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Broadband coherent diffractive imaging


Recent technological advances in attosecond science hold the promise of tracking electronic processes at the shortest space and time scales. However, the necessary imaging methods combining attosecond temporal resolution with nanometre spatial resolution are currently lacking. Regular coherent diffractive imaging, based on the diffraction of quasi-monochromatic illumination by a sample, is inherently incompatible with the extremely broad nature of attosecond spectra. Here, we present an approach that enables coherent diffractive imaging using broadband illumination. The method is based on a numerical monochromatization of the broadband diffraction pattern by the regularized inversion of a matrix that depends only on the spectrum of the diffracted radiation. Experimental validations using visible and hard X-ray radiation show the applicability of the method. Because of its generality and ease of implementation we expect this method to find widespread applications such as in petahertz electronics or attosecond nanomagnetism.

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Fig. 1: Principle of the numerical monochromatization.
Fig. 2: Experimental validation in the visible spectrum.
Fig. 3: Resolution of the reconstructions as a function of the signal level.
Fig. 4: X-ray experimental validation using synchrotron radiation.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

Code availability

The developed Python code is available at under the BSD license.


  1. Krausz, F. & Ivanov, M. Attosecond physics. Rev. Mod. Phys. 81, 163–234 (2009).

    Article  ADS  Google Scholar 

  2. Galmann, L., Cirelli, C. & Keller, U. Attosecond science: recent highlights and future trends. Annu. Rev. Phys. Chem. 63, 447–469 (2012).

    Article  ADS  Google Scholar 

  3. Calegari, F., Sansone, G., Stagira, S., Vozzi, C. & Nisoli, M. Advances in attosecond science. J. Phys. B 49, 062001 (2016).

    Article  ADS  Google Scholar 

  4. Lindroth, E. et al. Challenges and opportunities in attosecond and XFEL science. Nat. Rev. Phys. 1, 107–111 (2019).

    Article  Google Scholar 

  5. Takahashi, E. J., Lan, P. & Midorikawa, K. Generation of an isolated attosecond pulse with microjoule-level energy. In Conference on Lasers and Electro-Optics Paper QTh5B.10 (OSA, 2012).

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

    Article  Google Scholar 

  7. Ravasio, A. et al. Single-shot diffractive imaging with a table-top femtosecond soft X-ray laser-harmonics source. Phys. Rev. Lett. 103, 028104 (2009).

    Article  ADS  Google Scholar 

  8. Teichmann, S. M., Silva, F., Cousin, S. L., Hemmer, M. & Biegert, J. 0.5-keV soft X-ray attosecond continua. Nat. Commun. 7, 11493 (2016).

    Article  ADS  Google Scholar 

  9. Popmintchev, T. et al. Bright coherent ultrahigh harmonics in the keV X-ray regime from mid-infrared femtosecond lasers. Science 336, 1287–1291 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  10. Ding, Y., Huang, Z., Ratner, D., Bucksbaum, P. & Merdji, H. Generation of attosecond x-ray pulses with a multicycle two-color enhanced self-amplified spontaneous emission scheme. Phys. Rev. Spec. Top. Accel. Beams 22, 060703 (2009).

    Article  Google Scholar 

  11. Hartmann, N. et al. Attosecond time–energy structure of X-ray free-electron laser pulses. Nat. Photon. 12, 215–220 (2018).

    Article  ADS  Google Scholar 

  12. Gorkhover, T. et al. Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles. Nat. Photon. 10, 93–97 (2016).

    Article  ADS  Google Scholar 

  13. Miao, J. W., Charalambous, P., Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344 (1999).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Nishino, Y., Takahashi, Y., Imamoto, N., Ishikawa, T. & Maeshima, K. Three-dimensional visualization of a human chromosome using coherent X-ray diffraction. Phys. Rev. Lett. 102, 018101 (2009).

    Article  ADS  Google Scholar 

  16. Chapman, H. N. & Nugent, K. A. Coherent lensless X-ray imaging. Nat. Photon. 4, 833–839 (2010).

    Article  ADS  Google Scholar 

  17. Ekeberg, T. et al. Three-dimensional reconstruction of the giant mimivirus particle with an x-ray free-electron laser. Phys. Rev. Lett. 114, 098102 (2015).

    Article  ADS  Google Scholar 

  18. Miao, J., Ishikawa, T., Robinson, I. K. & Murnane, M. M. Beyond crystallography: diffractive imaging using coherent x-ray light sources. Science 348, 530–535 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  19. Duarte, J. et al. Computed stereo lensless X-ray imaging. Nat. Photon. 13, 449–453 (2019).

