The advent of accelerator-driven free-electron lasers (FEL) has opened new avenues for high-resolution structure determination via diffraction methods that go far beyond conventional X-ray crystallography methods1,2,3,4,5,6,7,8,9,10. These techniques rely on coherent scattering processes that require the maintenance of first-order coherence of the radiation field throughout the imaging procedure. Here we show that higher-order degrees of coherence, displayed in the intensity correlations of incoherently scattered X-rays from an FEL, can be used to image two-dimensional objects with a spatial resolution close to or even below the Abbe limit. This constitutes a new approach towards structure determination based on incoherent processes11,12, including fluorescence emission or wavefront distortions, generally considered detrimental for imaging applications. Our method is an extension of the landmark intensity correlation measurements of Hanbury Brown and Twiss13 to higher than second order, paving the way towards determination of structure and dynamics of matter in regimes where coherent imaging methods have intrinsic limitations14.

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R.S., T.M., A.C., D.B. and J.v.Z. gratefully acknowledge funding by the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German Research Foundation (DFG) in the framework of the German excellence initiative. A.C. and D.B. gratefully acknowledge financial support by the Staedtler Foundation and the Cusanuswerk, Bischöfliche Studienförderung, respectively. We acknowledge support of the Helmholtz Association through project oriented funds. I.V. acknowledges the support of the Virtual Institute VH-VI-403 of the Helmholtz Association. Y.O. and S.W. acknowledge support by the Partnership for Innovation, Education and Research (PIER) between DESY and the University of Hamburg. We are grateful to the FLASH machine operators, to the technical staff at FLASH for excellent FEL conditions, and to Holger Meyer for his contributions to the design of the experimental set-up. We appreciate fruitful discussions with E. Weckert and H. N. Chapman.

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  1. Institut für Optik, Information und Photonik, Universität Erlangen-Nürnberg, Staudtstraße 1, 91058 Erlangen, Germany

    • Raimund Schneider
    • , Thomas Mehringer
    • , Anton Classen
    • , Daniel Bhatti
    • , Felix Waldmann
    •  & Joachim von Zanthier
  2. Erlangen Graduate School in Advanced Optical Technologies (SAOT), Universität Erlangen-Nürnberg, Paul-Gordan-Straße 6, 91052 Erlangen, Germany

    • Raimund Schneider
    • , Thomas Mehringer
    • , Anton Classen
    • , Daniel Bhatti
    •  & Joachim von Zanthier
  3. Department Physik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany

    • Giuseppe Mercurio
    • , Lukas Wenthaus
    • , Adrian Benz
    •  & Wilfried Wurth
  4. Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany

    • Giuseppe Mercurio
    • , Lukas Wenthaus
    •  & Wilfried Wurth
  5. Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, 22607 Hamburg, Germany

    • Günter Brenner
    • , Oleg Gorobtsov
    • , Lars Bocklage
    • , Sergey Lazarev
    • , Kai Schlage
    • , Petr Skopintsev
    • , Svenja Willing
    • , Ivan Zaluzhnyy
    • , Wilfried Wurth
    • , Ivan A. Vartanyants
    •  & Ralf Röhlsberger
  6. The Hamburg Centre for Ultrafast Imaging, Luruper Chaussee 149, 22761 Hamburg, Germany

    • Lars Bocklage
    •  & Ralf Röhlsberger
  7. Institut für Physikalische Chemie, Universität Hamburg, Grindelallee 117, 20146 Hamburg, Germany

    • Birgit Fischer
  8. National Research Tomsk Polytechnic University (TPU), Prospekt Lenina 30, 634050 Tomsk, Russia

    • Sergey Lazarev
  9. Nuclear Safety Institute, Russian Academy of Sciences, Bolshaya Tulskaya ul. 52, 115191 Moscow, Russia

    • Yuri Obukhov
  10. Institut für Nanostruktur- und Festkörperphysik, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany

    • Jochen Wagner
  11. National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Kashirskoe shosse 31, Moscow 115409, Russia

    • Ivan Zaluzhnyy
    •  & Ivan A. Vartanyants


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J.v.Z., R.R. and I.A.V. conceived the experiment and coordinated the experimental efforts. R.S. and T.M. designed the experimental layout and provided post-measurement analysis and evaluation of experimental data. G.M. designed and built the experimental set-up. G.M., L.W., R.S., T.M., O.G., S.L., P.S. and I.Z. carried out the experiment at FLASH/DESY. A.C. and F.W. developed the idea of sequential spatial frequency filtering in 1D and 2D using higher-order intensity correlations. A.C. and D.B. developed quantum path analysis of the method and mathematical explanation for sub-Abbe resolution. A.B. installed the motor control of the diffusor stage. L.B. coordinated efforts to characterize diffusors and samples. B.F. provided silica particles for production of diffusors. K.S. prepared diffusors and thin film coatings. J.W. prepared the hole mask of the artificial benzene molecule used as sample. S.W. participated in preparation and characterization of diffusors. G.B. provided the operation of the beamline PG2 at FLASH. Y.O. participated in discussion of the theoretical basis of quantum imaging. W.W. provided the end station for measurements at the PG2 beamline. R.S., T.M., J.v.Z., R.R. and I.A.V. wrote the manuscript with contributions and improvements from all authors.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Joachim von Zanthier.

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