Abstract

We proposed and experimentally demonstrated a rotation-free approach of holographic imaging by using an extended arc reference. From the diffraction intensity, the objects were retrieved using a two-step algorithm without a prior knowledge of the information of the sample and reference. This scheme alleviates the convergence problem of coherent diffractive imaging and also promises to achieve a high resolution.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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]
  2. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  3. J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
    [CrossRef]
  4. J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray Crystallography to allow the imaing of noncrystalline materials, cells and single protein Complexes,” Annu. Rev. Phys. Chem. 59, 387–410 (2008).
    [CrossRef]
  5. J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986).
    [CrossRef]
  6. S. Marchesini, H. He, H. N. Chapman, S. P. Hau-Riege, A. Noy, M. R. Howells, U. Weierstall, and J. H. Spence, “X-ray image reconstrunction from a diffraction pattern alone,” Phys. Rev. B 68, 140101 (2003).
    [CrossRef]
  7. S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
    [CrossRef] [PubMed]
  8. W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
    [CrossRef]
  9. R. L. Sandberg, D. A. Raymondson, C. La-o-vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, C. H. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. 34, 1618–1620 (2009).
    [CrossRef] [PubMed]
  10. S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
    [CrossRef]
  11. S. G. Podorov, K. M. Pavlov, and D. M. Paganin, “A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaing,” Opt. Express 15, 9954–9962 (2007).
    [CrossRef] [PubMed]
  12. M. Guizar-Sicairos and J. R. Fienup, “Holography with extended reference by autocorrelation linear differential operation,” Opt. Express 15, 17592–17612 (2007).
    [CrossRef] [PubMed]
  13. M. Guizar-Sicairos and J. R. Fienup, “Direct image reconstruction from a Fourier intensity pattern using HERALDO,” Opt. Lett. 33, 2668–2670 (2008).
    [CrossRef] [PubMed]
  14. D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
    [CrossRef] [PubMed]
  15. D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
    [CrossRef]
  16. M. Guizar-Sicairos, D. L. Zhu, J. R. Fienup, B. Wu, A. Scherz, and J. Stöhr, “Holographic x-ray image reconstruction through the application of differential and integral operators,” Opt. Lett. 35, 928–930 (2010).
    [CrossRef] [PubMed]
  17. Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
    [CrossRef]
  18. J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987).
    [CrossRef]

2010 (4)

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
[CrossRef] [PubMed]

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

M. Guizar-Sicairos, D. L. Zhu, J. R. Fienup, B. Wu, A. Scherz, and J. Stöhr, “Holographic x-ray image reconstruction through the application of differential and integral operators,” Opt. Lett. 35, 928–930 (2010).
[CrossRef] [PubMed]

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

2009 (1)

2008 (3)

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray Crystallography to allow the imaing of noncrystalline materials, cells and single protein Complexes,” Annu. Rev. Phys. Chem. 59, 387–410 (2008).
[CrossRef]

M. Guizar-Sicairos and J. R. Fienup, “Direct image reconstruction from a Fourier intensity pattern using HERALDO,” Opt. Lett. 33, 2668–2670 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (1)

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

2004 (1)

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef] [PubMed]

2003 (1)

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

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]

1987 (1)

1986 (1)

1982 (1)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
[CrossRef]

1972 (1)

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

Acremann, Y.

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

Bajt, S.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Barty, A.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Bogan, M. J.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Boutet, S.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Boutu1, W.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
[CrossRef] [PubMed]

Carré, B.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
[CrossRef] [PubMed]

Chapman, H. N.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

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

Charalambous, P.

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]

Chen, K.

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

Cui, C.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Earnest, T.

J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray Crystallography to allow the imaing of noncrystalline materials, cells and single protein Complexes,” Annu. Rev. Phys. Chem. 59, 387–410 (2008).
[CrossRef]

Eberhardt, W.

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef] [PubMed]

Eisebitt, S.

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef] [PubMed]

Farle, M.

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

Fienup, J. R.

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
[CrossRef] [PubMed]

M. Guizar-Sicairos, D. L. Zhu, J. R. Fienup, B. Wu, A. Scherz, and J. Stöhr, “Holographic x-ray image reconstruction through the application of differential and integral operators,” Opt. Lett. 35, 928–930 (2010).
[CrossRef] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Direct image reconstruction from a Fourier intensity pattern using HERALDO,” Opt. Lett. 33, 2668–2670 (2008).
[CrossRef] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Holography with extended reference by autocorrelation linear differential operation,” Opt. Express 15, 17592–17612 (2007).
[CrossRef] [PubMed]

J. R. Fienup, “Reconstruction of a complex-valued object from the modulus of its Fourier transform using a support constraint,” J. Opt. Soc. Am. A 4, 118–123 (1987).
[CrossRef]

J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. A 3, 1897–1907 (1986).
[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
[CrossRef]

Fischer, P.

