• A Corrigendum to this article was published on 16 October 2014

This article has been updated

Abstract

In X-ray Fourier-transform holography, images are formed by exploiting the interference pattern between the X-rays scattered from the sample and a known reference wave. To date, this technique has only been possible with a limited set of special reference waves. We demonstrate X-ray Fourier-transform holography with an almost unrestricted choice for the reference wave, permitting experimental geometries to be designed according to the needs of each experiment and opening up new avenues to optimize signal-to-noise and resolution. The optimization of holographic references can aid the development of holographic techniques to meet the demands of resolution and fidelity required for single-shot imaging applications with X-ray lasers.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Change history

  • 16 October 2014

    The original version of this Article contained an error in the spelling of the author Emanuele Pedersoli, which was incorrectly given as Emmanuele Pedersoli. This has now been corrected in both the PDF and HTML versions of the Article.

References

  1. 1.

    et al. Massively parallel x-ray holography. Nat. Photonics 2, 560–563 (2008).

  2. 2.

    et al. X-ray holographic microscopy with zone plates applied to biological samples in the water window using 3rd harmonic radiation from the free-electron laser flash. Opt. Express 19, 11059–11070 (2011).

  3. 3.

    et al. Lensless imaging of magnetic nanostructures by X-ray spectro-holography. Nature 432, 885–888 (2004).

  4. 4.

    et al. Microscopic reversal behavior of magnetically capped nanospheres. Phys. Rev. B 81, 064411 (2010).

  5. 5.

    et al. Origin of magnetic switching field distribution in bit patterned media based on pre-patterned substrates. Appl. Phys. Lett. 99, 062502 (2011).

  6. 6.

    et al. Femtosecond single-shot imaging of nanoscale ferromagnetic order in co=pd multilayers using resonant x-ray holography. Phys. Rev. Lett. 108, 267403 (2012).

  7. 7.

    et al. Digital in-line holography with femtosecond vuv radiation provided by the free-electron laser flash. Opt. Express 17, 8220–8228 (2009).

  8. 8.

    et al. Coherent imaging using seeded free-electron laser pulses with variable polarization: first results and research opportunities. Rev. Sci. Instrum. 84, 051301 (2013).

  9. 9.

    et al. High-resolution imaging by Fourier-transform X-ray holography. Science 256, 1009–1012 (1992).

  10. 10.

    et al. Multiple reference fourier transform holography with soft x rays. Appl. Phys. Lett. 89, 163112 (2006).

  11. 11.

    , & A non-iterative reconstruction method for direct and unambiguous coherent diffractive imaging. Opt. Express 15, 9954–9962 (2007).

  12. 12.

    & Holography with extended reference by autocorrelation linear differential operation. Opt. Express 15, 17592–17612 (2007).

  13. 13.

    et al. Monolithic focused reference beam x-ray holography. Nat. Commun. 5, 3008 (2014).

  14. 14.

    et al. High-resolution x-ray lensless imaging by differential holographic encoding. Phys. Rev. Lett. 105, 043901 (2010).

  15. 15.

    & Direct retrieval of a complex wave from its diffraction pattern. Opt. Commun 281, 5114–5121 (2008).

  16. 16.

    , , , & Fast deterministic approach to exit-wave reconstruction. Phys. Rev. A. 85, 013816 (2012).

  17. 17.

    & Methods of conjugate gradients for solving linear systems. J. Res. Nat. Bur. Stand 49, 409 (1952).

  18. 18.

    et al. Fast deterministic single-exposure coherent diffractive imaging at subangstrom resolution. Phys. Rev. B 87, 094115 (2013).

  19. 19.

    et al. Deterministic electron ptychography at atomic resolution. Phys. Rev. B 89, 064101 (2014).

  20. 20.

    et al. Quantitative image reconstruction of gan quantum dots from oversampled diffraction intensities alone. Phys. Rev. Lett. 95, 085503 (2005).

  21. 21.

    , , , & Reconstruction of a yeast cell from x-ray diffraction data. Acta Crystallogr. A A62, 248–261 (2006).

  22. 22.

    & Solving Least Squares Problems Prentice-Hall (1987).

  23. 23.

    & A fast non-negativity-constrained least squares algorithm. J. Chemometr. 11, 393–401 (1997).

  24. 24.

    et al. The fermi@elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications. New J. Phys. 12, 075002 (2010).

