Abstract

Important nuances of a process or processes in action can be obtained from the phase retrieval of diffraction patterns for analysis of transient events. A significant limitation associated with the iterative approach is that predictive input functions are needed and can result in situations of nonconvergence. In dealing with a transient event recorded as a series of Fourier magnitude patterns, such a hit-and-miss characteristic, on the surface, appears computationally daunting. We report and demonstrate a strategy here that effectively minimizes this by using a prior retrieved frame as the predictive function for the current retrieval process.

© 2012 Optical Society of America

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  1. M. C. Newton, R. Harder, X. Huang, G. Xiong, and I. K. Robinson, “Phase retrieval of diffraction from highly strained crystals,” Phys. Rev. B 82, 165 436 (2010).
    [CrossRef]
  2. D. Montiel, M. Sutton, and M. Grant, “Phase retrieval from speckle patterns of ordering systems,” Phys. Rev. E 80, 041112 (2009).
    [CrossRef]
  3. J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a single double-wall carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
    [CrossRef]
  4. A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
    [CrossRef]
  5. X. Rondeau, E. Thiébaut, M. Tallon, and R. A. Foy, “Phase retrieval from speckle images,” J. Opt. Soc. Am. A 24, 3354–3365 (2007).
    [CrossRef]
  6. W. Gong and S. Han, “Phase-retrieval ghost imaging of complex-valued objects,” Phys. Rev. A 82, 023828 (2010).
    [CrossRef]
  7. R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901 (2006).
    [CrossRef]
  8. J. Miao, K. O. Hodgson, and D. Sayre, “An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images,” Proc. Natl. Acad. Sci. USA 98, 6641–6645 (2001).
    [CrossRef]
  9. Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102, 018101 (2009).
    [CrossRef]
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    [CrossRef]
  11. F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. B. Chen, J. K. Stamnes, A. J. Devaney, H. M. Pedersen, and K. Stamnes, “Reconstruction algorithm for diffraction tomography of diffuse photon density waves in a random medium,” Pure Appl. Opt. 7, 1161–1180 (1998).
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    [CrossRef]
  22. J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
    [CrossRef]
  23. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
    [CrossRef]
  24. A. Neild, J. T. Padding, Y. Lu, B. Bhaduri, W. J. Briels, and T. W. Ng, “Translational and rotational coupling in Brownian rods near a solid surface,” Phys. Rev. E 82, 041126 (2010).
    [CrossRef]
  25. B. Bhaduri, A. Neild, and T. W. Ng, “Directional Brownian diffusion dynamics in carbon nanofibers,” Appl. Phys. Lett. 92, 084105 (2008).
    [CrossRef]
  26. R. D. Luggar, J. A. Horrocks, R. D. Speller, and R. J. Lacey, “Determination of the geometric blurring of an energy x-ray diffraction (EDXRD) system and its use in the simulation of experimentally derived diffraction profiles,” Nucl. Instrum. Methods Phys. Res. A 383, 610–618 (1996).
    [CrossRef]
  27. S. V. Tipnis, V. V. Nagarkar, V. Gaysinskiy, S. R. Miller, and I. Shestakova, “High-speed x-ray imaging camera for time-resolved diffraction studies,” IEEE Trans. Nucl. Sci. 49, 2415–2419 (2002).
    [CrossRef]
  28. M. Bergh, G. Huldt, N. Timneanu, F. R. N. C. Maia, and J. Hajdu, “Feasibility of imaging living cells at subnanometer resolutions by ultrafast x-ray diffraction,” Q. Rev. Biophys. 41, 181–204 (2008).
    [CrossRef]

2011

2010

C. Wu, T. W. Ng, and A. Neild, “Phase and amplitude retrieval of objects embedded in a sinusoidal background from its diffraction pattern,” Appl. Opt. 49, 1831–1837 (2010).
[CrossRef]

M. C. Newton, R. Harder, X. Huang, G. Xiong, and I. K. Robinson, “Phase retrieval of diffraction from highly strained crystals,” Phys. Rev. B 82, 165 436 (2010).
[CrossRef]

W. Gong and S. Han, “Phase-retrieval ghost imaging of complex-valued objects,” Phys. Rev. A 82, 023828 (2010).
[CrossRef]

K. Kawahara, K. Gohara, Y. Maehara, T. Dobashi, and O. Kamimura, “Beam-divergence deconvolution for diffractive imaging,” Phys. Rev. B 81, 081404 (2010).
[CrossRef]