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

Frank, M.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Friedenberger, N.

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

Gauthier, D.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
[CrossRef] [PubMed]

Ge, X.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
[CrossRef] [PubMed]

Gerchberg, R. W.

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

Guizar-Sicairos, M.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
[CrossRef] [PubMed]

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

M. Guizar-Sicairos, D. L. Zhu, J. R. Fienup, B. Wu, A. Scherz, and J. Stöhr, “Holographic x-ray image reconstruction through the application of differential and integral operators,” Opt. Lett. 35, 928–930 (2010).
[CrossRef] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Direct image reconstruction from a Fourier intensity pattern using HERALDO,” Opt. Lett. 33, 2668–2670 (2008).
[CrossRef] [PubMed]

M. Guizar-Sicairos and J. R. Fienup, “Holography with extended reference by autocorrelation linear differential operation,” Opt. Express 15, 17592–17612 (2007).
[CrossRef] [PubMed]

Günther, Ch.

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

Hajdu, J.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Hau-Riege, S. P.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

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

Hellwig, O.

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef] [PubMed]

Howells, M. R.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

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

Ishikawa, T.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray Crystallography to allow the imaing of noncrystalline materials, cells and single protein Complexes,” Annu. Rev. Phys. Chem. 59, 387–410 (2008).
[CrossRef]

Kapteyn, C. H.

Kimura, H.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Kirz, J.

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]

La-o-vorakiat, C.

Lee, J.Y.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Lörgen1, M.

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef] [PubMed]

Lüning, J.

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef] [PubMed]

Marchesini, S.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

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

Matsubara, E.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Matsui, S.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

McNulty, I.

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

Merdji, H.

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
[CrossRef] [PubMed]

Miao, J.

R. L. Sandberg, D. A. Raymondson, C. La-o-vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, C. H. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. 34, 1618–1620 (2009).
[CrossRef] [PubMed]

J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray Crystallography to allow the imaing of noncrystalline materials, cells and single protein Complexes,” Annu. Rev. Phys. Chem. 59, 387–410 (2008).
[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]

Murnane, M. M.

Nagasono, M.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Nishino, Y.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Noy, A.

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

Nozaki, K.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Ohashi, H.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Okada, M.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Okaya, M.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Ollefs, K.

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

Paganin, D. M.

Paul, A.

Pavlov, K. M.

Podorov, S. G.

Raines, K. S.

Raymondson, D. A.

Rick, R.

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

Sakdinawat, A.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Sandberg, R. L.

Saxton, W. O.

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

Sayre, D.

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]

Scherz, A.

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

M. Guizar-Sicairos, D. L. Zhu, J. R. Fienup, B. Wu, A. Scherz, and J. Stöhr, “Holographic x-ray image reconstruction through the application of differential and integral operators,” Opt. Lett. 35, 928–930 (2010).
[CrossRef] [PubMed]

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

Schlotter, W. F.

R. L. Sandberg, D. A. Raymondson, C. La-o-vorakiat, A. Paul, K. S. Raines, J. Miao, M. M. Murnane, C. H. Kapteyn, and W. F. Schlotter, “Tabletop soft-x-ray Fourier transform holography with 50 nm resolution,” Opt. Lett. 34, 1618–1620 (2009).
[CrossRef] [PubMed]

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef] [PubMed]

Seibert, M. M.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Shaevitz, J. W.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Shapiro, D. A.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Shen, Q.

J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray Crystallography to allow the imaing of noncrystalline materials, cells and single protein Complexes,” Annu. Rev. Phys. Chem. 59, 387–410 (2008).
[CrossRef]

Spence, J. C. H.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Spence, J. H.

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

Stöhr, J.

M. Guizar-Sicairos, D. L. Zhu, J. R. Fienup, B. Wu, A. Scherz, and J. Stöhr, “Holographic x-ray image reconstruction through the application of differential and integral operators,” Opt. Lett. 35, 928–930 (2010).
[CrossRef] [PubMed]

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef] [PubMed]

Szöke, A.

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Tanaka, Y.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Tono, K.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Tyliszczak, T.

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

Uozaki, Y.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Wackerman, C. C.

Weierstall, U.

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

Wu, B.

M. Guizar-Sicairos, D. L. Zhu, J. R. Fienup, B. Wu, A. Scherz, and J. Stöhr, “Holographic x-ray image reconstruction through the application of differential and integral operators,” Opt. Lett. 35, 928–930 (2010).
[CrossRef] [PubMed]

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

Yabashi, M.

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Zhu, D. L.