  25. 25.

    et al. Highly coherent and stable pulses from the FERMI seeded free-electron laser in the extreme ultraviolet. Nat. Photonics 6, 699–704 (2012).

  26. 26.

    et al. Two-stage seeded soft-x-ray free-electron laser. Nat. Photon 7, 913–918 (2013).

  27. 27.

    et al. Femtosecond diffractive imaging with a soft-X-ray free-electron laser. Nat. Phys. 2, 839–843 (2006).

  28. 28.

    et al. Single mimivirus particles intercepted and imaged with an x-ray laser. Nature 470, 78–81 (2011).

  29. 29.

    et al. High-fidelity direct coherent diffractive imaging of condensed matter. Phys. Rev. B 84, 144122 (2011).

  30. 30.

    Relaxed averaged alternating reflections for diffraction imaging. Inverse Probl. 21, 37–50 (2005).

  31. 31.

    et al. X-ray image reconstruction from a diffraction pattern alone. Phys. Rev. B 68, 140101 (2003).

  32. 32.

    et al. High-resolution ab initio three-dimensional x-ray diffraction microscopy. J. Opt. Soc. Am. A 23, 1179–1200 (2006).

  33. 33.

    et al. Fresnel coherent diffractive imaging. Phys. Rev. Lett. 97, 025506 (2006).

  34. 34.

    , , , & Direct exit-wave reconstruction from a single defocused image. Ultramicroscopy 111, 1455–1460 (2011).

Download references

Acknowledgements

We thank Professor L.J. Allen for useful discussion and feedback. This research was supported under the Australian Research Council’s Centre of Excellence programme and DECRA funding schemes (Project Nos DE130100739 and DE140100624). FERMI project of Elettra Sincrotrone Trieste is partially supported by the Italian Ministry of University and Research under grant numbers FIRB-RBAP045JF2 and FIRB-RBAP06AWK3 and by the grant from Friuli Venezia Giulia Region: Nanotox 0060-2009. F.C., E.P. and L.R. thank N. Mahne, C. Svetina, M. Zangrando and the Fermi Commissioning Team for the valuable technical support during the measurement preparation.

Author information

Author notes

    • Andrew V. Martin
    •  & Adrian J. D’Alfonso

    These authors contributed equally to this work

Affiliations

  1. ARC Centre of Excellence for Coherent X-ray Science, School of Physics, The University of Melbourne, Melbourne, Victoria 3010, Australia

    • Andrew V. Martin
  2. School of Physics, University of Melbourne, Melbourne, Victoria 3010, Australia

    • Adrian J. D’Alfonso
  3. Center for Free-Electron Laser Science, DESY, Hamburg 22607, Germany

    • Fenglin Wang
    • , Richard Bean
    • , Richard A. Kirian
    • , Francesco Stellato
    • , Chun Hong Yoon
    •  & Henry N. Chapman
  4. Fermi, Elettra Sincrotrone Trieste, SS 14-km 163.5, Basovizza, Trieste 34149, Italy

    • Flavio Capotondi
    • , Emanuele Pedersoli
    •  & Lorenzo Raimondi
  5. European XFEL GmbH, Albert Einstein Ring 19, Hamburg 22761, Germany

    • Chun Hong Yoon
  6. University of Hamburg, Luruper Chaussee 149, Hamburg 22761, Germany

    • Henry N. Chapman

Authors

  1. Search for Andrew V. Martin in:

  2. Search for Adrian J. D’Alfonso in:

  3. Search for Fenglin Wang in:

  4. Search for Richard Bean in:

  5. Search for Flavio Capotondi in:

  6. Search for Richard A. Kirian in:

  7. Search for Emanuele Pedersoli in:

  8. Search for Lorenzo Raimondi in:

  9. Search for Francesco Stellato in:

  10. Search for Chun Hong Yoon in:

  11. Search for Henry N. Chapman in:

Contributions

The reconstruction theory and methods were developed by A.V.M. and A.J.D. The samples were designed by A.V.M. and F.W. and they were prepared by F.S. The experiment was performed by F.W., R.B., F.C., R.A.K., E.P., L.R. and C.H.Y. in consultation with H.N.C. The reconstructions were performed by A.V.M. and A.J.D., who also wrote the manuscript with input from all authors.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Andrew V. Martin.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/ncomms5661

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.