Abstract

The post-experiment processing of X-ray Diffraction Microscopy data is often time-consuming and difficult. This is mostly due to the fact that even if a preliminary result has been reconstructed, there is no definitive answer as to whether or not a better result with more consistently retrieved phases can still be obtained. We show here that the first step in data analysis, the assembly of two-dimensional diffraction patterns from a large set of raw diffraction data, is crucial to obtaining reconstructions of highest possible consistency. We have developed software that automates this process and results in consistently accurate diffraction patterns. We have furthermore derived some criteria of validity for a tool commonly used to assess the consistency of reconstructions, the phase retrieval transfer function, and suggest a modified version that has improved utility for judging reconstruction quality.

© 2010 Optical Society of America

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2010

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

2009

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

X. Huang, H. Miao, J. Steinbrener, J. Nelson, D. Shapiro, A. Stewart, J. Turner, and C. Jacobsen, “Signal-tonoise and radiation exposure considerations in conventional and diffraction x-ray microscopy,” Opt. Express 17, 13541–13553 (2009).
[CrossRef] [PubMed]

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (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] [PubMed]

2008

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

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

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

2007

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method,” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission X-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
[CrossRef] [PubMed]

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

2006

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

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from x-ray diffraction data,” Acta Crystallogr. A 62, 248–261 (2006).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

2005

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

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

2003

V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40–55 (2003).
[CrossRef]

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

J. Miao, K. Hodgson, T. Ishikawa, C. Larabell, M. LeGros, and Y. Nishino, “Imaging whole escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. U.S.A. 100, 110–112 (2003).
[CrossRef] [PubMed]

2002

J. Miao, T. Ishikawa, B. Johnson, E. Anderson, B. Lai, and K. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

2001

I. Robinson, I. Vartanyants, G. Williams, M. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

1999

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

1993

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: Photoabsorption, scattering, transmission, and reflection at E=50–30,000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

1992

J. Rodenburg, and R. Bates, “The theory of super-resolution electron microscopy via wigner-distribution deconvolution,” Philos. Trans. R. Soc. Lond. 339, 521–553 (1992).
[CrossRef]

1991

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

1989

1987

M. H. J. Koch, M. C. Vega, Z. Sayers, and A. M. Michon, “The superstructure of chromatin and its condensation mechanism,” Eur. Biophys. J. 14, 307–319 (1987).
[CrossRef] [PubMed]

1982

1978

1977

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, “Transmission microscopy of unmodified biological materials: Comparative radiation dosages with electrons and ultrasoft x-ray photons,” Ultramicroscopy 2, 337–341 (1977).
[CrossRef] [PubMed]

1957

J. M. Cowley, and A. F. Moodie, “Fourier images. I. The point source,” Proc. Phys. Soc. B 70, 486–496 (1957).
[CrossRef]

1952

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5, 843 (1952).
[CrossRef]

Abbey, B.

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

Anderson, E.

J. Miao, T. Ishikawa, B. Johnson, E. Anderson, B. Lai, and K. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

Artyukhin, A. B.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

Barty, A.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

Bates, R.

J. Rodenburg, and R. Bates, “The theory of super-resolution electron microscopy via wigner-distribution deconvolution,” Philos. Trans. R. Soc. Lond. 339, 521–553 (1992).
[CrossRef]

Baumann, T.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

Beerlink, A.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Beetz, T.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

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

Boye, R.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Browne, M. T.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

Buckley, C. J.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

Bunk, O.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

Burghammer, M.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Chapman, H.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

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

Chapman, H. N.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

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

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
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Chen, C.-C.

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method,” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

Clark, J.

B. Abbey, K. Nugent, G. Williams, J. Clark, A. Peele, M. Pfeifer, M. de Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4, 394–398 (2008).
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J. M. Cowley, and A. F. Moodie, “Fourier images. I. The point source,” Proc. Phys. Soc. B 70, 486–496 (1957).
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Cui, C.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

Cullis, A.

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: Photoabsorption, scattering, transmission, and reflection at E=50–30,000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

de Jonge, M.

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

Dhal, B. B.

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

Dierolf, M.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Dobson, B.

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

Elser, V.

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from x-ray diffraction data,” Acta Crystallogr. A 62, 248–261 (2006).
[CrossRef]

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

V. Elser, “Phase retrieval by iterated projections,” J. Opt. Soc. Am. A 20, 40–55 (2003).
[CrossRef]

Feder, R.