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

A. Neild, J. T. Padding, Y. Lu, B. Bhaduri, W. J. Briels, and T. W. Ng, “Translational and rotational coupling in Brownian rods near a solid surface,” Phys. Rev. E 82, 041126 (2010).
[CrossRef]

2009

D. Montiel, M. Sutton, and M. Grant, “Phase retrieval from speckle patterns of ordering systems,” Phys. Rev. E 80, 041112 (2009).
[CrossRef]

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102, 018101 (2009).
[CrossRef]

D. Pliakis and S. Minardi, “Phase front retrieval by means of an iterative shadowgraphic method,” J. Opt. Soc. Am. A 26, 99–107 (2009).
[CrossRef]

N. Nakajima, “Phase retrieval from a high-numerical-aperture intensity distribution by use of an aperture-array filter,” J. Opt. Soc. Am. A 26, 2172–2180 (2009).
[CrossRef]

2008

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

B. Bhaduri, A. Neild, and T. W. Ng, “Directional Brownian diffusion dynamics in carbon nanofibers,” Appl. Phys. Lett. 92, 084105 (2008).
[CrossRef]

M. Bergh, G. Huldt, N. Timneanu, F. R. N. C. Maia, and J. Hajdu, “Feasibility of imaging living cells at subnanometer resolutions by ultrafast x-ray diffraction,” Q. Rev. Biophys. 41, 181–204 (2008).
[CrossRef]

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]

2007

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of the optimization technique to non-crystalline x-ray diffraction microscopy—Guided Hybrid Input-Output Method (GHIO),” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

X. Rondeau, E. Thiébaut, M. Tallon, and R. A. Foy, “Phase retrieval from speckle images,” J. Opt. Soc. Am. A 24, 3354–3365 (2007).
[CrossRef]

2006

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901 (2006).
[CrossRef]

2005

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

J. S. Wu and J. C. H. Spence, “Phasing diffraction data from a stream of hydrated proteins,” J. Opt. Soc. Am. A 22, 1453–1459 (2005).
[CrossRef]

2004

W. McBride, N. L. O’Leary, and L. J. Allen, “Retrieval of a complex-valued object from its diffraction pattern,” Phys. Rev. Lett. 93, 233902 (2004).
[CrossRef]

2003

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a single double-wall carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

2002

S. V. Tipnis, V. V. Nagarkar, V. Gaysinskiy, S. R. Miller, and I. Shestakova, “High-speed x-ray imaging camera for time-resolved diffraction studies,” IEEE Trans. Nucl. Sci. 49, 2415–2419 (2002).
[CrossRef]

2001

J. Miao, K. O. Hodgson, and D. Sayre, “An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images,” Proc. Natl. Acad. Sci. USA 98, 6641–6645 (2001).
[CrossRef]

1998

B. Chen, J. K. Stamnes, A. J. Devaney, H. M. Pedersen, and K. Stamnes, “Reconstruction algorithm for diffraction tomography of diffuse photon density waves in a random medium,” Pure Appl. Opt. 7, 1161–1180 (1998).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

1996

R. D. Luggar, J. A. Horrocks, R. D. Speller, and R. J. Lacey, “Determination of the geometric blurring of an energy x-ray diffraction (EDXRD) system and its use in the simulation of experimentally derived diffraction profiles,” Nucl. Instrum. Methods Phys. Res. A 383, 610–618 (1996).
[CrossRef]

Allen, L. J.

W. McBride, N. L. O’Leary, and L. J. Allen, “Retrieval of a complex-valued object from its diffraction pattern,” Phys. Rev. Lett. 93, 233902 (2004).
[CrossRef]

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. 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]

Bauer, G.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Beetz, T.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Benner, W. H.

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]

Bergh, M.

M. Bergh, G. Huldt, N. Timneanu, F. R. N. C. Maia, and J. Hajdu, “Feasibility of imaging living cells at subnanometer resolutions by ultrafast x-ray diffraction,” Q. Rev. Biophys. 41, 181–204 (2008).
[CrossRef]

Bhaduri, B.

