Abstract

Tomographic coherent imaging requires the reconstruction of a series of two-dimensional projections of the object. We show that using the solution for the image of one projection as the starting point for the reconstruction of the next projection offers a reliable and rapid approach to the image reconstruction. The method is demonstrated on simulated and experimental data. This technique also simplifies reconstructions using data with curved incident wavefronts.

© 2010 Optical Society of America

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2010 (1)

2009 (4)

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]

E. Lima, L. Wiegart, P. Pernot, M. Howells, J. Timmins, F. Zontone, and A. Madsen, “Cryogenic x-ray diffraction microscopy for biological samples,” Phys. Rev. Lett. 103, - (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. Vine, G. Williams, B. Abbey, M. Pfeifer, J. Clark, M. de Jonge, I. McNulty, A. Peele, and K. Nugent, “Ptychographic fresnel coherent diffractive imaging,” Phys. Rev. A 80, 063823 (2009).
[CrossRef]

2008 (7)

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]

B. Abbey, G. Williams, M. Pfeifer, J. Clark, C. Putkunz, A. Torrance, I. McNulty, T. Levin, A. Peele, and K. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett. 93, 214101 (2008).
[CrossRef]

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

G. Williams, E. Hanssen, A. Peele, M. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. de Jonge, S. Vogt, L. Tilley, and K. Nugent, “High-resolution x-ray imaging of plasmodium falciparum-infected red blood cells,” Cytom. Part A 73A, 949–957 (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]

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

J. Clark, G. Williams, H. Quiney, L. Whitehead, M. de Jonge, E. Hanssen, M. Altissimo, K. Nugent, and A. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16, 3342 (2008).
[CrossRef] [PubMed]

2007 (2)

S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007).
[CrossRef] [PubMed]

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, “Effectiveness of iterative algorithms in recovering phase in the presence of noise,” Acta Crystallogr. A 63, 36–42 (2007).
[CrossRef]

2006 (6)

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] [PubMed]

H. Quiney, A. Peele, Z. Cai, D. Paterson, and K. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys. 2, 101–104 (2006).
[CrossRef]

M. Pfeifer, G. Williams, I. Vartanyants, R. Harder, and I. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[CrossRef] [PubMed]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. 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]

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

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

2005 (3)

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

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

H. Quiney, K. Nugent, and A. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett. 30, 1638–1640 (2005).
[CrossRef] [PubMed]

2004 (1)

J. Rodenburg and H. Faulkner, “A phase retrieval algorithm for shifting illumination,” App. Phys. Lett. 85, 4795–4797 (2004).
[CrossRef]

2003 (3)

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. Nat. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

K. Nugent, A. Peele, H. Chapman, and A. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

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

2002 (1)

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]

1999 (1)

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

1994 (1)

A. R. Hare and G. R. Morrison, “Near-field soft x-ray diffraction modelled by the multislice method,” J. Mod. Opt. 41,31–48 (1994).
[CrossRef]

1993 (1)

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,” Atomic Data and Nuclear Data Tables 54, 181–342 (1993).
[CrossRef]

1984 (1)

R. Bates, “Uniqueness of solutions to two-dimensional fourier phase problems for localized and positive images,” Comput. Vision Graph. 25, 205–217 (1984).
[CrossRef]

1982 (1)

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A pratical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

1957 (1)

J. M. Cowley and A. F. Moddie, “The scattering of electrons by atoms and crystals. i. a new theoretical approach,” Acta Crystallogr. 10, 609–619 (1957).
[CrossRef]

Abbey, B.

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

G. Williams, E. Hanssen, A. Peele, M. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. de Jonge, S. Vogt, L. Tilley, and K. Nugent, “High-resolution x-ray imaging of plasmodium falciparum-infected red blood cells,” Cytom. Part A 73A, 949–957 (2008).
[CrossRef]

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]

B. Abbey, G. Williams, M. Pfeifer, J. Clark, C. Putkunz, A. Torrance, I. McNulty, T. Levin, A. Peele, and K. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett. 93, 214101 (2008).
[CrossRef]

Altissimo, M.

