Abstract

We demonstrate high spatial resolution phase retrieval of a non-periodic gold nano-structure using the method of Fresnel coherent diffractive imaging. The result is quantitative to better than 10% and does not rely on any a priori knowledge of the sample.

© 2008 Optical Society of America

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  1. 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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
    [CrossRef]
  2. S. Marchesini, "Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval," Rev. Sci. Instrum. 78, 011301 (2007).
    [CrossRef] [PubMed]
  3. V. Elser, "Phase retrieval by iterated projections," J. Opt. Soc. Am. A 20, 40-55 (2003).
    [CrossRef]
  4. P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre, "Reconstruction of a yeast cell from X-ray diffraction data," Acta Crystallogr. Sect. A 62, 248-261 (2006).
    [CrossRef]
  5. G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, "Effectiveness of iterative algorithms in recoveringphase in the presence of noise," Acta Crystallogr. Sect. A 63, 36-42 (2007).
    [CrossRef]
  6. J. C. H. Spence, U. Weierstall, and M. Howells, "Coherence and sampling requirements for diffractive imaging," Ultramicroscopy 101, 149-152 (2004).
    [CrossRef] [PubMed]
  7. I. A. Vartanyants and I. K. Robinson, "Imaging of quantum array structures with coherent and partially coherent diffraction," J. Synchrotron Radiat. 10, 409-415 (2003).
    [CrossRef] [PubMed]
  8. R. H. T. Bates, "Fourier phase problems are uniquely solvable in more than one dimension. 1: Underlying theory," Optik 61, 247-262 (1982).
  9. J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, "Transmission microscopy without lenses for objects of unlimited size," Ultramicroscopy 107, 227-231 (2007).
    [CrossRef]
  10. H. M. Quiney, K. A. Nugent, and A. G. Peele, "Iterative image reconstruction algorithms using wave-front Intensity and phase variation," Opt. Lett. 30, 1638-1640 (2005).
    [CrossRef] [PubMed]
  11. H. M. Quiney, A. G. Peele, Z. Cai, D. Paterson, and K. A. Nugent, "Diffractive imaging of highly focused X-ray fields," Nat. Phys. 2, 101-104 (2006).
    [CrossRef]
  12. G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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]
  13. G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104102 (2007).
    [CrossRef]
  14. T. A. Pitts and J. F. Greenleaf, "Fresnel transform phase retrieval from magnitude," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1035-1045 (2003).
    [CrossRef] [PubMed]
  15. C. Q. Tran, A. G. Peele, D. Paterson, A. Roberts, I. McNulty, and K. A. Nugent, "Synchrotron beam coherence: a spatially resolved measurement," Opt. Lett. 30, 204-206 (2005).
    [CrossRef] [PubMed]
  16. J. H. Hubbell, Wm. J. Veigle, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross setions," J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in  6, 615 (1977).
    [CrossRef]

2007 (4)

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, "Effectiveness of iterative algorithms in recoveringphase in the presence of noise," Acta Crystallogr. Sect. A 63, 36-42 (2007).
[CrossRef]

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, "Transmission microscopy without lenses for objects of unlimited size," Ultramicroscopy 107, 227-231 (2007).
[CrossRef]

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104102 (2007).
[CrossRef]

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

2006 (4)

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

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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[CrossRef]

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

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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 (2)

2004 (1)

J. C. H. Spence, U. Weierstall, and M. Howells, "Coherence and sampling requirements for diffractive imaging," Ultramicroscopy 101, 149-152 (2004).
[CrossRef] [PubMed]

2003 (3)

I. A. Vartanyants and I. K. Robinson, "Imaging of quantum array structures with coherent and partially coherent diffraction," J. Synchrotron Radiat. 10, 409-415 (2003).
[CrossRef] [PubMed]

T. A. Pitts and J. F. Greenleaf, "Fresnel transform phase retrieval from magnitude," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1035-1045 (2003).
[CrossRef] [PubMed]

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

1982 (1)

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

1975 (1)

J. H. Hubbell, Wm. J. Veigle, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross setions," J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in  6, 615 (1977).
[CrossRef]

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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, 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.

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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[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).

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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[CrossRef]

Briggs, E. A.

J. H. Hubbell, Wm. J. Veigle, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross setions," J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in  6, 615 (1977).
[CrossRef]

Brown, R. T.

J. H. Hubbell, Wm. J. Veigle, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross setions," J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in  6, 615 (1977).
[CrossRef]

Cai, Z.

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

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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[CrossRef]

Cromer, D. T.

J. H. Hubbell, Wm. J. Veigle, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross setions," J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in  6, 615 (1977).
[CrossRef]

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, "Transmission microscopy without lenses for objects of unlimited size," Ultramicroscopy 107, 227-231 (2007).
[CrossRef]

de Jonge, M. D.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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, C. Q. Tran, 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.

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

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

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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[CrossRef]

Greenleaf, J. F.