A. Neild, J. T. Padding, Y. Lu, B. Bhaduri, W. J. Briels, and T. W. Ng, “Translational and rotational coupling in Brownian rods near a solid surface,” Phys. Rev. E 82, 041126 (2010).
[CrossRef]

B. Bhaduri, A. Neild, and T. W. Ng, “Directional Brownian diffusion dynamics in carbon nanofibers,” Appl. Phys. Lett. 92, 084105 (2008).
[CrossRef]

Boeck, T.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Bogan, M. J.

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]

Borghi, R.

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901 (2006).
[CrossRef]

Boutet, 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]

Briels, W. J.

A. Neild, J. T. Padding, Y. Lu, B. Bhaduri, W. J. Briels, and T. W. Ng, “Translational and rotational coupling in Brownian rods near a solid surface,” Phys. Rev. E 82, 041126 (2010).
[CrossRef]

Chapman, H. N.

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]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

Chen, B.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

B. Chen, J. K. Stamnes, A. J. Devaney, H. M. Pedersen, and K. Stamnes, “Reconstruction algorithm for diffraction tomography of diffuse photon density waves in a random medium,” Pure Appl. Opt. 7, 1161–1180 (1998).
[CrossRef]

Chen, C.-C.

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of the optimization technique to non-crystalline x-ray diffraction microscopy—Guided Hybrid Input-Output Method (GHIO),” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

Devaney, A. J.

B. Chen, J. K. Stamnes, A. J. Devaney, H. M. Pedersen, and K. Stamnes, “Reconstruction algorithm for diffraction tomography of diffuse photon density waves in a random medium,” Pure Appl. Opt. 7, 1161–1180 (1998).
[CrossRef]

Dobashi, T.

K. Kawahara, K. Gohara, Y. Maehara, T. Dobashi, and O. Kamimura, “Beam-divergence deconvolution for diffractive imaging,” Phys. Rev. B 81, 081404 (2010).
[CrossRef]

Elser, V.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Foy, R. A.

Frank, M.

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]

Gao, M.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a single double-wall carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Gaysinskiy, V.

S. V. Tipnis, V. V. Nagarkar, V. Gaysinskiy, S. R. Miller, and I. Shestakova, “High-speed x-ray imaging camera for time-resolved diffraction studies,” IEEE Trans. Nucl. Sci. 49, 2415–2419 (2002).
[CrossRef]

Gohara, K.

K. Kawahara, K. Gohara, Y. Maehara, T. Dobashi, and O. Kamimura, “Beam-divergence deconvolution for diffractive imaging,” Phys. Rev. B 81, 081404 (2010).
[CrossRef]

Gong, W.

W. Gong and S. Han, “Phase-retrieval ghost imaging of complex-valued objects,” Phys. Rev. A 82, 023828 (2010).
[CrossRef]

Gori, F.

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901 (2006).
[CrossRef]

Grant, M.

D. Montiel, M. Sutton, and M. Grant, “Phase retrieval from speckle patterns of ordering systems,” Phys. Rev. E 80, 041112 (2009).
[CrossRef]

Hajdu, J.

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]

M. Bergh, G. Huldt, N. Timneanu, F. R. N. C. Maia, and J. Hajdu, “Feasibility of imaging living cells at subnanometer resolutions by ultrafast x-ray diffraction,” Q. Rev. Biophys. 41, 181–204 (2008).
[CrossRef]

Han, S.

W. Gong and S. Han, “Phase-retrieval ghost imaging of complex-valued objects,” Phys. Rev. A 82, 023828 (2010).
[CrossRef]

Harder, R.

M. C. Newton, R. Harder, X. Huang, G. Xiong, and I. K. Robinson, “Phase retrieval of diffraction from highly strained crystals,” Phys. Rev. B 82, 165 436 (2010).
[CrossRef]

Hau-Riege, S. P.

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]

Hodgson, K. O.

J. Miao, K. O. Hodgson, and D. Sayre, “An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images,” Proc. Natl. Acad. Sci. USA 98, 6641–6645 (2001).
[CrossRef]

Horrocks, J. A.

R. D. Luggar, J. A. Horrocks, R. D. Speller, and R. J. Lacey, “Determination of the geometric blurring of an energy x-ray diffraction (EDXRD) system and its use in the simulation of experimentally derived diffraction profiles,” Nucl. Instrum. Methods Phys. Res. A 383, 610–618 (1996).
[CrossRef]

Howells, M.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Huang, X.