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]

Artyukhin, A.

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

Bajt, S.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

Barty, A.

A. Barty, S. Marchesini, H. Chapman, C. Cui, M. Howells, D. Shapiro, A. Minor, J. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. Hau-Riege, A. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. Kin-ney, “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, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. 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.

R. Bates, “Uniqueness of solutions to two-dimensional fourier phase problems for localized and positive images,” Comput. Vision Graph. 25, 205–217 (1984).
[CrossRef]

Baumann, T.

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

Beetz, T.

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. 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. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” P. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Ben-ner, H.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

Bergh, M.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

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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, K. Hodgson, T. Ishikawa, C. Larabell, M. LeGros, and Y. Nishino, “Imaging whole escherichia coli bacteria by using single-particle x-ray diffraction,” Proc. Nat. Acad. Sci. USA 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.

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]

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] [PubMed]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. 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. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” P. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Jefimovs, K.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[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.

I. Johnson, K. Jefimovs, O. Bunk, C. David, M. Dierolf, J. Gray, D. Renker, and F. Pfeiffer, “Coherent diffractive imaging using phase front modifications,” Phys. Rev. Lett. 100, 155503 (2008).
[CrossRef] [PubMed]

Jonge, M. de

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

G. Williams, E. Hanssen, A. Peele, M. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. de Jonge, S. Vogt, L. Tilley, and K. Nugent, “High-resolution x-ray imaging of plasmodium falciparum-infected red blood cells,” Cytom. Part A 73A, 949–957 (2008).
[CrossRef]

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]

J. Clark, G. Williams, H. Quiney, L. Whitehead, M. de Jonge, E. Hanssen, M. Altissimo, K. Nugent, and A. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16, 3342 (2008).
[CrossRef] [PubMed]

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

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A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial Mathematics, 1988).

Kim, S.

Kin-ney, J.

A. Barty, S. Marchesini, H. Chapman, C. Cui, M. Howells, D. Shapiro, A. Minor, J. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. Hau-Riege, A. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. Kin-ney, “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.

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. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” P. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

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

Kuhlmann, M.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

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. Nat. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

Lee, R.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

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. Nat. Acad. Sci. USA 100, 110–112 (2003).
[CrossRef] [PubMed]

Levin, T.

B. Abbey, G. Williams, M. Pfeifer, J. Clark, C. Putkunz, A. Torrance, I. McNulty, T. Levin, A. Peele, and K. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett. 93, 214101 (2008).
[CrossRef]

Lima, E.

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]

E. Lima, L. Wiegart, P. Pernot, M. Howells, J. Timmins, F. Zontone, and A. Madsen, “Cryogenic x-ray diffraction microscopy for biological samples,” Phys. Rev. Lett. 103, - (2009).
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D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” P. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

London, R.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

Madsen, A.

E. Lima, L. Wiegart, P. Pernot, M. Howells, J. Timmins, F. Zontone, and A. Madsen, “Cryogenic x-ray diffraction microscopy for biological samples,” Phys. Rev. Lett. 103, - (2009).
[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] [PubMed]

Maia, F.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

Mancuso, A.

K. Nugent, A. Peele, H. Chapman, and A. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

Marchesini, S.

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

S. Marchesini, “A unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78, 011301 (2007).
[CrossRef] [PubMed]

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

H. Chapman, A. Barty, S. Marchesini, A. Noy, S. 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]

McNulty, I.

J. Clark, C. Putkunz, M. Pfeifer, A. Peele, G. Williams, B. Chen, K. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express 18, 1981–1993 (2010).
[CrossRef] [PubMed]

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

B. Abbey, G. Williams, M. Pfeifer, J. Clark, C. Putkunz, A. Torrance, I. McNulty, T. Levin, A. Peele, and K. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett. 93, 214101 (2008).
[CrossRef]

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]

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

Miao, J.

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. Nat. Acad. Sci. USA 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, “Extending the methodology of x-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Minor, A.

