Fourier transform

Degree of coherence

Optics

Physics

Coherent diffraction imaging

Electron

Wavefront

Scattering

Diffraction

Free-electron laser

Coherence (philosophical gambling strategy)

Laser

Quantum mechanics

Phase retrieval

Free electron model

Nature Physics

The intensity correlations in incoherently scattered X-rays from a free-electron laser can be exploited to image 2D objects with a resolution close to or below the diffraction limit. 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.

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