M. C. Newton, R. Harder, X. Huang, G. Xiong, and I. K. Robinson, “Phase retrieval of diffraction from highly strained crystals,” Phys. Rev. B 82, 165 436 (2010).
[CrossRef]

Hüe, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

Huldt, G.

M. Bergh, G. Huldt, N. Timneanu, F. R. N. C. Maia, and J. Hajdu, “Feasibility of imaging living cells at subnanometer resolutions by ultrafast x-ray diffraction,” Q. Rev. Biophys. 41, 181–204 (2008).
[CrossRef]

Imamoto, N.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102, 018101 (2009).
[CrossRef]

Ishikawa, T.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102, 018101 (2009).
[CrossRef]

Jacobsen, C.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Kamimura, O.

K. Kawahara, K. Gohara, Y. Maehara, T. Dobashi, and O. Kamimura, “Beam-divergence deconvolution for diffractive imaging,” Phys. Rev. B 81, 081404 (2010).
[CrossRef]

Kawahara, K.

K. Kawahara, K. Gohara, Y. Maehara, T. Dobashi, and O. Kamimura, “Beam-divergence deconvolution for diffractive imaging,” Phys. Rev. B 81, 081404 (2010).
[CrossRef]

Kirz, J.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Lacey, R. J.

R. D. Luggar, J. A. Horrocks, R. D. Speller, and R. J. Lacey, “Determination of the geometric blurring of an energy x-ray diffraction (EDXRD) system and its use in the simulation of experimentally derived diffraction profiles,” Nucl. Instrum. Methods Phys. Res. A 383, 610–618 (1996).
[CrossRef]

Lee, T. K.

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of the optimization technique to non-crystalline x-ray diffraction microscopy—Guided Hybrid Input-Output Method (GHIO),” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

Li, E.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Lima, E.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Liu, Y.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Lu, Y.

A. Neild, J. T. Padding, Y. Lu, B. Bhaduri, W. J. Briels, and T. W. Ng, “Translational and rotational coupling in Brownian rods near a solid surface,” Phys. Rev. E 82, 041126 (2010).
[CrossRef]

Luggar, R. D.

R. D. Luggar, J. A. Horrocks, R. D. Speller, and R. J. Lacey, “Determination of the geometric blurring of an energy x-ray diffraction (EDXRD) system and its use in the simulation of experimentally derived diffraction profiles,” Nucl. Instrum. Methods Phys. Res. A 383, 610–618 (1996).
[CrossRef]

Maehara, Y.

K. Kawahara, K. Gohara, Y. Maehara, T. Dobashi, and O. Kamimura, “Beam-divergence deconvolution for diffractive imaging,” Phys. Rev. B 81, 081404 (2010).
[CrossRef]

Maeshima, K.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102, 018101 (2009).
[CrossRef]

Maia, F.

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]

Maia, F. R. N. C.

M. Bergh, G. Huldt, N. Timneanu, F. R. N. C. Maia, and J. Hajdu, “Feasibility of imaging living cells at subnanometer resolutions by ultrafast x-ray diffraction,” Q. Rev. Biophys. 41, 181–204 (2008).
[CrossRef]

Maiden, A. M.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

Marcelli, A.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Marchesini, 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]

Marklund, E.

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]

McBride, W.

W. McBride, N. L. O’Leary, and L. J. Allen, “Retrieval of a complex-valued object from its diffraction pattern,” Phys. Rev. Lett. 93, 233902 (2004).
[CrossRef]

Metzger, T. H.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Miao, H.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Miao, J.

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of the optimization technique to non-crystalline x-ray diffraction microscopy—Guided Hybrid Input-Output Method (GHIO),” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

J. Miao, K. O. Hodgson, and D. Sayre, “An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images,” Proc. Natl. Acad. Sci. USA 98, 6641–6645 (2001).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

Midgley, P. A.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

Miller, S. R.

S. V. Tipnis, V. V. Nagarkar, V. Gaysinskiy, S. R. Miller, and I. Shestakova, “High-speed x-ray imaging camera for time-resolved diffraction studies,” IEEE Trans. Nucl. Sci. 49, 2415–2419 (2002).
[CrossRef]

Minardi, S.

Ming, H.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Mocuta, C.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Montiel, D.

D. Montiel, M. Sutton, and M. Grant, “Phase retrieval from speckle patterns of ordering systems,” Phys. Rev. E 80, 041112 (2009).
[CrossRef]

Mundboth, K.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Nagahara, L. A.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a single double-wall carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Nagarkar, V. V.

