Abstract
Incoherent diffractive imaging (IDI) promises structural analysis with atomic resolution based on intensity interferometry of pulsed X-ray fluorescence emission. However, its experimental realization is still pending and a comprehensive theory of contrast formation has not been established to date. Explicit expressions are derived for the equal-pulse two-point intensity correlations, as the principal measured quantity of IDI, with full control of the prefactors, based on a simple model of stochastic fluorescence emission. The model considers the photon detection statistics, the finite temporal coherence of the individual emissions, as well as the geometry of the scattering volume. The implications are interpreted in view of the most relevant quantities, including the fluorescence lifetime, the excitation pulse, as well as the extent of the scattering volume and pixel size. Importantly, the spatiotemporal overlap between any two emissions in the sample can be identified as a crucial factor limiting the contrast and its dependency on the sample size can be derived. The paper gives rigorous estimates for the optimum sample size, the maximum photon yield and the expected signal-to-noise ratio under optimal conditions. Based on these estimates, the feasibility of IDI experiments for plausible experimental parameters is discussed. It is shown in particular that the mean number of photons per detector pixel which can be achieved with X-ray fluorescence is severely limited and as a consequence imposes restrictive constraints on possible applications.
Highlights
X-ray diffraction capitalizes on the fact that microscopic signals of scattered waves add up coherently and form a macroscopic interference pattern which can be captured by X-ray detectors in the far-field
We develop a time-dependent probabilistic model for incoherent emissions following a short excitation pulse that accounts for the geometry of scatterers and detector
The model we describe, neither depends on the nature of the excitation pulse nor on the particular type of transitions, and should be applicable to other spectral ranges, in particular the optical regime, and even other kinds of incoherent emissions
Summary
X-ray diffraction capitalizes on the fact that microscopic signals of scattered waves add up coherently and form a macroscopic interference pattern which can be captured by X-ray detectors in the far-field. In the work of Classen et al (2017), a simple time-independent quantummechanical model was used to show that the two-point correlations of the fluorescence intensity are proportional to the very same structure factor SðqÞ which emerges in coherent scattering plus a constant offset. They proposed a method to extract spatial information from incoherent diffraction patterns, which they termed incoherent diffractive imaging (IDI) in analogy to coherent diffractive imaging (CDI) (Miao et al, 1999, 2015; Chapman et al, 2006). The main symbols used throughout the article are listed in Appendix C for reference
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