Split-pulse x-ray photon correlation spectroscopy has been proposed as one of the unique capabilities made possible with x-ray free electron lasers. It enables characterization of atomic-scale structural dynamics that dictates the macroscopic properties of various disordered material systems. Central to the experimental concept are x-ray optics that are capable of splitting an individual coherent femtosecond x-ray pulse into two distinct pulses, introduce an adjustable time delay between them, and then recombine the two pulses at the sample position such that they generate two coherent scattering patterns in rapid succession. Recent developments in such optics showed that, while true “amplitude-splitting” optics at hard x-ray wavelengths remains a technical challenge, wavefront and wavelength splitting are both feasible, able to deliver two micron-sized focused beams to the sample with sufficient relative stability. Here we show, however, that the conventional approach to speckle visibility spectroscopy using these beam-splitting techniques can be problematic, even leading to a decoupling of speckle visibility and material dynamics. In response, we discuss the details of the experimental approaches and data analysis protocols for addressing issues caused by subtle beam dissimilarities for both wavefront- and wavelength-splitting setups. We also show that in some scattering geometries, the $Q$-space mismatch can be resolved by using two beams of slightly different incidence angles and slightly different wavelengths at the same time. Instead of measuring the visibility of weak speckle patterns, the time correlation in sample structure is encoded in the “side band” of the spatial autocorrelation of the summed speckle patterns and can be retrieved straightforwardly from the experimental data. We demonstrate this with a numerical simulation.

We present the concept and a prototypical implementation of a compact x-ray split-delay system that is capable of performing continuous on-the-fly delay scans over a range of $\sim 10\mathrm{ps}$ with sub-100 nanoradian pointing stability. The system consists of four channel-cut silicon crystals, two of which have gradually varying gap sizes from intentional 5 deg asymmetric cuts. The delay adjustment is realized by linear motions of these two monolithic varying-gap channel cuts, where the x-ray beam experiences pairs of anti-parallel reflections, and thus becomes less sensitive in output beam pointing to motion imperfections of the translation stages. The beam splitting is accomplished by polished crystal edges. A high degree of mutual coherence between the two branches at the focus is observed by analyzing small-angle coherent x-ray scattering patterns. We envision a wide range of applications including single-shot x-ray pulse temporal diagnostics, studies of high-intensity x-ray–matter interactions, as well as measurement of dynamics in disordered material systems using split-pulse x-ray photon correlation spectroscopy.

The recent demonstration of the `nanosecond double-bunch' operation mode,i.e.two X-ray pulses separated in time between 0.35 and hundreds of nanoseconds and by increments of 0.35 ns, offers new opportunities to investigate ultrafast dynamics in diverse systems of interest. However, in order to reach its full potential, this mode of operation requires the precise characterization of the intensity of each X-ray pulse within each pulse pair for any time separation. Here, a transmissive single-shot diagnostic that achieves this goal for time separations larger than 0.7 ns with a precision better than 5% is presented. It also provides real-time monitoring feedback to help tune the accelerator parameters to deliver double pulse intensity distributions optimized for specific experimental goals.

X-ray speckle visibility spectroscopy using X-ray free-electron lasers has long been proposed as a probe of fast dynamics in noncrystalline materials. In this paper, numerical modeling is presented to show how the data interpretation of visibility spectroscopy can be impacted by the nonidealities of real-life X-ray detectors. Using simulated detector data, this work provides a detailed analysis of the systematic errors of several contrast extraction algorithms in the context of low-count-rate X-ray speckle visibility spectroscopy and their origins are discussed. Here, it was found that the finite detector charge cloud and pixel size lead to an unavoidable `degeneracy' in photon position determination, and that the contrasts extracted using different algorithms can all be corrected by a simple linear model. The results suggest that experimental calibration of the correction coefficient at the count rate of interest is possible and essential. This allows computationally lightweight algorithms to be implemented for on-the-fly analysis.

We report observations of nanosecond nonuniform colloidal dynamics in a free flowing liquid jet using ultrafast x-ray speckle visibility spectroscopy. Utilizing a nanosecond double-bunch mode, the Linac Coherent Light Source free electron laser produced pairs of femtosecond coherent hard x-ray pulses. By exploring anisotropy in the visibility of summed speckle patterns which relates to the correlation functions, we evaluate not only the average particle flow rate in a colloidal nanoparticle jet, but also the nonuniform flow field within. The methodology presented here establishes the foundation for the study of nano- and atomic-scale inhomogeneous fluctuations in complex matter using x-ray free electron laser sources.