S. V. Tipnis, V. V. Nagarkar, V. Gaysinskiy, S. R. Miller, and I. Shestakova, “High-speed x-ray imaging camera for time-resolved diffraction studies,” IEEE Trans. Nucl. Sci. 49, 2415–2419 (2002).
[CrossRef]

Nakajima, N.

Neild, A.

C. Wu, T. W. Ng, and A. Neild, “Phase and amplitude retrieval of objects embedded in a sinusoidal background from its diffraction pattern,” Appl. Opt. 49, 1831–1837 (2010).
[CrossRef]

A. Neild, J. T. Padding, Y. Lu, B. Bhaduri, W. J. Briels, and T. W. Ng, “Translational and rotational coupling in Brownian rods near a solid surface,” Phys. Rev. E 82, 041126 (2010).
[CrossRef]

B. Bhaduri, A. Neild, and T. W. Ng, “Directional Brownian diffusion dynamics in carbon nanofibers,” Appl. Phys. Lett. 92, 084105 (2008).
[CrossRef]

Neiman, A. M.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Newton, M. C.

M. C. Newton, R. Harder, X. Huang, G. Xiong, and I. K. Robinson, “Phase retrieval of diffraction from highly strained crystals,” Phys. Rev. B 82, 165 436 (2010).
[CrossRef]

Ng, T. W.

C. Wu, T. W. Ng, and A. Neild, “Phase and amplitude retrieval of objects embedded in a sinusoidal background from its diffraction pattern,” Appl. Opt. 49, 1831–1837 (2010).
[CrossRef]

A. Neild, J. T. Padding, Y. Lu, B. Bhaduri, W. J. Briels, and T. W. Ng, “Translational and rotational coupling in Brownian rods near a solid surface,” Phys. Rev. E 82, 041126 (2010).
[CrossRef]

B. Bhaduri, A. Neild, and T. W. Ng, “Directional Brownian diffusion dynamics in carbon nanofibers,” Appl. Phys. Lett. 92, 084105 (2008).
[CrossRef]

Nishino, Y.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102, 018101 (2009).
[CrossRef]

Nugent, K. A.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

O’Leary, N. L.

W. McBride, N. L. O’Leary, and L. J. Allen, “Retrieval of a complex-valued object from its diffraction pattern,” Phys. Rev. Lett. 93, 233902 (2004).
[CrossRef]

Osten, W.

Padding, J. T.

A. Neild, J. T. Padding, Y. Lu, B. Bhaduri, W. J. Briels, and T. W. Ng, “Translational and rotational coupling in Brownian rods near a solid surface,” Phys. Rev. E 82, 041126 (2010).
[CrossRef]

Pedersen, H. M.

B. Chen, J. K. Stamnes, A. J. Devaney, H. M. Pedersen, and K. Stamnes, “Reconstruction algorithm for diffraction tomography of diffuse photon density waves in a random medium,” Pure Appl. Opt. 7, 1161–1180 (1998).
[CrossRef]

Pedrini, G.

Pliakis, D.

Riot, V.

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]

Robinson, I. K.

M. C. Newton, R. Harder, X. Huang, G. Xiong, and I. K. Robinson, “Phase retrieval of diffraction from highly strained crystals,” Phys. Rev. B 82, 165 436 (2010).
[CrossRef]

Rodenburg, J. M.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

Rohner, U.

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]

Rondeau, X.

Santarsiero, M.

R. Borghi, F. Gori, and M. Santarsiero, “Phase and amplitude retrieval in ghost diffraction from field-correlation measurements,” Phys. Rev. Lett. 96, 183901 (2006).
[CrossRef]

Sayre, D.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

J. Miao, K. O. Hodgson, and D. Sayre, “An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images,” Proc. Natl. Acad. Sci. USA 98, 6641–6645 (2001).
[CrossRef]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15, 1662–1669 (1998).
[CrossRef]

Schmidbauer, M.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Seibert, M. M.

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]

Shapiro, D.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Shestakova, I.

S. V. Tipnis, V. V. Nagarkar, V. Gaysinskiy, S. R. Miller, and I. Shestakova, “High-speed x-ray imaging camera for time-resolved diffraction studies,” IEEE Trans. Nucl. Sci. 49, 2415–2419 (2002).
[CrossRef]

Speller, R. D.

