Abstract

Coherent diffractive imaging is a method by which iterative methods are employed to recover image information about a finite object from its coherent diffraction pattern. We employ methods borrowed from density functional theory to show that an image can be recovered in a single non-iterative step for a finite sample subject to phase-curved illumination. The result also yields a new approach to quantitative x-ray phase-contrast imaging.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. W. 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]
  2. J. R. Fienup, "Phase retrieval algorithms- a comparison," Appl. Opt. 21, 2758-2769 (1982).
    [CrossRef] [PubMed]
  3. V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. A. 20, 40-55 (2003).
    [CrossRef]
  4. S. Marchesini, H. He, H. N. Chapman, S. P Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. C. H. Spence, "X-ray image reconstruction from a diffraction pattern alone," Phys. Rev. B. 68, 140101 (2003).
    [CrossRef]
  5. D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
    [CrossRef] [PubMed]
  6. I. K. Robinson, I. A. Vartanyants, G. J. Williams, M. A. Pfeifer, and J. A. Pitney, "Reconstruction of the shapes of gold nanocrystals using coherent X-ray diffraction," Phys. Rev. Lett. 87, 195505 (2001).
    [CrossRef] [PubMed]
  7. M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson, "Three-dimensional mapping of a deformation field inside a nanocrystal," Nature 442, 63-66 (2006).
    [CrossRef] [PubMed]
  8. R. Neutze, R. Wouts, D. van der Spoel, E. Weckert, and J. Hajdu, "Potential for biomolecular imaging with femtosecond X-ray pulses," Nature 406, 752-757 (2000).
    [CrossRef] [PubMed]
  9. H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
    [CrossRef]
  10. A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
    [CrossRef]
  11. M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003).
    [CrossRef] [PubMed]
  12. D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
    [CrossRef] [PubMed]
  13. P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
    [CrossRef]
  14. K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X-rays," Phys. Rev. Lett. 77, 2961-2964 (1996).
    [CrossRef] [PubMed]
  15. K. A. Nugent, D. Paganin, and T. E. Gureyev, "A phase odyssey," Physics Today 54, 27-32 (2001).
    [CrossRef]
  16. G. J. Williams, H. M. Quiney, B. B. Dhal, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, "Fresnel coherent diffractive imaging," Phys. Rev. Lett. 97, 025506 (2006).
    [CrossRef] [PubMed]
  17. D. Sayre, "Some implications of a theorem due to Shannon," Acta. Cryst. 5, 843 (1952).
    [CrossRef]
  18. J. Miao, D. Sayre, and H. N. Chapman, "Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects," J. Opt. Soc. Am. A 15, 1662-1669 (1998).
    [CrossRef]
  19. K. A. Nugent, "X-ray non-interferometric phase imaging: a unified picture," J. Opt. Soc. Am. A 24, 536-547 (2007).
    [CrossRef]
  20. M. R. Teague, "Deterministic phase retrieval: a Green�??s function solution," J. Opt. Soc. Am. 73, 1434-1441 (1983).
    [CrossRef]
  21. D. Paganin, Coherent X-ray Optics (Oxford University Press, 2005).
  22. K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, "Unique phase recovery for nonperiodic objects," Phys. Rev. Lett. 91, 203902 (2003).
    [CrossRef] [PubMed]
  23. T. E. Gureyev, A. Roberts, and K. A. Nugent, "Partially coherent fields, the transport of intensity equation, and phase uniqueness," J.Opt. Soc. Am. A. 12, 1942-1946 (1995).
    [CrossRef]
  24. R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension. 1: Underlying theory," Optik 61, 247-262 (1982).
  25. M. Abramowitz and I. Stegun (eds), Handbook of Mathematical Functions, Dover Publications, New York (1970).
  26. H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focussed X-ray fields," Nature Physics 2, 101-104 (2006).
    [CrossRef]
  27. P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Phys. Rev. B 136, B864 (1964).
    [CrossRef]
  28. D. Paganin and K. A. Nugent, "Noninterferometric phase imaging with partially coherent light," Phys. Rev. Lett. 802586-2589 (1998).
    [CrossRef]

2007 (1)

2006 (4)

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focussed X-ray fields," Nature Physics 2, 101-104 (2006).
[CrossRef]

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

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

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

2005 (1)

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

2003 (4)

V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. A. 20, 40-55 (2003).
[CrossRef]

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

M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003).
[CrossRef] [PubMed]

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

2001 (2)

K. A. Nugent, D. Paganin, and T. E. Gureyev, "A phase odyssey," Physics Today 54, 27-32 (2001).
[CrossRef]

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

2000 (1)