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, “Transmission microscopy of unmodified biological materials: Comparative radiation dosages with electrons and ultrasoft x-ray photons,” Ultramicroscopy 2, 337–341 (1977).
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Feldkamp, J. M.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Feser, M.

B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission X-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
[CrossRef] [PubMed]

Fienup, J.

Giewekemeyer, K.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: Photoabsorption, scattering, transmission, and reflection at E=50–30,000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Hau-Riege, S.

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

Hau-Riege, S. P.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

He, H.

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: Photoabsorption, scattering, transmission, and reflection at E=50–30,000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Hodgson, K.

J. Miao, K. Hodgson, T. Ishikawa, C. Larabell, M. LeGros, and Y. Nishino, “Imaging whole escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. U.S.A. 100, 110–112 (2003).
[CrossRef] [PubMed]

J. Miao, T. Ishikawa, B. Johnson, E. Anderson, B. Lai, and K. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Holton, J.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

Hornberger, B.

B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission X-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
[CrossRef] [PubMed]

Howells, M.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

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

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

Howells, M. R.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

Huang, X.

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

X. Huang, H. Miao, J. Steinbrener, J. Nelson, D. Shapiro, A. Stewart, J. Turner, and C. Jacobsen, “Signal-tonoise and radiation exposure considerations in conventional and diffraction x-ray microscopy,” Opt. Express 17, 13541–13553 (2009).
[CrossRef] [PubMed]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

Hurst, A.

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

Ilavsky, J.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

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] [PubMed]

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] [PubMed]

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

J. Miao, K. Hodgson, T. Ishikawa, C. Larabell, M. LeGros, and Y. Nishino, “Imaging whole escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. U.S.A. 100, 110–112 (2003).
[CrossRef] [PubMed]

J. Miao, T. Ishikawa, B. Johnson, E. Anderson, B. Lai, and K. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Jacobsen, C.

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

X. Huang, H. Miao, J. Steinbrener, J. Nelson, D. Shapiro, A. Stewart, J. Turner, and C. Jacobsen, “Signal-tonoise and radiation exposure considerations in conventional and diffraction x-ray microscopy,” Opt. Express 17, 13541–13553 (2009).
[CrossRef] [PubMed]

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

B. Hornberger, M. Feser, and C. Jacobsen, “Quantitative amplitude and phase contrast imaging in a scanning transmission X-ray microscope,” Ultramicroscopy 107, 644–655 (2007).
[CrossRef] [PubMed]

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from x-ray diffraction data,” Acta Crystallogr. A 62, 248–261 (2006).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

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

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

Jefimovs, K.

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

Johnson, B.

J. Miao, T. Ishikawa, B. Johnson, E. Anderson, B. Lai, and K. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Johnson, I.

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

Kalbfleisch, S.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Kern, D.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

Kewish, C. M.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Kim, D. M.

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, “Transmission microscopy of unmodified biological materials: Comparative radiation dosages with electrons and ultrasoft x-ray photons,” Ultramicroscopy 2, 337–341 (1977).
[CrossRef] [PubMed]

Kinney, J. H.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

Kirz, J.

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

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

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, “Transmission microscopy of unmodified biological materials: Comparative radiation dosages with electrons and ultrasoft x-ray photons,” Ultramicroscopy 2, 337–341 (1977).
[CrossRef] [PubMed]

Koch, M. H. J.

M. H. J. Koch, M. C. Vega, Z. Sayers, and A. M. Michon, “The superstructure of chromatin and its condensation mechanism,” Eur. Biophys. J. 14, 307–319 (1987).
[CrossRef] [PubMed]

Kohmura, Y.

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

Lai, B.

J. Miao, T. Ishikawa, B. Johnson, E. Anderson, B. Lai, and K. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

Larabell, C.

J. Miao, K. Hodgson, T. Ishikawa, C. Larabell, M. LeGros, and Y. Nishino, “Imaging whole escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. U.S.A. 100, 110–112 (2003).
[CrossRef] [PubMed]

Lee, T. K.

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method,” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

Lee, T.-K.

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

LeGros, M.

J. Miao, K. Hodgson, T. Ishikawa, C. Larabell, M. LeGros, and Y. Nishino, “Imaging whole escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. U.S.A. 100, 110–112 (2003).
[CrossRef] [PubMed]

Lima, E.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

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

London, R. A.

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] [PubMed]

Maiden, A. M.

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

Marchesini, S.

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

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

McNulty, I.

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

Menzel, A.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

Miao, H.