R. D. Luggar, J. A. Horrocks, R. D. Speller, and R. J. Lacey, “Determination of the geometric blurring of an energy x-ray diffraction (EDXRD) system and its use in the simulation of experimentally derived diffraction profiles,” Nucl. Instrum. Methods Phys. Res. A 383, 610–618 (1996).
[CrossRef]

Spence, J. C. H.

Spiller, E.

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]

Stamnes, J. K.

B. Chen, J. K. Stamnes, A. J. Devaney, H. M. Pedersen, and K. Stamnes, “Reconstruction algorithm for diffraction tomography of diffuse photon density waves in a random medium,” Pure Appl. Opt. 7, 1161–1180 (1998).
[CrossRef]

Stamnes, K.

B. Chen, J. K. Stamnes, A. J. Devaney, H. M. Pedersen, and K. Stamnes, “Reconstruction algorithm for diffraction tomography of diffuse photon density waves in a random medium,” Pure Appl. Opt. 7, 1161–1180 (1998).
[CrossRef]

Stangl, J.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Sutton, M.

D. Montiel, M. Sutton, and M. Grant, “Phase retrieval from speckle patterns of ordering systems,” Phys. Rev. E 80, 041112 (2009).
[CrossRef]

Svenda, M.

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]

Sweeney, F.

F. Hüe, J. M. Rodenburg, A. M. Maiden, F. Sweeney, and P. A. Midgley, “Wave-front phase retrieval in transmission electron microscopy via ptychography,” Phys. Rev. B 82, 121415 (2010).
[CrossRef]

Takahashi, Y.

Y. Nishino, Y. Takahashi, N. Imamoto, T. Ishikawa, and K. Maeshima, “Three-dimensional visualization of a human chromosome using coherent x-ray diffraction,” Phys. Rev. Lett. 102, 018101 (2009).
[CrossRef]

Tallon, M.

Thibault, P.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Thiébaut, E.

Tian, Y.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Timneanu, N.

M. Bergh, G. Huldt, N. Timneanu, F. R. N. C. Maia, and J. Hajdu, “Feasibility of imaging living cells at subnanometer resolutions by ultrafast x-ray diffraction,” Q. Rev. Biophys. 41, 181–204 (2008).
[CrossRef]

Tipnis, S. V.

S. V. Tipnis, V. V. Nagarkar, V. Gaysinskiy, S. R. Miller, and I. Shestakova, “High-speed x-ray imaging camera for time-resolved diffraction studies,” IEEE Trans. Nucl. Sci. 49, 2415–2419 (2002).
[CrossRef]

Vartanyants, I.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a single double-wall carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Vartanyants, I. A.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Wang, C. W.

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of the optimization technique to non-crystalline x-ray diffraction microscopy—Guided Hybrid Input-Output Method (GHIO),” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

Wang, J.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Wilkins, S. W.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Woods, B.

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]

Wu, C.

Wu, J. S.

Wu, Z.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Xiong, G.

M. C. Newton, R. Harder, X. Huang, G. Xiong, and I. K. Robinson, “Phase retrieval of diffraction from highly strained crystals,” Phys. Rev. B 82, 165 436 (2010).
[CrossRef]

Yefanov, O. M.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Zhang, F.

Zhang, R.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a single double-wall carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Zhu, P.

Y. Liu, B. Chen, E. Li, J. Wang, A. Marcelli, S. W. Wilkins, H. Ming, Y. Tian, K. A. Nugent, P. Zhu, and Z. Wu, “Phase retrieval in x-ray imaging based on using structured illumination,” Phys. Rev. A 78, 023817 (2008).
[CrossRef]

Zozulya, A. V.

A. V. Zozulya, O. M. Yefanov, I. A. Vartanyants, K. Mundboth, C. Mocuta, T. H. Metzger, J. Stangl, G. Bauer, T. Boeck, and M. Schmidbauer, “Imaging of nanoislands in coherent grazing-incidence small-angle x-ray scattering experiments,” Phys. Rev. B 78, 121304 (2008).
[CrossRef]

Zuo, J. M.

J. M. Zuo, I. Vartanyants, M. Gao, R. Zhang, and L. A. Nagahara, “Atomic resolution imaging of a single double-wall carbon nanotube from diffraction intensities,” Science 300, 1419–1421 (2003).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

B. Bhaduri, A. Neild, and T. W. Ng, “Directional Brownian diffusion dynamics in carbon nanofibers,” Appl. Phys. Lett. 92, 084105 (2008).
[CrossRef]

IEEE Trans. Nucl. Sci.