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

1999 (2)

J. W. 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]

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
[CrossRef]

1998 (2)

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

D. Paganin and K. A. Nugent, "Noninterferometric phase imaging with partially coherent light," Phys. Rev. Lett. 802586-2589 (1998).
[CrossRef]

1997 (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

1996 (1)

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X-rays," Phys. Rev. Lett. 77, 2961-2964 (1996).
[CrossRef] [PubMed]

1995 (2)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

T. E. Gureyev, A. Roberts, and K. A. Nugent, "Partially coherent fields, the transport of intensity equation, and phase uniqueness," J.Opt. Soc. Am. A. 12, 1942-1946 (1995).
[CrossRef]

1983 (1)

1982 (2)

R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension. 1: Underlying theory," Optik 61, 247-262 (1982).

J. R. Fienup, "Phase retrieval algorithms- a comparison," Appl. Opt. 21, 2758-2769 (1982).
[CrossRef] [PubMed]

1964 (1)

P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Phys. Rev. B 136, B864 (1964).
[CrossRef]

1952 (1)

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

Arfelli, F.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Bajt, S.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

Barnea, Z.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X-rays," Phys. Rev. Lett. 77, 2961-2964 (1996).
[CrossRef] [PubMed]

Barty, A.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

Baruchel, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
[CrossRef]

Bates, R. H. T.

R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension. 1: Underlying theory," Optik 61, 247-262 (1982).

Beetz, T.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

Betz, O.

M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003).
[CrossRef] [PubMed]

Blob, R. W.

M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003).
[CrossRef] [PubMed]

Bogan, M. J.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

Boutel, S.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

Cai, Z.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focussed X-ray fields," Nature Physics 2, 101-104 (2006).
[CrossRef]

Chapman, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Chapman, H. N.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

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

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

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

Charalambous, P.

J. W. 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]

Cloetens, P.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
[CrossRef]

Cookson, D. F.

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X-rays," Phys. Rev. Lett. 77, 2961-2964 (1996).
[CrossRef] [PubMed]

Cooper, W. J.

M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003).
[CrossRef] [PubMed]

de Jonge, M. D.

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

Dhal, B. B.

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

Elser, V.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. A. 20, 40-55 (2003).
[CrossRef]

Fezzaa, K.

M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003).
[CrossRef] [PubMed]

Fienup, J. R.

Frank, M.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

Gmur, N.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Guigay, J. P.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
[CrossRef]

Gureyev, T. E.

K. A. Nugent, D. Paganin, and T. E. Gureyev, "A phase odyssey," Physics Today 54, 27-32 (2001).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X-rays," Phys. Rev. Lett. 77, 2961-2964 (1996).
[CrossRef] [PubMed]

T. E. Gureyev, A. Roberts, and K. A. Nugent, "Partially coherent fields, the transport of intensity equation, and phase uniqueness," J.Opt. Soc. Am. A. 12, 1942-1946 (1995).
[CrossRef]

Hajdu, J.

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

Harder, R.

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

Hau-Reige, S. P.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

Hau-Riege, S. P

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

He, H.

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

Henry, W.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

Hohenberg, P.

P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Phys. Rev. B 136, B864 (1964).
[CrossRef]

Howells, M.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

Howells, M. R.

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

Jacobsen, C.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

Johnston, R. E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Kirz, J.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

J. W. 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]

Kohn, V.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Kohn, W.

P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Phys. Rev. B 136, B864 (1964).
[CrossRef]

Kuznetsov, S.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Lee, W. K.

M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003).
[CrossRef] [PubMed]

Lima, E.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

Ludwig, W.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
[CrossRef]

Mancuso, A. P.

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

Marchesini, S.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

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

Menk, R.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Miao, H.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

Miao, J.

Miao, J. W.

J. W. 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]

Neiman, A. M.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

Neutze, R.

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

Noy, A.

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

Nugent, K. A.

K. A. Nugent, "X-ray non-interferometric phase imaging: a unified picture," J. Opt. Soc. Am. A 24, 536-547 (2007).
[CrossRef]

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

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focussed X-ray fields," Nature Physics 2, 101-104 (2006).
[CrossRef]

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

K. A. Nugent, D. Paganin, and T. E. Gureyev, "A phase odyssey," Physics Today 54, 27-32 (2001).
[CrossRef]

D. Paganin and K. A. Nugent, "Noninterferometric phase imaging with partially coherent light," Phys. Rev. Lett. 802586-2589 (1998).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X-rays," Phys. Rev. Lett. 77, 2961-2964 (1996).
[CrossRef] [PubMed]

T. E. Gureyev, A. Roberts, and K. A. Nugent, "Partially coherent fields, the transport of intensity equation, and phase uniqueness," J.Opt. Soc. Am. A. 12, 1942-1946 (1995).
[CrossRef]

Paganin, D.