A. Barty, S. Marchesini, H. Chapman, C. Cui, M. Howells, D. Shapiro, A. Minor, J. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. Hau-Riege, A. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. Kin-ney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
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J. M. Cowley and A. F. Moddie, “The scattering of electrons by atoms and crystals. i. a new theoretical approach,” Acta Crystallogr. 10, 609–619 (1957).
[CrossRef]

Moller, T.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
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A. R. Hare and G. R. Morrison, “Near-field soft x-ray diffraction modelled by the multislice method,” J. Mod. Opt. 41,31–48 (1994).
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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. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” P. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
[CrossRef]

Nelson, J.

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

Noy, A.

A. Barty, S. Marchesini, H. Chapman, C. Cui, M. Howells, D. Shapiro, A. Minor, J. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. Hau-Riege, A. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. Kin-ney, “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. 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]

Nugent, K.

J. Clark, C. Putkunz, M. Pfeifer, A. Peele, G. Williams, B. Chen, K. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express 18, 1981–1993 (2010).
[CrossRef] [PubMed]

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

G. Williams, E. Hanssen, A. Peele, M. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. de Jonge, S. Vogt, L. Tilley, and K. Nugent, “High-resolution x-ray imaging of plasmodium falciparum-infected red blood cells,” Cytom. Part A 73A, 949–957 (2008).
[CrossRef]

B. Abbey, G. Williams, M. Pfeifer, J. Clark, C. Putkunz, A. Torrance, I. McNulty, T. Levin, A. Peele, and K. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett. 93, 214101 (2008).
[CrossRef]

J. Clark, G. Williams, H. Quiney, L. Whitehead, M. de Jonge, E. Hanssen, M. Altissimo, K. Nugent, and A. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16, 3342 (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]

H. Quiney, A. Peele, Z. Cai, D. Paterson, and K. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys. 2, 101–104 (2006).
[CrossRef]

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

H. Quiney, K. Nugent, and A. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett. 30, 1638–1640 (2005).
[CrossRef] [PubMed]

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

K. Nugent, A. Peele, H. Chapman, and A. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

Paganin, D.

D. Paganin, Coherent X-Ray Optics (Oxford University Press, 2006).
[CrossRef]

Paterson, D.

H. Quiney, A. Peele, Z. Cai, D. Paterson, and K. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys. 2, 101–104 (2006).
[CrossRef]

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

Peele, A.

J. Clark, C. Putkunz, M. Pfeifer, A. Peele, G. Williams, B. Chen, K. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express 18, 1981–1993 (2010).
[CrossRef] [PubMed]

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

G. Williams, E. Hanssen, A. Peele, M. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. de Jonge, S. Vogt, L. Tilley, and K. Nugent, “High-resolution x-ray imaging of plasmodium falciparum-infected red blood cells,” Cytom. Part A 73A, 949–957 (2008).
[CrossRef]

B. Abbey, G. Williams, M. Pfeifer, J. Clark, C. Putkunz, A. Torrance, I. McNulty, T. Levin, A. Peele, and K. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett. 93, 214101 (2008).
[CrossRef]

J. Clark, G. Williams, H. Quiney, L. Whitehead, M. de Jonge, E. Hanssen, M. Altissimo, K. Nugent, and A. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16, 3342 (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]

H. Quiney, A. Peele, Z. Cai, D. Paterson, and K. Nugent, “Diffractive imaging of highly focused x-ray fields,” Nat. Phys. 2, 101–104 (2006).
[CrossRef]

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

H. Quiney, K. Nugent, and A. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett. 30, 1638–1640 (2005).
[CrossRef] [PubMed]