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

X. Huang, H. Miao, J. Steinbrener, J. Nelson, D. Shapiro, A. Stewart, J. Turner, and C. Jacobsen, “Signal-tonoise and radiation exposure considerations in conventional and diffraction x-ray microscopy,” Opt. Express 17, 13541–13553 (2009).
[CrossRef] [PubMed]

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

Miao, J.

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method,” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

J. Miao, K. Hodgson, T. Ishikawa, C. Larabell, M. LeGros, and Y. Nishino, “Imaging whole escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. U.S.A. 100, 110–112 (2003).
[CrossRef] [PubMed]

J. Miao, T. Ishikawa, B. Johnson, E. Anderson, B. Lai, and K. Hodgson, “High resolution 3D x-ray diffraction microscopy,” Phys. Rev. Lett. 89, 088303 (2002).
[CrossRef] [PubMed]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Michon, A. M.

M. H. J. Koch, M. C. Vega, Z. Sayers, and A. M. Michon, “The superstructure of chromatin and its condensation mechanism,” Eur. Biophys. J. 14, 307–319 (1987).
[CrossRef] [PubMed]

Minor, A. M.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

Moodie, A. F.

J. M. Cowley, and A. F. Moodie, “Fourier images. I. The point source,” Proc. Phys. Soc. B 70, 486–496 (1957).
[CrossRef]

Neiman, A.

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

Neiman, A. M.

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

Neimmn, A. M.

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

Nelson, J.

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

X. Huang, H. Miao, J. Steinbrener, J. Nelson, D. Shapiro, A. Stewart, J. Turner, and C. Jacobsen, “Signal-tonoise and radiation exposure considerations in conventional and diffraction x-ray microscopy,” Opt. Express 17, 13541–13553 (2009).
[CrossRef] [PubMed]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[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] [PubMed]

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

J. Miao, K. Hodgson, T. Ishikawa, C. Larabell, M. LeGros, and Y. Nishino, “Imaging whole escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Natl. Acad. Sci. U.S.A. 100, 110–112 (2003).
[CrossRef] [PubMed]

Noy, A.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

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

Nugent, K.

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

Nugent, K. A.

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

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

Paterson, D.

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

Patommel, J.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Peele, A.

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

Peele, A. G.

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

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

Pfeifer, M.

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

I. Robinson, I. Vartanyants, G. Williams, M. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

Pfeiffer, F.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

Pitney, J.

I. Robinson, I. Vartanyants, G. Williams, M. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

Quiney, H. M.

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

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

Ramunno-Johnson, D.

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

Riekel, C.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Risbud, S. H.

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

Rivers, M.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

Robinson, I.

I. Robinson, I. Vartanyants, G. Williams, M. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

Rodenburg, J.

J. Rodenburg, A. Hurst, A. Cullis, B. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007).
[CrossRef] [PubMed]

J. Rodenburg, and R. Bates, “The theory of super-resolution electron microscopy via wigner-distribution deconvolution,” Philos. Trans. R. Soc. Lond. 339, 521–553 (1992).
[CrossRef]

Rodenburg, J. M.

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

Rosen, M. D.

Rosen, R.

Salditt, T.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

Sayers, Z.

M. H. J. Koch, M. C. Vega, Z. Sayers, and A. M. Michon, “The superstructure of chromatin and its condensation mechanism,” Eur. Biophys. J. 14, 307–319 (1987).
[CrossRef] [PubMed]

Sayre, D.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from x-ray diffraction data,” Acta Crystallogr. A 62, 248–261 (2006).
[CrossRef]

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

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, “Transmission microscopy of unmodified biological materials: Comparative radiation dosages with electrons and ultrasoft x-ray photons,” Ultramicroscopy 2, 337–341 (1977).
[CrossRef] [PubMed]

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5, 843 (1952).
[CrossRef]

Schoeder, S.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Schroer, C. G.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Schropp, A.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Schwab, A.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Shapiro, D.

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

X. Huang, H. Miao, J. Steinbrener, J. Nelson, D. Shapiro, A. Stewart, J. Turner, and C. Jacobsen, “Signal-tonoise and radiation exposure considerations in conventional and diffraction x-ray microscopy,” Opt. Express 17, 13541–13553 (2009).
[CrossRef] [PubMed]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from x-ray diffraction data,” Acta Crystallogr. A 62, 248–261 (2006).
[CrossRef]

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

Shapiro, D. A.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

Song, C.

