Unified Approach to Time-resolved X-ray and Electron Diffraction Imaging 

Time-resolved X-ray diffraction (TR-XRD) and ultrafast electron diffraction (TR-UED) are leading tools for imaging structural and electronic dynamics, yet they are commonly modeled with parallel often incompatible approximations. We present a unified, quantum-field-based description of ultrafast diffraction imaging that places TR-XRD and TR-UED within a single measurement framework. Starting from a density-matrix formulation for "matter + probe," we derive an expression for the detected diffraction signal in terms of a common scattering observable that naturally incorporates finite pulse duration, probe bandwidth, and detector energy acceptance (gating). This approach makes the correspondence between X-ray and electron diffraction explicit and identifies where they differ: for electrons, additional contributions arise from charge current coupling (and, in the high-energy regime, relativistic current terms) that can become non-negligible for sub-femtosecond probes and 200 keV~MeV beams. We outline practical criteria for when standard quasi-static or purely charge-density models suffice and when current-density effects must be retained. The formalism is designed to be directly computable from electronic-structure inputs; we illustrate the workflow on prototypical condensed-matter targets (e.g., graphene), enabling consistent cross-modality simulations and experiment design for ultrafast imaging of coupled electronic and nuclear motion.