Extracting contrast in an X-ray speckle visibility spectroscopy experiment under imperfect conditions

Abstract

Pump–probe experiments at synchrotrons and free-electron lasers to study ultrafast dynamics in materials far from equilibrium have been well established, but techniques to investigate equilibrium dynamics on the nano- and pico-second timescales remain underdeveloped and experimentally challenging. A promising approach relies on a double-probe X-ray speckle visibility spectroscopy setup at split-and-delay beamlines of X-ray free-electron lasers. However, the logistics in consistently producing two collinear, perfectly overlapping pulses necessary to conduct a faithful experiment is difficult to achieve. In this paper, a method is introduced to extract contrast in the case where an angular misalignment and imperfect overlap exists between the two pulses. Numerical simulations of a dynamical system show that contrast can still be extracted for significant angular misalignments accompanied by partial overlap between the two pulses.

From Femtoseconds to Hours—Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays

“…For dynamics studies, both beams need to probe the same sample volume. This introduces several challenges, e.g., as both beams may experience different sizes or shapes, that have an impact on the measured speckle contrasts because of partially overlapping beams [179,180]. Furthermore, the pulses are reflected by several silicon mirrors with fixed bandwidth, resulting to large pulse-to-pulse intensity fluctuations as only few of the spectral spikes generated in the SASE process are transmitted through the split-and-delay unit [157].…”

On the analysis of two-time correlation functions: equilibrium versus non-equilibrium systems

“…In the case of lowintensity statistics, while equation (4) with its definition of contrast and the definitions of Corr-TTC and G-TTC are mathematically true, they are not operational. In such instances, the contrast needs to be determined from the binomial distribution, and alternative data analysis methods, as well as experimental procedures, are employed instead of TTCs to obtain the intermediate scattering function (Roseker et al, 2018;Hua et al, 2020;Hruszkewycz et al, 2012). These approaches are beyond the scope of the current article.…”