J. Miao, C.-C. Chen, C. Song, Y. Nishino, Y. Kohmura, T. Ishikawa, D. Ramunno-Johnson, T.-K. Lee, and S. H. Risbud, “Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy,” Phys. Rev. Lett. 97, 215503 (2006).
[CrossRef] [PubMed]

Spence, J.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

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

Spence, J. C. H.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

Spiller, E.

D. Sayre, J. Kirz, R. Feder, D. M. Kim, and E. Spiller, “Transmission microscopy of unmodified biological materials: Comparative radiation dosages with electrons and ultrasoft x-ray photons,” Ultramicroscopy 2, 337–341 (1977).
[CrossRef] [PubMed]

Starodub, D.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

Steinbrener, J.

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

X. Huang, H. Miao, J. Steinbrener, J. Nelson, D. Shapiro, A. Stewart, J. Turner, and C. Jacobsen, “Signal-tonoise and radiation exposure considerations in conventional and diffraction x-ray microscopy,” Opt. Express 17, 13541–13553 (2009).
[CrossRef] [PubMed]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

Stephan, S.

C. G. Schroer, R. Boye, J. M. Feldkamp, J. Patommel, A. Schropp, A. Schwab, S. Stephan, M. Burghammer, S. Schoeder, and C. Riekel, “Coherent x-ray diffraction imaging with nanofocused illumination,” Phys. Rev. Lett. 101, 090801 (2008).
[CrossRef] [PubMed]

Stewart, A.

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

X. Huang, H. Miao, J. Steinbrener, J. Nelson, D. Shapiro, A. Stewart, J. Turner, and C. Jacobsen, “Signal-tonoise and radiation exposure considerations in conventional and diffraction x-ray microscopy,” Opt. Express 17, 13541–13553 (2009).
[CrossRef] [PubMed]

Stolken, J.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

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] [PubMed]

Thibault, P.

K. Giewekemeyer, P. Thibault, S. Kalbfleisch, A. Beerlink, C. M. Kewish, M. Dierolf, F. Pfeiffer, and T. Salditt, “Quantitative biological imaging by ptychographic x-ray diffraction microscopy,” Proc. Natl. Acad. Sci. U.S.A. 107, 529–534 (2010).
[CrossRef]

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning x-ray diffraction microscopy,” Science 321, 379–382 (2008).
[CrossRef] [PubMed]

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from x-ray diffraction data,” Acta Crystallogr. A 62, 248–261 (2006).
[CrossRef]

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

Tran, C. Q.

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

Trebes, J. E.

Turner, J.

X. Huang, H. Miao, J. Steinbrener, J. Nelson, D. Shapiro, A. Stewart, J. Turner, and C. Jacobsen, “Signal-tonoise and radiation exposure considerations in conventional and diffraction x-ray microscopy,” Opt. Express 17, 13541–13553 (2009).
[CrossRef] [PubMed]

X. Huang, J. Nelson, J. Kirz, E. Lima, S. Marchesini, H. Miao, A. Neiman, D. Shapiro, J. Steinbrener, A. Stewart, J. Turner, and C. Jacobsen, “Soft x-ray diffraction microscopy of a frozen hydrated yeast cell,” Phys. Rev. Lett. 103, 198101 (2009).
[CrossRef]

Turner, J. J.

J. Nelson, X. Huang, J. Steinbrener, D. Shapiro, J. Kirz, S. Marchesini, A. M. Neiman, J. J. Turner, and C. Jacobsen, “High-resolution x-ray diffraction microscopy of specifically labeled yeast cells,” Proc. Natl. Acad. Sci. U.S.A. 107, 7235–7239 (2010).
[CrossRef] [PubMed]

van Buuren, T.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

Vartanyants, I.

I. Robinson, I. Vartanyants, G. Williams, M. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

Vega, M. C.

M. H. J. Koch, M. C. Vega, Z. Sayers, and A. M. Michon, “The superstructure of chromatin and its condensation mechanism,” Eur. Biophys. J. 14, 307–319 (1987).
[CrossRef] [PubMed]

Wang, C. W.

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method,” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

Weierstall, U.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. P. Hau-Riege, C. Cui, M. Howells, R. Rosen, H. He, J. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, “High resolution ab initio three-dimensional x-ray diffraction microscopy,” J. Opt. Soc. Am. A 23, 1179–1200 (2006).
[CrossRef]

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

Willey, T.

