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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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.
The developed Python code is available at https://github.com/jhuijts under the BSD license.
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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.
The authors declare no competing interests
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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.
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). https://doi.org/10.1038/s41566-020-0660-7