Speckle contrast of interfering fluorescence X-rays

Abstract

With the development of X-ray free-electron lasers (XFELs), producing pulses of femtosecond durations comparable with the coherence times of X-ray fluorescence, it has become possible to observe intensity–intensity correlations due to the interference of emission from independent atoms. This has been used to compare durations of X-ray pulses and to measure the size of a focusedX-ray beam, for example. Here it is shown that it is also possible to observe the interference of fluorescence photons through the measurement of the speckle contrast of angle-resolved fluorescence patterns. Speckle contrast is often used as a measure of the degree of coherence of the incident beam or the fluctuations of the illuminated sample as determined from X-ray diffraction patterns formed by elastic scattering, rather than from fluorescence patterns as addressed here. Commonly used approaches to estimate speckle contrast were found to suffer when applied to XFEL-generated fluorescence patterns due to low photon counts and a significant variation of the excitation pulse energy from shot to shot. A new method to reliably estimate speckle contrast under such conditions, using a weighting scheme, is introduced. The method is demonstrated by comparing the speckle contrast of fluorescence observed with pulses of 3 fs to 15 fs duration.

Imaging via Correlation of X-Ray Fluorescence Photons

“…In the classical limit, the origin of the g (2) (0) − 1 = ⟨I( ⃗ k) 2 ⟩/⟨I( ⃗ k)⟩ 2 − 1 map should reveal the visibility factor β. With low photon counts, however, the expected value diverges [7,11] and does not give a reliable analysis. In addition, this value is overly sensitive to background as compared with other values of ⃗ q, due to elastically scattered photons and detector noise.…”

“…In the classical view, waves from independent emitters will interfere if they arrive at the detector and overlap within the coherence time of the emission, τ c , which is less than 1 fs for K-shell fluorescence from most elements. Using femtosecond-duration pulses from X-ray free-electron lasers, it becomes possible to excite fluorescence in atoms throughout a sample within a time comparable to τ c , such that this interference can be observed without the need for a fast gating detector [2,[5][6][7]. Unlike elastic scattering, where the phases of scattered waves have stationary phase relationships with each other that are dependent on the positions of the scatterers in three-dimensional space, the phases of the fluorescence waves have no such stationary relationship and fluctuate from pulse to pulse.…”