Real-Space Inversion and Super-Resolution of Ultrafast Scattering using Natural Scattering Kernels

Abstract

Directly resolving in real-space multiple atomic motions using ultrafast x-ray or electron scattering 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 introduce an approach to resolve ultrafast diffuse scattering signals in real space below the diffraction limit, and recover multiple atomic motions de-novo, using a scattering basis representation that is composed of the measurement parameters and constraints, and the subsequent inversion analysis. We leverage signal priors, such as smoothness and sparsity to deconvolve the spatially transformed signals using convex optimization. We validate the approach on simulated and experimental data, demonstrate super-resolution in real space, and discuss the recovery accuracy and resolution limits vs signal fidelity.Comment: 6 pages, 4 figure