ABSTRACT
X-ray waveguides are routinely used at synchrotron light sources in imaging setups and as a platform for experiments with quantum emitters, providing nanometer-sized confinement - even x-ray optics on a chip has been showcased. X-ray waveguides are weakly guiding and experience significant material absorption, such that the established waveguide theory is not immediately applicable. Here, a general self-contained nano-optical theory of planar waveguides is derived, which is appropriate for hard x-ray energies. Solutions of the electromagnetic fields and its Green's functions are derived in detail. Asymptotic expansions into resonant and non-resonant modes are derived, which are particularly useful in the presence of strong material absorption. A method to reliably find the resonant modes of x-ray waveguide structures is presented. Based on the general theory, certain common experimental geometries, namely evanescent coupling in grazing-incidence, front-coupling in forward-incidence and radiation from buried emitters, are discussed in more detail. Complementing the analytic discussion, numerical tools are provided and applied to quantitatively extract the main figures of merit. The theory provides an analytic foundation for the interpretation of past and future experiments and, combined with the numerical tools, will facilitate the computer-aided design of x-ray waveguides.
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.
ABSTRACT
Propagation-based phase-contrast X-ray imaging is by now a well established imaging technique, which - as a full-field technique - is particularly useful for tomography applications. Since it can be implemented with synchrotron radiation and at laboratory micro-focus sources, it covers a wide range of applications. A limiting factor in its development has been the phase-retrieval step, which was often performed using methods with a limited regime of applicability, typically based on linearization. In this work, a much larger set of algorithms, which covers a wide range of cases (experimental parameters, objects and constraints), is compiled into a single toolbox - the HoloTomoToolbox - which is made publicly available. Importantly, the unified structure of the implemented phase-retrieval functions facilitates their use and performance test on different experimental data.
