Frequency-, Time-, and Wavevector-Resolved Ultrafast Incoherent Diffraction of Noisy X-ray Pulses

We study theoretically incoherent time-resolved X-ray diffraction of fluctuating sources such as free electron lasers, as well as coherent sources with controllably added randomness. We find that the temporal resolution is strongly eroded by the noise. By considering frequency resolution of the signal, we find that the statistical properties of the noise carry important information allowing us to restore the temporal resolution. We propose a multidimensional stochastic resonance treatment to shape the optical window and extract this information from signals. Using the frequency-dependent stochastic phase as a frequency marker allows to improve the spectral resolution as well via intensity correlations. Frequency-tuned field correlation functions are used to modify the effective frequency gating and extract specific charge density contributions to the diffraction pattern while maintaining temporal resolution.