M. Guizar-Sicairos, D. L. Zhu, J. R. Fienup, B. Wu, A. Scherz, and J. Stöhr, “Holographic x-ray image reconstruction through the application of differential and integral operators,” Opt. Lett. 35, 928–930 (2010).
[CrossRef] [PubMed]

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

Annu. Rev. Phys. Chem. (1)

J. Miao, T. Ishikawa, Q. Shen, and T. Earnest, “Extending X-ray Crystallography to allow the imaing of noncrystalline materials, cells and single protein Complexes,” Annu. Rev. Phys. Chem. 59, 387–410 (2008).
[CrossRef]

App. Opt. (1)

J. R. Fienup, “Phase retrieval algorithms: a comparison,” App. Opt. 21, 2758–2769 (1982).
[CrossRef]

Appl. Phys. Express (1)

Y. Nishino, Y. Tanaka, M. Okada, M. Okaya, Y. Uozaki, K. Nozaki, M. Yabashi, M. Nagasono, K. Tono, H. Kimura, H. Ohashi, S. Matsui, T. Ishikawa, and E. Matsubara, “Femtosecond snapshot holography with extended reference using extreme ultraviolet free-electron laser,” Appl. Phys. Express 3, 102701 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

W. F. Schlotter, R. Rick, K. Chen, A. Scherz, J. Stöhr, J. Lüning, S. Eisebitt, Ch. Günther, W. Eberhardt, O. Hellwig, and I. McNulty, “Multiple reference Fourier transform holography with soft x rays,” Appl. Phys. Lett. 89, 163112 (2006).
[CrossRef]

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

Nat. Photonics (1)

S. Marchesini, S. Boutet, A. Sakdinawat, M. J. Bogan, S. Bajt, A. Barty, H. N. Chapman, M. Frank, S. P. Hau-Riege, A. Szöke, C. Cui, D. A. Shapiro, M. R. Howells, J. C. H. Spence, J. W. Shaevitz, J.Y. Lee, J. Hajdu, and M. M. Seibert, “Massively parallel X-ray holography,” Nat. Photonics 2, 560–563 (2008).
[CrossRef]

Nature (2)

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]

S. Eisebitt, J. Lüning, W. F. Schlotter, M. Lörgen1, O. Hellwig, W. Eberhardt, and J. Stöhr, “Lensless imaging of magnetic nanostructures by X-ray spectro-holography,” Nature 432, 885–888 (2004).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Optik (1)

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

Phys. Rev. B (1)

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

Phys. Rev. Let. (1)

D. L. Zhu, M. Guizar-Sicairos, B. Wu, A. Scherz, Y. Acremann, T. Tyliszczak, P. Fischer, N. Friedenberger, K. Ollefs, M. Farle, J. R. Fienup, and J. Stöhr, “High-resolution X-ray lensless imaging by differential holographic encoding,” Phys. Rev. Let. 105, 043901 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

D. Gauthier, M. Guizar-Sicairos, X. Ge, W. Boutu1, B. Carré, J. R. Fienup, and H. Merdji, “Single-shot Femtosecond X-ray holography using extended references,” Phys. Rev. Lett. 105, 093901 (2010).
[CrossRef] [PubMed]

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 (4)

Fig. 1
Fig. 1

(a) Sample under study. The colorbar indicates the intensity in linear scale. (b) Simulated diffraction pattern of the sample. The colorbar indicates the intensity in logarithmic scale. (c) Image reconstructed by the polar derivative operator in step 1. The colorbar is same to (a).

Fig. 2
Fig. 2

(a) Image reconstructed with the two-step algorithms. The colorbar is same to Fig. 1(a). (b) The evolution of the error as a function of iteration step. Green dash-dotted line: HIO algorithms and a static support constrain are used. Blue dashed line: HIO and shrinkwrap algorithms are used. Red solid line: our two-step algorithm is used.

Fig. 3
Fig. 3

(a) Experimental diffraction of the sample number 3 shown in Fig. 1(a). The colorbar in (a) shows the intensity in logarithmic scale. (b) and (c) are the images retrieved from the experimental diffraction in step 1 and 2, respectively. The colorbars are same to Fig. 1(a). (d), (e) and (f) are similar to (a)–(c), but for another sample of LAN.

Fig. 4
Fig. 4

(a) Experimental diffraction of the sample number 3 with the reference rotated to 0 degree. The colorbar in (a) shows the intensity in logarithmic scale. (b) and (c) are the images retrieved from the experimental diffraction in step 1 and 2, respectively. The colorbars are same to Fig. 1(a), 1(d), 1(e), and 1(f) are similar to (a)–(c), but the reference is rotated to 45 degree.

Equations (3)

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

L ( 1 ( | U f | 2 ) ) = L ( o o + r r ) + L ( r o ) + L ( o r )
= L ( o o + r r ) + ( x r y y r x ) o [ r y ( x o ) r x ( y o ) ] + o ( x r y y r x ) [ ( x o ) r y ( y o ) r x ]
= L ( o o + r r ) + i = 1 , 2 [ o * ( x i x , y i y ) + o ( x x i , y y i ) ] [ r y ( x o ) r x ( y o ) ] [ ( x o ) r y ( y o ) r x ]

Metrics