    Article  ADS  Google Scholar 

  20. Fienup, J. R. Phase retrieval for undersampled broadband images. J. Opt. Soc. Am. A 16, 1831–1837 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  21. Williams, G. O. et al. Fourier transform holography with high harmonic spectra for attosecond imaging applications. Opt. Lett. 40, 3205–3208 (2015).

    Article  ADS  Google Scholar 

  22. Gonzalez, A. I. Single Shot Lensless Imaging with Coherence and Wavefront Characterization of Harmonic and FEL sources. PhD thesis, Université Paris-Saclay (2016).

  23. Witte, S., Tenner, V. T., Noom, D. W. & Eikema, K. S. Lensless diffractive imaging with ultra-broadband table-top sources: from infrared to extreme-ultraviolet wavelengths. Light Sci. Appl. 3, e163 (2014).

    Article  ADS  Google Scholar 

  24. Meng, Y. et al. Octave-spanning hyperspectral coherent diffractive imaging in the extreme ultraviolet range. Opt. Express 23, 28960–28969 (2015).

    Article  ADS  Google Scholar 

  25. Batey, D. J., Claus, D. & Rodenburg, J. M. Information multiplexing in ptychography. Ultramicroscopy 138, 13–21 (2014).

    Article  Google Scholar 

  26. Enders, B. et al. Ptychography with broad-bandwidth radiation. Appl. Phys. Lett. 104, 171104 (2014).

    Article  ADS  Google Scholar 

  27. Enders, B. & Thibault, P. A computational framework for ptychographic reconstructions. Proc. R. Soc. Lond. A 472, 20160640 (2016).

    ADS  Google Scholar 

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

    Google Scholar 

  29. Abbey, B. et al. Lensless imaging using broadband X-ray sources. Nat. Photon. 5, 420–424 (2011).

    Article  ADS  Google Scholar 

  30. Dilanian, R. A. et al. Diffractive imaging using a polychromatic high-harmonic generation soft-x-ray source. J. Appl. Phys. 106, 023110 (2009).

    Article  ADS  Google Scholar 

  31. Chen, B. et al. Multiple wavelength diffractive imaging. Phys. Rev. A 79, 023809 (2009).

    Article  ADS  Google Scholar 

  32. Teichmann, S., Chen, B., Dilanian, R. A., Hannaford, P. & Van Dao, L. Experimental aspects of multiharmonic-order coherent diffractive imaging. J. Appl. Phys. 108, 023106 (2010).

    Article  ADS  Google Scholar 

  33. Chen, B. et al. Diffraction imaging: the limits of partial coherence. Phys. Rev. B 86, 235401 (2012).

    Article  ADS  Google Scholar 

  34. Paganin, D. Coherent X-Ray Optics (Oxford University Press, 2007).

  35. Hansen, P. C. REGULARIZATION TOOLS: A matlab package for analysis and solution of discrete ill-posed problems. Numerical Algorithms 6, 1–35 (1994).

    Article  ADS  MathSciNet  Google Scholar 

  36. Huijts, J. Broadband Coherent X-ray Diffractive Imaging and Developments Towards a High Repetition Rate Mid-IR Driven keV High Harmonic Source. PhD thesis, Université Paris-Saclay (2019).

  37. Elser, V., Rankenburg, I. & Thibault, P. Searching with iterated maps. Proc. Natl Acad. Sci. USA 104, 418–423 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  38. Marchesini, S. A unified evaluation of iterative projection algorithms for phase retrieval. Rev. Sci. Instrum. 78, 011301 (2007).

    Article  ADS  Google Scholar 

  39. Somogyi, A. et al. Optical design and multi-length-scale scanning spectro-microscopy possibilities at the Nanoscopium beamline of Synchrotron Soleil. J. Synchrot. Radiat. 22, 1118–1129 (2015).

    Article  Google Scholar 

  40. Mandula, O., Elzo Aizarna, M., Eymery, J., Burghammer, M. & Favre-Nicolin, V. PyNX.Ptycho: a computing library for X-ray coherent diffraction imaging of nanostructures. J. Appl. Crystallogr. 49, 1842–1848 (2016).

    Article  Google Scholar 

  41. Variola, A., Haissinski, J., Loulergue, A. & Zomer, F. (eds) ThomX Technical Design Report (2014);

  42. Günther, B. et al. The Munich Compact Light Source: biomedical research at a laboratory-scale inverse-Compton synchrotron X-ray source. Microsc. Microanal. 24, 984–985 (2018).

    Article  Google Scholar 

  43. Zhang, B. et al. Full field tabletop EUV coherent diffractive imaging in a transmission geometry. Opt. Express 21, 21970–21980 (2013).