K. A. Nugent, D. Paganin, and T. E. Gureyev, "A phase odyssey," Physics Today 54, 27-32 (2001).
[CrossRef]

D. Paganin and K. A. Nugent, "Noninterferometric phase imaging with partially coherent light," Phys. Rev. Lett. 802586-2589 (1998).
[CrossRef]

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X-rays," Phys. Rev. Lett. 77, 2961-2964 (1996).
[CrossRef] [PubMed]

Paterson, D.

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

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focussed X-ray fields," Nature Physics 2, 101-104 (2006).
[CrossRef]

Peele, A. G.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focussed X-ray fields," Nature Physics 2, 101-104 (2006).
[CrossRef]

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

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

Pfeifer, M. A.

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

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

Pisano, E.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Pitney, J. A.

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

Quiney, H. M.

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focussed X-ray fields," Nature Physics 2, 101-104 (2006).
[CrossRef]

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

Roberts, A.

T. E. Gureyev, A. Roberts, and K. A. Nugent, "Partially coherent fields, the transport of intensity equation, and phase uniqueness," J.Opt. Soc. Am. A. 12, 1942-1946 (1995).
[CrossRef]

Robinson, I. K.

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

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

Sayers, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Sayre, D.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

J. W. 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]

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

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

Schelokov, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Schlenker, M

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
[CrossRef]

Shapiro, D.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

Snigirev, A.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Snigireva, I.

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Spence, J. C. H.

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

Teague, M. R.

Thibault, P.

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

Thomlinson, W.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

van der Spoel, D.

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

van Dyck, D.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
[CrossRef]

van Landuyt, J.

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
[CrossRef]

Vartanyants, I. A.

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

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

Washburn, D.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Weckert, E.

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

Weierstall, U.

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

Westneat, M. W.

M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003).
[CrossRef] [PubMed]

Williams, G. J.

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

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

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

Woods, B. W.

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

Wouts, R.

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

Zhong, Z.

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Acta. Cryst. (1)

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

Appl. Opt. (1)

Appl. Phys. Lett. (1)

P. Cloetens, W. Ludwig, J. Baruchel, D. van Dyck, J. van Landuyt, J. P. Guigay, and M Schlenker, "Holotomography: quantitative phase tomographywith micrometre resolution using hard synchrotron radiation X-rays," Appl. Phys. Lett. 75, 2912-2914 (1999).
[CrossRef]

J. Opt. Soc. A. (1)

V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. A. 20, 40-55 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

J.Opt. Soc. Am. A. (1)

T. E. Gureyev, A. Roberts, and K. A. Nugent, "Partially coherent fields, the transport of intensity equation, and phase uniqueness," J.Opt. Soc. Am. A. 12, 1942-1946 (1995).
[CrossRef]

Nature (3)

J. W. 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]

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

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

Nature Physics (2)

H. N. Chapman, A. Barty, M. J. Bogan, S. Boutel, M. Frank, S. P. Hau-Reige, S. Marchesini, B. W. Woods, S. Bajt, W. Henry. Benner, R. A. London, E. Plonjes, M. Kuhlmann, R. Treusch, S. Dusterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Moller, C. Bostedt, M. Hoener, D. A. Shapiro, K. O. Hodgson, D. van der Spoel, F. Burmeister, M. Bergh, C. Caleman, G. Huldt, M. Seibert, F. R. N. C. Maia, R. W. Lee, A. Szoke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft X-ray free-electron laser," Nature Physics 2, 839-843 (2006).
[CrossRef]

H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focussed X-ray fields," Nature Physics 2, 101-104 (2006).
[CrossRef]

Optik (1)

R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension. 1: Underlying theory," Optik 61, 247-262 (1982).