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B. Abbey, G. Williams, M. Pfeifer, J. Clark, C. Putkunz, A. Torrance, I. McNulty, T. Levin, A. Peele, and K. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett. 93, 214101 (2008).
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H. Quiney, K. Nugent, and A. Peele, “Iterative image reconstruction algorithms using wave-front intensity and phase variation,” Opt. Lett. 30, 1638–1640 (2005).
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G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, “Effectiveness of iterative algorithms in recovering phase in the presence of noise,” Acta Crystallogr. A 63, 36–42 (2007).
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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).
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D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. Neiman, and D. Sayre, “Biological imaging by soft x-ray diffraction microscopy,” P. Natl. Acad. Sci. USA 102, 15343–15346 (2005).
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H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
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[CrossRef] [PubMed]

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
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H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
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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).
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A. Barty, S. Marchesini, H. Chapman, C. Cui, M. Howells, D. Shapiro, A. Minor, J. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. Hau-Riege, A. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. Kin-ney, “Three-dimensional coherent x-ray diffraction imaging of a ceramic nanofoam: Determination of structural deformation mechanisms,” Phys. Rev. Lett. 101, 055501 (2008).
[CrossRef] [PubMed]

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H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
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[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] [PubMed]

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

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G. Williams, E. Hanssen, A. Peele, M. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. de Jonge, S. Vogt, L. Tilley, and K. Nugent, “High-resolution x-ray imaging of plasmodium falciparum-infected red blood cells,” Cytom. Part A 73A, 949–957 (2008).
[CrossRef]

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E. Lima, L. Wiegart, P. Pernot, M. Howells, J. Timmins, F. Zontone, and A. Madsen, “Cryogenic x-ray diffraction microscopy for biological samples,” Phys. Rev. Lett. 103, - (2009).
[CrossRef]

Timneanu, N.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

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B. Abbey, G. Williams, M. Pfeifer, J. Clark, C. Putkunz, A. Torrance, I. McNulty, T. Levin, A. Peele, and K. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett. 93, 214101 (2008).
[CrossRef]

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

Treusch, R.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

Tschentscher, T.

H. Chapman, A. Barty, M. Bogan, S. Boutet, M. Frank, S. Hau-Riege, S. Marchesini, B. Woods, S. Bajt, H. Ben-ner, R. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. Shapiro, K. Hodgson, D. Van der Spoel, F. Burmeister, M. Bergh, C. Cale-man, G. Huldt, M. Seibert, F. Maia, R. Lee, A. Szoke, N. Timneanu, and J. Hajdu, “Femtosecond diffractive imaging with a soft-x-ray free-electron laser,” Nat. Phys. 2, 839–843 (2006).
[CrossRef]

Turner, J.

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]

Vartanyants, I.

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, “Effectiveness of iterative algorithms in recovering phase in the presence of noise,” Acta Crystallogr. A 63, 36–42 (2007).
[CrossRef]

M. Pfeifer, G. Williams, I. Vartanyants, R. Harder, and I. Robinson, “Three-dimensional mapping of a deformation field inside a nanocrystal,” Nature 442, 63–66 (2006).
[CrossRef] [PubMed]

Vine, D.

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

Vogt, S.

G. Williams, E. Hanssen, A. Peele, M. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. de Jonge, S. Vogt, L. Tilley, and K. Nugent, “High-resolution x-ray imaging of plasmodium falciparum-infected red blood cells,” Cytom. Part A 73A, 949–957 (2008).
[CrossRef]

Weierstall, U.

A. Barty, S. Marchesini, H. Chapman, C. Cui, M. Howells, D. Shapiro, A. Minor, J. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. Hau-Riege, A. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. Kin-ney, “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. 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]

Whitehead, L.

Wiegart, L.

E. Lima, L. Wiegart, P. Pernot, M. Howells, J. Timmins, F. Zontone, and A. Madsen, “Cryogenic x-ray diffraction microscopy for biological samples,” Phys. Rev. Lett. 103, - (2009).
[CrossRef]

Willey, T.

A. Barty, S. Marchesini, H. Chapman, C. Cui, M. Howells, D. Shapiro, A. Minor, J. Spence, U. Weierstall, J. Ilavsky, A. Noy, S. Hau-Riege, A. Artyukhin, T. Baumann, T. Willey, J. Stolken, T. van Buuren, and J. Kin-ney, “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.