T. A. Pitts and J. F. Greenleaf, "Fresnel transform phase retrieval from magnitude," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1035-1045 (2003).
[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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[CrossRef]

Howells, M.

J. C. H. Spence, U. Weierstall, and M. Howells, "Coherence and sampling requirements for diffractive imaging," Ultramicroscopy 101, 149-152 (2004).
[CrossRef] [PubMed]

Howerton, R. J.

J. H. Hubbell, Wm. J. Veigle, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross setions," J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in  6, 615 (1977).
[CrossRef]

Hubbell, J. H.

J. H. Hubbell, Wm. J. Veigle, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross setions," J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in  6, 615 (1977).
[CrossRef]

Hurst, A. C.

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, "Transmission microscopy without lenses for objects of unlimited size," Ultramicroscopy 107, 227-231 (2007).
[CrossRef]

Jacobsen, C.

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

Marchesini, S.

S. Marchesini, "Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval," Rev. Sci. Instrum. 78, 011301 (2007).
[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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[CrossRef]

McNulty, I.

Nugent, K. A.

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104102 (2007).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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 focused X-ray fields," Nat. Phys. 2, 101-104 (2006).
[CrossRef]

C. Q. Tran, A. G. Peele, D. Paterson, A. Roberts, I. McNulty, and K. A. Nugent, "Synchrotron beam coherence: a spatially resolved measurement," Opt. Lett. 30, 204-206 (2005).
[CrossRef] [PubMed]

H. M. Quiney, K. A. Nugent, and A. G. Peele, "Iterative image reconstruction algorithms using wave-front Intensity and phase variation," Opt. Lett. 30, 1638-1640 (2005).
[CrossRef] [PubMed]

Paterson, D.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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 focused X-ray fields," Nat. Phys. 2, 101-104 (2006).
[CrossRef]

C. Q. Tran, A. G. Peele, D. Paterson, A. Roberts, I. McNulty, and K. A. Nugent, "Synchrotron beam coherence: a spatially resolved measurement," Opt. Lett. 30, 204-206 (2005).
[CrossRef] [PubMed]

Peele, A. G.

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104102 (2007).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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 focused X-ray fields," Nat. Phys. 2, 101-104 (2006).
[CrossRef]

C. Q. Tran, A. G. Peele, D. Paterson, A. Roberts, I. McNulty, and K. A. Nugent, "Synchrotron beam coherence: a spatially resolved measurement," Opt. Lett. 30, 204-206 (2005).
[CrossRef] [PubMed]

H. M. Quiney, K. A. Nugent, and A. G. Peele, "Iterative image reconstruction algorithms using wave-front Intensity and phase variation," Opt. Lett. 30, 1638-1640 (2005).
[CrossRef] [PubMed]

Pfeifer, M.

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, "Effectiveness of iterative algorithms in recoveringphase in the presence of noise," Acta Crystallogr. Sect. A 63, 36-42 (2007).
[CrossRef]

Pitts, T. A.

T. A. Pitts and J. F. Greenleaf, "Fresnel transform phase retrieval from magnitude," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1035-1045 (2003).
[CrossRef] [PubMed]

Quiney, H. M.

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104102 (2007).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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 focused X-ray fields," Nat. Phys. 2, 101-104 (2006).
[CrossRef]

H. M. Quiney, K. A. Nugent, and A. G. Peele, "Iterative image reconstruction algorithms using wave-front Intensity and phase variation," Opt. Lett. 30, 1638-1640 (2005).
[CrossRef] [PubMed]

Roberts, A.

Robinson, I.

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, "Effectiveness of iterative algorithms in recoveringphase in the presence of noise," Acta Crystallogr. Sect. A 63, 36-42 (2007).
[CrossRef]

Robinson, I. K.

I. A. Vartanyants and I. K. Robinson, "Imaging of quantum array structures with coherent and partially coherent diffraction," J. Synchrotron Radiat. 10, 409-415 (2003).
[CrossRef] [PubMed]

Rodenburg, J. M.

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, "Transmission microscopy without lenses for objects of unlimited size," Ultramicroscopy 107, 227-231 (2007).
[CrossRef]

Sayre, D.

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

Shapiro, D.

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

Spence, J. C. H.

J. C. H. Spence, U. Weierstall, and M. Howells, "Coherence and sampling requirements for diffractive imaging," Ultramicroscopy 101, 149-152 (2004).
[CrossRef] [PubMed]

Thibault, P.

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

Tran, C. Q.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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]

C. Q. Tran, A. G. Peele, D. Paterson, A. Roberts, I. McNulty, and K. A. Nugent, "Synchrotron beam coherence: a spatially resolved measurement," Opt. Lett. 30, 204-206 (2005).
[CrossRef] [PubMed]

Vartanyants, I.

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, "Effectiveness of iterative algorithms in recoveringphase in the presence of noise," Acta Crystallogr. Sect. A 63, 36-42 (2007).
[CrossRef]

Vartanyants, I. A.

