Quantum imaging with incoherently scattered light from a free-electron laser

Raimund Schneider ,Lars Bocklage ,W Würth ,Sergey Lazarev ,Anton Classen ,Ivan A Zaluzhnyy ,Günter Brenner ,Birgit Fischer ,Ralf Röhlsberger ,Lukas Wenthaus ,Ivan A Vartanyants ,Jochen Wagner ,Daniel Bhatti ,A Benz ,Giuseppe Mercurio ,Petr Skopintsev ,Thomas Mehringer ,Oleg Gorobtsov ,Yuri N Obukhov ,Kai Schlage ,Svenja Willing ,Felix Waldmann ,J Von Zanthier

doi:10.1038/nphys4301

Abstract

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 methods. 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 processes, including Compton scattering, 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 Twiss to higher than second-order paving the way towards determination of structure and dynamics of matter in regimes where coherent imaging methods have intrinsic limitations.

Highlights

The advent of accelerator-driven free-electron lasers (FEL) has opened new avenues for high-resolution structure determination via di raction methods that go far beyond conventional X-ray crystallography methods[1,2,3,4,5,6,7,8,9,10]
We go still further and employ the method to image arbitrary two-dimensional incoherently scattering objects radiating in the vacuum ultraviolet
The extension from one dimension24to two dimensions is non-trivial and even unexpected in view of the tremendously enlarged parameter space for the possible phase combinations determining the higher-order correlation functions. It constitutes a major breakthrough of the scheme as it allows application of the method for real imaging applications— for example, imaging of arbitrary two-dimensional (2D) objects on a substrate

Summary

UN b dx HM dy

Independently from each other (see Supplementary Information). In our experiment, a two-dimensional object mask is placed behind the diffusor, consisting of six square-cut holes in a hexagonal arrangement to mimic the carbon atoms in a benzene molecule emitting incoherent fluorescence radiation. When placing all but one detector at the so-called magic positions (MP; refs 23,24), only specific spatial frequency vectors of the object appear within a given correlation function of order m. After evaluating g (m)(r1; MP) for m = 3, 4, 5, with the fixed detectors aligned at the MP along the x-axis as well as along the y-axis (resulting in a total of six 2D correlation functions), the set of spatial frequency vectors ζexp of the benzene structure is derived from the best 2D fit to the experimental data (see Supplementary Information). For the investigated benzene structure only the set containing both spatial frequency vectors 1 and 1 provides a solution for the source arrangement in real space,

Author contributions

Findings

Additional information