S. V. Tipnis, V. V. Nagarkar, V. Gaysinskiy, S. R. Miller, and I. Shestakova, “High-speed x-ray imaging camera for time-resolved diffraction studies,” IEEE Trans. Nucl. Sci. 49, 2415–2419 (2002).
[CrossRef]

J. Opt. Soc. Am. A

Nano Lett.

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]

Nucl. Instrum. Methods Phys. Res. A

R. D. Luggar, J. A. Horrocks, R. D. Speller, and R. J. Lacey, “Determination of the geometric blurring of an energy x-ray diffraction (EDXRD) system and its use in the simulation of experimentally derived diffraction profiles,” Nucl. Instrum. Methods Phys. Res. A 383, 610–618 (1996).
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Supplementary Material (1)

» Media 1: MPG (2544 KB)     

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Figures (8)

Fig. 1.
Fig. 1.

Pictorial description of the proposed efficient phase retrieval strategy. A random predictive function is used in the iteration process to retrieve the first image frame from the diffraction pattern, but subsequent image frames are processed using the previous retrieved frame as predictive function.

Fig. 2.
Fig. 2.

Images from frames (a) 1, (b) 2, and (c) 100 taken from a video sequence of a cell undergoing mitosis (Media 1). The corresponding retrieved frames are presented in (d) using a random predictive function, and (e) and (f) using the proposed approach. The retrieval images are qualitatively good.

Fig. 3.
Fig. 3.

Plots of typical reconstruction error versus iteration number trends found and categorized from curves I to IV. The occurrence of curve IV, in which convergence occurred in one iteration, was obtained only when using the proposed method and not with the random phase prediction approach.

Fig. 4.
Fig. 4.

(a) Plots of the distribution of the lowest reconstruction error obtained of frame 1 by using different random predictive functions over 50 times (blue diamond markers) and that for frames 2 to 50 in the image sequence using the proposed method (orange square markers). The latter values are significantly lower. (b) Corresponding plots of the number of iterations needed to meet the benchmark of 10 4 . The proposed method demanded significantly fewer iterations.

Fig. 5.
Fig. 5.

Plots of the distribution of the lowest RMS phase difference obtained of frame 1 by using different random predictive functions over 50 times (blue diamond markers) and that for frames 2 to 50 in the image sequence using the proposed method (orange square markers). The trend closely mimics Fig. 4(a).

Fig. 6.
Fig. 6.

Phase difference distribution of the reconstructed images of frames (a) 2 and (b) 100. While the level of difference is low, there are regions where it is heightened.

Fig. 7.
Fig. 7.

Plots of the distribution of the lowest RMS phase difference obtained by using the different SNR values introduced. The trend shows a falloff in error that is initially steep but is gradual after SNR = 200 .

Fig. 8.
Fig. 8.

Phase difference distribution of the reconstructed images of frames replete with noise such that (a)  SNR = 5 and (b)  SNR = 200 . At low SNR, the deterioration is more evident and image wide.

Equations (7)

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f ( x , y ) = g ( x , y ) e i θ ( x , y ) .
f 1 , 1 ( x , y ) = F 1 ( ( | F 1 ( u , v ) | ) × F 1 , 0 ( u , v ) | F 1 , 0 ( u , v ) | ) ,
f 1 , 1 ( x , y ) = { f 1 , 1 ( x , y ) x , y , f 1 , 1 ( x , y ) S f 1 , 0 ( x , y ) β f 1 , 1 ( x , y ) x , y , f 1 , 1 ( x , y ) S C ,
f 1 , j ( x , y ) = { f 1 , j ( x , y ) x , y , f 1 , j ( x , y ) S f 1 , j 1 ( x , y ) β f 1 , j ( x , y ) x , y , f 1 , j ( x , y ) S C .
E 1 , j = ( ( x , y ) S f 1 , j ( x , y ) ( x , y ) S f 1 , j ( x , y ) ) .
ξ = x = 1 , y = 1 x = X , y = Y ( θ r ( x , y ) θ ( x , y ) ) 2 X Y .
Noise ( u , v ) = F ( u , v ) SNR × random,

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