    Article  ADS  Google Scholar 

  44. Guizar-Sicairos, M., Thurman, S. T. & Fienup, J. R. Efficient subpixel image registration algorithms. Opt. Lett. 33, 156–158 (2008).

    Article  ADS  Google Scholar 

  45. Fienup, J. R. Reconstruction of an object from the modulus of its Fourier transform. Opt. Lett. 3, 27–29 (1978).

    Article  ADS  Google Scholar 

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We acknowledge financial support from the European Union through the Future and Emerging Technologies (FET) Open H2020: VOXEL (grant 665207) and PETACom (grant 829153) and the integrated initiative of European laser research infrastructure (LASERLAB-EUROPE) (grant agreement no. 654148). Support from the French ministry of research through the 2013 Agence Nationale de Recherche (ANR) grants ‘NanoImagine’, 2014 ‘ultrafast lensless Imaging with Plasmonic Enhanced Xuv generation (IPEX)’, 2016 ‘High rEpetition rate Laser for Lensless Imaging in the Xuv (HELLIX)’; from the DGA RAPID grant ‘SWIM’, from the Centre National de Compétences en Nanosciences (C’NANO) research programme through the NanoscopiX grant; the LABoratoire d’EXcelence Physique Atoms Lumiére Matiére—LABEX PALM (ANR-10-LABX-0039-PALM), through the grants ‘Plasmon-X’ and ‘HIgh repetition rate Laser hArmonics in Crystals (HILAC)’ and, finally, the Action de Soutien á la Technologie et á la Recherche en Essonne (ASTRE) programme through the ‘NanoLight’ grant are also acknowledged. We would like to acknowledge the support of F. Fortuna and L. Delbsq from CSNSM, IN2P3, Orsay for sample fabrication. We aknowledge M. Hanna (LCF, IOGS Palaiseau), F. Guichard (Amplitude Techologies), M. Natile (Amplitude Techologies) and Y. Zaouter (Amplitude Techologies) for support during the experimental validation of the method in the visible spectrum. We aknowledge G. Dovillaire and S. Bucourt (Imagine Optic, Orsay, France) for providing the CCD camera. We also appreciate discussions with T. Auguste, F. Maia, H. Chapman, L. Shi, M. Kovacev and B. Daurer on the principle and implementation of the method and acknowledge access to the Davinci computer cluster of the Laboratory of Molecular Biophysics (Uppsala University, Sweden) and support by M. Hantke on the use of Condor. Contributions to the detector development from K. Desjardins from SOLEIL (Saint Aubin, France) were crucial to the success of the synchrotron experiment.

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Authors and Affiliations



J.H. and H.M. proposed the physical concept. J.H. developed the monochromatization method and performed the experiment in the visible spectrum, H.M. and J.H. devised the experiments, all authors performed the X-ray demonstration. Monochromatization of the synchrotron data was performed by J.H., phase retrieval by S.F. All authors discussed the results and contributed to writing the manuscript.

Corresponding author

Correspondence to Hamed Merdji.

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The authors declare no competing interests

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Extended data

Extended Data Fig. 1 Information flowchart of our method.

Based solely on the measured broadband diffraction pattern and the measured spectrum of the diffracted radiation, the broadband diffraction pattern (b) is monochromatised (yielding m). C is the matrix containing the spectral information, CGLS stands for Conjugate Gradient Least Squares, the regularisation method used to minimize the amount of inverted noise (see Methods).

Extended Data Fig. 2 Pushing the bandwidth in a broadband X-ray CDI simulation.

The ideal reconstruction a and reconstructions for 5 to 40% bandwidth b-e at a signal level of 1014 photons in the broadband pattern.

Source data

Supplementary information

Supplementary Information

Supplementary discussion and Table 1.

Supplementary Video 1

Video of the monochromatization process of the broadband diffraction pattern from the experiment in the visible spectrum (main text, Fig. 2). As mentioned in the Methods section of the main text, the monochromatization is performed in a regularized way by adding Krylov basis vectors. By increasing the number of basis vectors k, the matrix-vector problem is inverted, approaching the exact solution. In this video, the diffraction pattern is monochromatized by using up to k = 20 basis vectors.

Supplementary Video 2

Video of the monochromatization process of the broadband diffraction pattern from the hard X-ray simulation at 20% bandwidth (see the reconstruction in Extended Data Fig. 2), illustrating the behaviour of semi-convergence. As mentioned in the Methods section of the main text, the monochromatization is performed by adding Krylov basis vectors. As the number of basis vectors k is increased, first the signal is inverted (up to about k = 10), then gradually the inverted noise starts to dominate (up to k = 60).

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Huijts, J., Fernandez, S., Gauthier, D. et al. Broadband coherent diffractive imaging. Nat. Photonics 14, 618–622 (2020).

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