A. Barty, S. Marchesini, H. N. Chapman, C. Cui, M. R. Howells, D. A. Shapiro, A. M. Minor, J. C. H. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. P. Hau-Riege, A. B. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. H. Kinney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

Williams, G.

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

I. Robinson, I. Vartanyants, G. Williams, M. Pfeifer, and J. Pitney, “Reconstruction of the shapes of gold nanocrystals using coherent x-ray diffraction,” Phys. Rev. Lett. 87, 195505 (2001).
[CrossRef] [PubMed]

Williams, G. J.

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

Williams, S.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

Zhang, X.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

Acta Crystallogr.

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5, 843 (1952).
[CrossRef]

Acta Crystallogr. A

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

P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, “Reconstruction of a yeast cell from x-ray diffraction data,” Acta Crystallogr. A 62, 248–261 (2006).
[CrossRef]

Appl. Opt.

At. Data Nucl. Data Tables

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: Photoabsorption, scattering, transmission, and reflection at E=50–30,000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Eur. Biophys. J.

M. H. J. Koch, M. C. Vega, Z. Sayers, and A. M. Michon, “The superstructure of chromatin and its condensation mechanism,” Eur. Biophys. J. 14, 307–319 (1987).
[CrossRef] [PubMed]

J. Electron Spectrosc. Relat. Phenom.

M. Howells, T. Beetz, H. Chapman, C. Cui, J. Holton, C. Jacobsen, J. Kirz, E. Lima, S. Marchesini, H. Miao, D. Sayre, D. Shapiro, J. Spence, and D. Starodub, “An assessment of the resolution limitation due to radiation damage in x-ray diffraction microscopy,” J. Electron Spectrosc. Relat. Phenom. 170, 4–12 (2009).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Phys.

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

Nature

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “An extension of the methods of x-ray crystallography to allow imaging of micron-size non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Opt. Commun.

C. Jacobsen, S. Williams, E. Anderson, M. T. Browne, C. J. Buckley, D. Kern, J. Kirz, M. Rivers, and X. Zhang, “Diffraction-limited imaging in a scanning transmission x-ray microscope,” Opt. Commun. 86, 351–364 (1991).
[CrossRef]

Opt. Express

Opt. Lett.

Philos. Trans. R. Soc. Lond.

J. Rodenburg, and R. Bates, “The theory of super-resolution electron microscopy via wigner-distribution deconvolution,” Philos. Trans. R. Soc. Lond. 339, 521–553 (1992).
[CrossRef]

Phys. Rev. B

C.-C. Chen, J. Miao, C. W. Wang, and T. K. Lee, “Application of optimization technique to noncrystalline x-ray diffraction microscopy: Guided hybrid input-output method,” Phys. Rev. B 76, 064113 (2007).
[CrossRef]

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

Phys. Rev. Lett.

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

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Figures (8)

Fig. 8.
Fig. 8.

Flowchart of AMP. The processes in red involve weighted normalization and weighted averaging as described in Sec. 2.2 and outlined in pseudocode in Algorithm 1 and Algorithm 2, respectively.

Fig. 1.
Fig. 1.

Assembled diffraction intensities of data collected on a freeze-dried labeled yeast cell. On the left, the same quadrant of the entire array is shown on a false color logarithmic scale for both AMP-assembled data (in black) and data assembled by hand (in red). An inset shows the highest spatial frequencies of the merged intensities on a false color linear scale. The AMP-assembled intensities show good contrast for speckles all the way to highest spatial frequencies where the hand assembled intensities are dominated by noise. On the right, the power spectral densities for both arrays are plotted on a log-log scale. The hand-assembled data does not follow a straight power law indicating scaling errors between low and high spatial frequency data. The peak at 40 µm−1 in the PSD of the hand-assembled data is due to a cosmic ray; its location is indicated by the white arrow.

Fig. 2.
Fig. 2.

Final averaged reconstructions of both AMP-assembled diffraction intensities and hand-assembled diffraction intensities obtained in experiments on gold-labeled freeze-dried yeast [25]. Magnitude is represented as brightness and phase as hue according to the inset color bar. The hand-assembled reconstruction shows streaks and other variations in intensity that would not be expected in the cell; the AMP-assembled reconstruction provides an improved visual appearance.

Fig. 3.
Fig. 3.

The magnitude resulting from a sum of random phases with Gaussian phase distribution characterized by σθ , calculated for a range of values of σθ . Since the phase retrieval transfer function or PRTF measures the magnitude (at a particular spatial frequency) of the average of many iterates, this figure provides insight into the range of phase variations between the iterates.

