# From Femtoseconds to Hours--Measuring Dynamics over 18 Orders of Magnitude with Coherent X-rays
## 1 Introduction  
With the advent of third generation synchrotron radiation sources in the early 1990s, the application of coherent X-ray beams has become possible for the first time. This is demonstrated in Figure 1a showing Airy fringes from Fraunhofer diffraction measured at the coherence beamline ID10 of ESRF [1, 2]. Thanks to the marked increase of brilliance the coherent flux has risen many orders of magnitude compared to previous sources, paving the way for new coherence-based techniques [3], such as coherent diffractive imaging (CDI) [4, 5], X-ray ptychography [6] and X-ray photon correlation spectroscopy (XPCS). The rise of hard X-ray free-electron lasers (FEL) and the step to the next-generation storage rings based on the multibend achromat lattice [7, 8] will significantly expand the applications of these techniques [9]. XPCS benefits in a larger degree than any other technique from the increasing brilliance. Beyond the new facilities, many upgrades in beamline and detector technology have improved the spatial and temporal resolution of these techniques. For instance, XPCS particularly profits from the development of two-dimensional detectors, allowing for real-time experiments up to sub-ms time resolution. In this article, we review the major achievements using XPCS during the last decade. XPCS probes the dynamic properties of matter by analyzing temporal correlations in real time [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]. It is the X-ray analogue to dynamical light scattering (DLS) [20], extending the probed length scale to atomic dimensions. Similar to DLS, it relies on the coherent properties of the beam. When a coherent X-ray beam is scattered by a sample, a grainy diffraction pattern, the so-called speckle pattern, is generated. If the sample changes its structure over time, so does the speckle pattern, which is tracked by XPCS. After the first measurements of X-ray speckles [22] XPCS has been demonstrated in 1994 [1,21], see Figure 1b. In the following, dedicated beamlines for XPCS have been established at the European Synchrotron Radiation Facility (ESRF) in France [23,24] and at the Advanced Photon Source (APS) at Argonne National Laboratory (USA) [25]. A second generation of XPCS beamlines was built at PETRA III and NSLS II during the last decade, that provided an increase of coherent flux and more flexibility on scattering geometries. Finally, XPCS is also a driving force for FEL science, such as at the X-ray Correlation Spectroscopy (XCS) instrument at LCLS [26] or the Materials Imaging and Dynamics (MID) instrument at the European XFEL [27]. The development of XPCS is highlighted in Figure 2 showing the number of XPCS publications per year as well as the associated subject areas. Therefore, a search on SCOUPS and Web of Science has been performed on \"X-ray Photon Correlation Spectroscopy\", its alternative name \"X-ray Intensity Fluctuation Spectroscopy\" (XIFS), and the related technique \"X-ray Speckle Visibility Spectroscopy\" (XSVS). Their appearance has been limited to titles, keywords, and abstract, so that the actual number of XPCS and XSVS publications is likely slightly larger. Since the late 1990s, the number of XPCS publications grew linearly, resulting to more than 40 publications in 2020. In addition, the starting dates of new beamlines and the ID10 (ESRF) upgrade are marked as well. While focussing first on slow dynamics on length scales of several 10 nm (i.e., using a small-angle scattering geometry) [28], the application of XPCS has extended recently on both time and length scales. Three main directions can be identified, that experienced a strong boost in the last 10 years: (1) extension of XPCS to milli- and microseconds thanks to new type of detectors and increased brilliance, (2) studies of molecular and atomic length scales, and (3) XPCS and XSVS studies at FEL sources.