Phys. Med. Biol. (1)

D. Chapman, W. Thomlinson, R. E. Johnston, D. Washburn, E. Pisano, N. Gmur, Z. Zhong, R. Menk, F. Arfelli, and D. Sayers, "Diffraction enhanced X-ray imaging," Phys. Med. Biol. 422015-2025 (1997).
[CrossRef] [PubMed]

Phys. Rev. B (1)

P. Hohenberg and W. Kohn, "Inhomogeneous electron gas," Phys. Rev. B 136, B864 (1964).
[CrossRef]

Phys. Rev. B. (1)

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

Phys. Rev. Lett. (5)

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

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

K. A. Nugent, T. E. Gureyev, D. F. Cookson, D. Paganin, and Z. Barnea, "Quantitative phase imaging using hard X-rays," Phys. Rev. Lett. 77, 2961-2964 (1996).
[CrossRef] [PubMed]

D. Paganin and K. A. Nugent, "Noninterferometric phase imaging with partially coherent light," Phys. Rev. Lett. 802586-2589 (1998).
[CrossRef]

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

Physics Today (1)

K. A. Nugent, D. Paganin, and T. E. Gureyev, "A phase odyssey," Physics Today 54, 27-32 (2001).
[CrossRef]

Proc. Nat. Acad. Sci. (1)

D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre, "Biological imaging by soft X-ray diffraction microscopy," Proc. Nat. Acad. Sci. 10215343-15346 (2005).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A. Snigirev, I. Snigireva, V. Kohn, S. Kuznetsov, and I. Schelokov, "On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation," Rev. Sci. Instrum. 66, 5486-5492 (1995).
[CrossRef]

Science (1)

M. W. Westneat, O. Betz, R. W. Blob, K. Fezzaa, W. J. Cooper, and W. K. Lee, "Tracheal respiration in insects visualized with synchrotron X-ray imaging," Science 299, 558-560 (2003).
[CrossRef] [PubMed]

Other (2)

M. Abramowitz and I. Stegun (eds), Handbook of Mathematical Functions, Dover Publications, New York (1970).

D. Paganin, Coherent X-ray Optics (Oxford University Press, 2005).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1.

Schematic representation of the imaging configuration. An X-ray source produces a wavefront that has significant spherical phase curvature in the plane of the diffracting object. The diffracted and undiffracted waves propagate paraxially to a distant plane where they are detected.

Fig. 2.
Fig. 2.

(a) Diffracting object used in the numerical work. The object is purely real and transmits 10% of the incident intensity. (b) The amplitude of the wavefield leaving the object. The illuminating field is Gaussian in amplitude and has a Fresnel number of 6 over the horizontal dimension of the object.

Fig. 3.
Fig. 3.

Logarithmic representation of the far-zone diffraction pattern for the exit wave.

Fig. 4.
Fig. 4.

(a) Approximate far-zone intensity derivative distribution (b) Exact far-zone intensity derivative distribution.

Fig. 5.
Fig. 5.

Non-iterative reconstruction of the diffracting object (a) and exit surface wave (b) using the scheme derived here. The reconstruction is not perfect but represents an excellent starting point for further iterative refinement.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

· I ( r , z ) Φ ( r , z ) = 2 π λ I ( r , z ) z
ψ ( r 2 , z 2 ) = i exp ( 2 π i Z λ ) λ Z exp ( i π r 2 2 λ Z ) ψ ( r 1 , z 1 ) exp ( i π r 1 2 λ Z ) exp ( 2 π i r 1 · r 2 λ Z ) d r 1
g ( w ) = exp ( i π w 2 λ Z ) S ( w ) ψ ( r 1 + w , z 1 ) ψ * ( r 1 , z 1 ) exp ( 2 π i r 1 · w λ Z ) d r 1 ,
I ( r 2 , z 2 ) z = S ( w ) g ( w ) Z exp ( 2 π i w · r 2 λ Z ) d w 1 Z r 2 . I ( r 2 , z ) .
g ( w ) Z = i π w 2 λ Z 2 g ( w ) 2 π i λ Z 2 exp ( i π w 2 λ Z ) S ( w ) w . r 1 ψ ( r 1 + w , z 1 ) ψ * ( r 1 , z 1 ) exp ( 2 π i r 1 · w λ Z ) d r 1 .
g ( w ) Z = 1 Z w . g ( w ) + i π w 2 λ Z 2 g ( w )
2 π i λ Z 2 exp ( i π w 2 λ Z ) S ( w ) ψ * ( r 1 , z 1 ) exp ( 2 π i r 1 · w λ Z ) w · ψ ( r 1 + w , z 1 ) d r 1
+ T [ S ( w ) , ψ ( r 1 , z 1 ) , w , Z ] .
ψ ( r , z ) = ψ 0 ( r , z ) + ε ψ S ( r , z ) ,
I 0 z = μ Z w 2 g 0 ( w ) exp ( 2 π i w · r λ Z ) d w

Metrics