Speckle-based x-ray phase contrast imaging at free-electron lasers*

X-ray free electron laser (XFEL)-based x-ray phase contrast imaging (XPCI) harnesses the highly-coherent, brilliant x-rays to probe into dynamic processes with femtosecond and submicron resolution. Optical elements, such as compound refractive lenses, are critically important for optimizing the imaging conditions specific to the experiment; however, introduced artefacts in the image cannot easily be eliminated with a simple flat field correction due to the stochastic nature and sample-induced distortion of the x-ray pulse. This makes both interpreting the image and retrieving the phase to extract quantitative information challenging. To address these challenges, we treated the image artefacts as a reference pattern and implemented a speckle-based approach to retrieve the phase. We demonstrate our approach on in-situ XPCI images of laser shock-induced void collapse in a polymer recorded at the Matter in Extreme Conditions (MEC) Instrument at the Linac Coherent Light Source (LCLS). We calculate the areal density from the recovered object phase, which informs our understanding and development of constitutive models of materials at extreme conditions.