A time-dependent semiclassical formalism is developed for the theory of incoherentdiffractive imaging (IDI), an atomically-precise imaging technique based on the principles of intensity interferometry. The technique is applied to image inner-shell X-ray fluorescence from heavy atoms excited by the femtosecond pulses of an X-ray free-electron laser (XFEL). Interference between emission from different atoms is expected when the XFEL pulse duration is shorter than the fluorescence lifetime. Simulations for atoms at the vertices of a simple icosahedral virus capsid are used to generate mock IDI diffraction patterns. These are then used to reconstruct the geometry by phase retrieval of the intensity correlation function between photons emitted independently from many different atoms at two different detector pixels. The dependence of the intensity correlation function on fluorescence lifetime relative to XFEL pulse duration is computed, and a simple expression for the visibility (or contrast) of IDI speckle as well as an upper bound on the IDI signal-to-noise ratio are obtained as a function of XFEL flux and lifetime. This indicates that compact XFELs, with reduced flux but attosecond pulses, should be ideally suited to 3D, atomic-resolution mapping of heavy atoms in materials science, chemistry, and biology. As IDI is a new technique, not much has yet been written about it in the literature. The current theoretical and experimental results are reviewed, including a discussion of signal-to-noise issues that have been raised regarding the idea that IDI is suitable for structural biology.

X-ray free electron lasers (XFELs) provide several orders of magnitude brighter x-rays than 3rd generation sources. However, the electron beamlines and undulator magnets required are on the scale of kilometers, costing billions of dollars with only a half dozen or so currently operating worldwide. One way to overcome these limitations is to prebunch the electron beam on the scale of the x-ray wavelength. In this paper one such scheme is discussed, which uses a nanopatterned grating called a dynamical beam stop. This uses diffraction from crystal planes of the etched portion of a grating to impart a transverse modulation which becomes a temporal modulation via an emittance exchange (EEX). To expand upon this topic, dynamical electron diffraction intensities for a 200 nm thick Si(001) unpatterned membrane are simulated via the multislice method and compared to experiment for various crystallographic orientations at MeV energies. From this as well as an analysis of the experimental inelastic plasmon diffuse scattering, it is determined that the optimal transverse modulation would be formed from a bright field image of the beam stop, with the nanopattern being etched all the way through the membrane. A model quantifying the quality of the modulation - the bunching factor - as a function of contrast and duty factor is formulated and the optimal modulation is determined analytically. A prototype beam stop is then imaged in a transmission electron microscope (TEM) at 200 KeV, with the measured bunching factor of 0.5 agreeing with the model and approaching a saturated XFEL. Using the angular spectrum method, it is determined that the spatial coherence of the MeV energy electron beam is insufficient for significant self-imaging to occur for gratings with pitches of hundreds of nanometers. Finally, the first-order EEX input requirements for the electron beam are examined in the transverse dimension as are newly proposed longitudinal requirements to compensate for lingering correlations between the initial and final longitudinal phase spaces.