J. Clark, C. Putkunz, M. Pfeifer, A. Peele, G. Williams, B. Chen, K. Nugent, C. Hall, W. Fullagar, S. Kim, and I. McNulty, “Use of a complex constraint in coherent diffractive imaging,” Opt. Express 18, 1981–1993 (2010).
[CrossRef] [PubMed]

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

G. Williams, E. Hanssen, A. Peele, M. Pfeifer, J. Clark, B. Abbey, G. Cadenazzi, M. de Jonge, S. Vogt, L. Tilley, and K. Nugent, “High-resolution x-ray imaging of plasmodium falciparum-infected red blood cells,” Cytom. Part A 73A, 949–957 (2008).
[CrossRef]

J. Clark, G. Williams, H. Quiney, L. Whitehead, M. de Jonge, E. Hanssen, M. Altissimo, K. Nugent, and A. Peele, “Quantitative phase measurement in coherent diffraction imaging,” Opt. Express 16, 3342 (2008).
[CrossRef] [PubMed]

B. Abbey, G. Williams, M. Pfeifer, J. Clark, C. Putkunz, A. Torrance, I. McNulty, T. Levin, A. Peele, and K. Nugent, “Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm,” App. Phys. Lett. 93, 214101 (2008).
[CrossRef]

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]

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, “Effectiveness of iterative algorithms in recovering phase in the presence of noise,” Acta Crystallogr. A 63, 36–42 (2007).
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Supplementary Material (1)

» Media 1: AVI (1457 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Experimental Parameters.

Fig. 2.
Fig. 2.

(a) Amplitude of the transmission function of an actual glass capillary reconstructed from an FCDI tomography data set. This dataset was used to define the parameters for the simulated data set used in this study. (b) Projection through the 3D reconstruction of the simulated capillary used throughout this study, showing the amplitude of the transmission function. The colour scale in both (a) and (b) represents x-ray transmission from 50% (blue) to 100% (white). (c) 3D reconstruction of the δ component of the refractive index, sectioned to display the central region. (d) and (e) Slices through the reconstructed glass capillary for the δ and β components of the refractive index. The red box indicates the regions from which the components were averaged.

Fig. 3.
Fig. 3.

(a) The number of iterations required to reach a self-consistent solution at the 1.0 × 10−4 level in simulated data. (b) Iterations required to reach a self-consistent solution at the 1.0 × 10−3 level during reconstructions of the insect wing.

Fig. 4.
Fig. 4.

Average reconstructed values for the x-ray simulation in the regions indicated in Fig. 2(d) and 2(e). Errors are calculated from the standard deviation of the region of interest.

Fig. 5.
Fig. 5.

(Media 1) (a) 25 combined frames of optical coherent diffraction data corresponding to ∣ψ̂∣2. Data has been logarithmically scaled to better depict both high angle scatter and holographic region. (b) Reconstruction of a single projection, showing the amplitude of the transmission function, ∣T∣. (c) Optical microscopy image of the damaged wing tip. (d) 3D rendering of reconstructed insect wing. In this qualitative view colours of features in the rendering were based on the segmentation of well-defined components in the histogram of densities.

Fig. 6.
Fig. 6.

The nominal number of computational operations used in various 3D reconstruction techniques.

Equations (5)

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χ 2 = ρ d [ ψ ̂ ( ρ d ) I ( ρ d ) ] 2 ρ d I ( ρ d ) ,
ψ ̂ e ( ρ d ) = ρ s ψ 0 ( ρ s ) T θ Δ θ e i π ρ s 2 λ z D e 2 πi ρ s ρ d d ρ s ; and
ψ ̂ θ ( ρ d ) = I θ ( ρ d ) ψ ̂ e ( ρ d ) ψ ̂ e ( ρ d ) .
ψ e , θ ( ρ s , z S ) = T θ ( ρ s ) ψ 0 ( ρ s , z S ) ,
T θ ( ρ s ) = exp [ k 2 i z p [ 1 n 2 ( ρ s , z p ) ] d z p ] .

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