Real-space recovery and super-resolution of ultrafast scattering and diffraction using natural scattering kernels

Directly resolving in real-space multiple atomic motions using ultrafast x-ray scattering or ultrafast electron diffraction is generally limited by the finite detector range. As a result, signal interpretation mostly relies on modeling and simulations of specific excitation pathways. Here, we demonstrate a model-free approach to resolve ultrafast diffuse scattering signals in real space and recover multiple atomic motions that take place simultaneously. We introduce a scattering basis representation that is composed of the measurement parameters and constraints and the subsequent inversion analysis. We then leverage signal priors, such as smoothness and sparsity to deconvolve and super-resolve the spatially transformed signals using convex optimization. We validate the approach on simulated data with detection limits similar to X-ray free-electron laser experiments and discuss the resolution limits and noise dependence on the accuracy of the recovery. This approach may bridge the widely used pair-distribution function analysis that requires much higher momentum transfer ranges with ultrafast X-ray scattering and electron diffraction experiments that are done in advanced light sources such as the LCLS.