Viewing time-resolved X-ray scattering data in a maximally sparse basis

Time-resolved X-ray scattering (TRXS) data on photoexcited molecules contains rich spatial and temporal information that can yield unique insights into ultrafast chemical dynamics. Recent advances in data analysis methodology have shown promise in reducing molecular motion to sparse data features, such as frequency-resolved X-ray scattering (FRXS) for temporal sparsity and natural scattering kernels (NSK) for spatial sparsity. However, these techniques fail to achieve sparsity along both axes simultaneously, posing a challenge for directly extracting molecular structure and dynamics.



Our remedy to this problem is to utilize a Hough transform applied to FRXS data to achieve simultaneous sparsity for two important classes of molecular motion: vibration and dissociation. Vibrations and dissociations have one-dimensional sparsity in FRXS data, appearing as linear features in (Q,ω) space. The Hough transform reduces these features to points in (slope, y-intercept) space. Molecular motion can then be extracted via simple one-dimensional lineouts of the Hough transform, yielding information such as vibrational frequency, dissociation velocity distribution, and fragment rovibrational states. Experimental results are presented to showcase the Hough transform technique.