple defocused CXDI. Focused X-rays are sequentially irradiated to isolated samples in the defocus plane. Multiple diffraction data are collected in the far field using a two-dimensional detector.

Fig. 2
Fig. 2

Flowchart of the iterative phase retrieval algorithm for multiple Fresnel CXDI. At each sample position, both the object and probe functions are updated. This process is repeated iteratively until suitable convergence is obtained.

Fig. 3
Fig. 3

(a) Sample-number dependence of the RMS error in the reconstruction. (b) Images of one of the original samples (upper) and the probe (lower) on the sample in the simulation. The scale bar is 2 μm. (c) Reconstructed phase images (upper) and the probe (lower) when the number of samples is 20 (left), 28 (middle), and 35 (right).

Fig. 4
Fig. 4

(a) Reconstructed phase images of the 32 samples. Inset is each SEM image. (b) Reconstructed intensities of two probe modes. The scale bar is 2 μm.

Equations (6)

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ψ i ( r ) = T i ( r ) × P ( r ) ,
I i ( q ) = | [ ψ i ( r ) ] | 2 = | Ψ i ( q ) | 2 ,
Ψ n , k i ( q ) = I i ( q ) k = 1 k = K | Ψ n , k i ( q ) | 2 Ψ n , k i ( q ) .
T n + 1 i ( r ) = T n i ( r ) + k = 1 k = K mode P n , k i * ( r ) [ ψ n , k i ( r ) ψ n , k i ( r ) ] k = 1 k = K mode | P n , k i ( r ) | 2 .
P n , k i + 1 ( r ) = P n , k i ( r ) + T n i * ( r ) [ ψ n , k i ( r ) ψ n , k i ( r ) ] | T n i ( r ) | 2 .
RMS error ( M ) = 1 M i = 1 M 1 X Y x = 1 , y = 1 x = X , y = Y [ arg [ T rec i ( r ) ] arg [ T input i ( r ) ] ] 2 ,

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