I. A. Vartanyants and I. K. Robinson, "Imaging of quantum array structures with coherent and partially coherent diffraction," J. Synchrotron Radiat. 10, 409-415 (2003).
[CrossRef] [PubMed]

Veigle, Wm. J.

J. H. Hubbell, Wm. J. Veigle, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross setions," J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in  6, 615 (1977).
[CrossRef]

Weierstall, U.

J. C. H. Spence, U. Weierstall, and M. Howells, "Coherence and sampling requirements for diffractive imaging," Ultramicroscopy 101, 149-152 (2004).
[CrossRef] [PubMed]

Williams, G.

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, "Effectiveness of iterative algorithms in recoveringphase in the presence of noise," Acta Crystallogr. Sect. A 63, 36-42 (2007).
[CrossRef]

Williams, G. J.

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104102 (2007).
[CrossRef]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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]

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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[CrossRef]

Acta Crystallogr. Sect. A (2)

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

G. Williams, M. Pfeifer, I. Vartanyants, and I. Robinson, "Effectiveness of iterative algorithms in recoveringphase in the presence of noise," Acta Crystallogr. Sect. A 63, 36-42 (2007).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control (1)

T. A. Pitts and J. F. Greenleaf, "Fresnel transform phase retrieval from magnitude," IEEE Trans. Ultrason. Ferroelectr. Freq. Control 50, 1035-1045 (2003).
[CrossRef] [PubMed]

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

J. Phys. Chem. Ref. Data (1)

J. H. Hubbell, Wm. J. Veigle, E. A. Briggs, R. T. Brown, D. T. Cromer, and R. J. Howerton, "Atomic form factors, incoherent scattering functions, and photon scattering cross setions," J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in  6, 615 (1977).
[CrossRef]

J. Synchrotron Radiat. (1)

I. A. Vartanyants and I. K. Robinson, "Imaging of quantum array structures with coherent and partially coherent diffraction," J. Synchrotron Radiat. 10, 409-415 (2003).
[CrossRef] [PubMed]

Nat. Phys. (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. Plönjes, M. Kuhlmann, R. Treusch, S. Düsterer, T. Tschentscher, J. R. Schneider, E. Spiller, T. Möller, 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. Szöke, N. Timneanu, and J. Hajdu, "Femtosecond diffractive imaging with a soft-X-ray free-electron laser," Nat. Phys. 2, 839-843 (2006).
[CrossRef]

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

Opt. Lett. (2)

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. Rev. B (1)

G. J. Williams, H. M. Quiney, A. G. Peele, and K. A. Nugent, "Coherent diffractive imaging and partial coherence," Phys. Rev. B 75, 104102 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, 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]

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

Ultramicroscopy (2)

J. M. Rodenburg, A. C. Hurst, and A. G. Cullis, "Transmission microscopy without lenses for objects of unlimited size," Ultramicroscopy 107, 227-231 (2007).
[CrossRef]

J. C. H. Spence, U. Weierstall, and M. Howells, "Coherence and sampling requirements for diffractive imaging," Ultramicroscopy 101, 149-152 (2004).
[CrossRef] [PubMed]

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Figures (3)

Fig. 2.
Fig. 2.

(a). Measured intensity where the scaling of the scatter outside the illumination area has been enhanced for clarity. The hologram can be seen just below the central stop. The diameter of the central stop at the CCD is approximately 1.15mm (b) Convergence of the error metric for 20 different random starting phase guesses.

Fig. 1.
Fig. 1.

Experimental schematic (not to scale).

Fig. 3.
Fig. 3.

(a). AFM height scan of the approximate region shown in (b). The solid line shows the line of the plot shown in (d). (b) STXM scan of the sample. The scale bar is 1 µm. (c) FCDI thickness reconstruction of the sample. The scale bar is 1 µm. The dotted line shows the line of the plot shown in (d) and the numbered white overlays show the regions averaged in the comparison with the AFM results shown in Table 1. (d) Plot of the FCDI thickness (dotted line) compared with the AFM measured height (solid line) for the sections shown in (c) and (a) respectively. (e) Tilted scanning electron microscope image of another, identically prepared, sample on the same substrate as the one used in the experiment. Some of the features have detached on this sample.

Tables (1)

Tables Icon

Table 1: Average AFM height and reconstructed thickness for the four areas indicated in Fig. 3(c).

Equations (4)

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

[ T ( r ) + 1 ] ψ inc ( r ) = ψ inc ( r ) exp [ ik 2 0 τ ( r ) ( n 2 ( r , z ) 1 ) dz ] ,
[ T ( r ) + 1 ] ψ inc ( r ) = ψ inc ( r ) exp [ ik 0 τ ( r ) δ ( r , z ) dz ] exp [ k 0 τ ( r ) β ( r , z ) dz ] .
χ k 2 = n = 0 N 1 [ I ( n ) ψ ̂ exit k ( n ) ] 2 n = 0 N 1 I ( n ) ,
ψ ̂ exit k

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