Prospects for Incoherent Diffractive Imaging at Compact X-ray Free-electron Lasers

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.