Fig. 4.
Fig. 4.

The use of a Wiener filter provides an improved measure of reconstructed image quality. This figure shows the phase retrieval transfer function (PRTF; shown in thick shaded lines at left) and power spectral density (PSD; right) curves corresponding to the reconstructions of Fig. 2. In the PSD curves, the square of the spatial-frequency-independent noise floor value ∣N2 is shown by a dashed line, and a linear fit to the square of the high spatial frequency trend of the measured signal ∣C(f)∣2 is shown with a thick shaded line. A Wiener filter function was then calculated according to Eqs. 11 and 12 and applied to the PRTF curve, leading to the Wiener-filtered PRTF curve or wPRTF curve which is shown in thin, non-shaded lines at left. Applying the Wiener-filter suppresses the artificially high PRTF-values of the hand-assembled reconstructed data (red) above a spatial frequency of about 25 µm−1 and underlines the higher quality of the reconstruction of the AMP-assembled data.

Fig. 5.
Fig. 5.

The Wiener-filtered phase retrieval transfer function (wPRTF) provides a good measure of reconstructed image quality over a wide range of photon exposures. Shown at right are a series of wPRTF curves for reconstructions of simulated data with several different photons per pixel values and simulated Poisson noise. The spatial frequency at which the wPRTF crosses the dashed 0.5 line is taken as effective resolution for each data set. On left, a power law fit to the power spectral density (PSD) of the data set with the highest photons per pixel value (black) is compared to a power law fit to the dose–resolution data (red) derived from the figure on the right. The magnitudes of both slopes agree within their error, indicating that the degree to which scattering decreases with spatial frequency in an object is equal to the degree at which reconstructed image resolution falls off with decreasing exposure [1].

Fig. 6.
Fig. 6.

Illustration of the effect of choosing different iterate averaging frequencies. For both the AMP-assembled experimental data at left, and the simulated data set at right, the difference map algorithm was first run for 5,000 iterations. Next, 100 iterates were taken every i th iteration (i ∈ {1,5,10,20,30,40,60,70,80,90,100,200}) to obtain a final result. Wiener-filtered phase retrieval transfer function (wPRTF) curves are plotted for each of the iterate averaging frequencies. An example reconstructed image is shown as an inset. As judged by the wPRTF, all iterate sampling frequencies give essentially the same result.

Fig. 7.
Fig. 7.

Changes in the wPRTF as a function of number of iterates averaged for A) AMP-assembled experimental data, B) hand-assembled experimental data, and C) simulated data. The RMS residual changes in the wPRTF (calculated using Eq. (13)) as one goes from i to i + 1 iterates averaged were then fitted to a function of the form y(x) = axb + c, plotted in red. The error bars indicate the standard deviation between 12 different averaging frequencies. A horizontal dashed line marks a value of RMS residual of 0.001 selected to compare the results for the three different data sets. Not surprisingly, the simulated data with no systematic errors converges most quickly with only 29 iterates averaged, while the higher quality AMP-assembled experimental data requires 31 iterates averaged and the hand-assembled experimental data requires 53 iterates averaged.

Tables (2)

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Algorithm 1 Weighted normalization

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Algorithm 2 Weighted averaging

Equations (13)

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χ 2 = k ( I k , 1 cI k , 2 ) 2 σ k 2 ,
k [ I k , 1 ( true ) ± σ k , 1 c ( I k , 2 ( true ) ± σ k , 2 ) ] 2 = 0 .
k [ ( I k , 1 ( true ) c I k , 2 ( true ) ) ) ± σ k , 1 ± c σ k , 2 ] 2
k ( σ k , 1 + σ k , 2 ) 2 k ( σ k , 1 2 + σ k , 2 2 )
σ k = ( σ k , 1 2 + σ k , 2 2 ) ,
d d c k I k , 1 c I k , 2 2 σ k 2 = 0 .
c = k I k , 1 I k , 2 σ k 2 k I k , 2 2 σ k 2 .
I k avg = i 1 σ ¯ i , k 2 I i , k i 1 σ ¯ i , k 2 ,
σ k 2 = 1 i 1 σ i , k 2
PRTF ( f ) = f = const . o ˜ ( f ) f = const . I ( f )
W ( f ) = S ( f ) 2 S ( f ) 2 + N ( f ) 2
PSD ( f ) = C ( f ) 2 = S ( f ) 2 + N 2
RMS i + 1 = Σ ( wPRTF i wPRTF i + 1 ) 2 N ,

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