X-ray imaging with high numerical aperture X-ray optics

The advent of highly brilliant synchrotron X-ray sources and the development of X-ray optics offer new capabilities to examine materials with high photon energy X-rays that can offer nano-scale resolution. This thesis aims to explore new ways to study nano-structured samples by employing state-of-the-art high numerical aperture multilayer Laue lenses (MLLs) fabricated in our group. The work in this thesis presents two novel X-ray imaging techniques: robust ptychographic X-ray speckle tracking (R-PXST) and convergent beam crystallography (CBC). The former technique provides access to highly magnified images of samples free of aberrations and is capable of reconstructing the wavefront of the beam formed by the lens. This technique plays an important role for our group since it enables robust and precise lens characterisation with low-coherence and low-brilliance laboratory X-ray sources. The latter is a novel type of protein structure determination technique that investigates the diffraction pattern formed by an incident divergent beam scattering from a protein crystal. This technique allows one to reconstruct the atomic structure of a crystalline sample as well as its spatial projection map from the convergent beam patterns.The goal of this thesis was to establish a theoretical and data processing framework for the above techniques. As a practical realisation of these techniques, two data analysis software suites, pyrost and cbclib, were devised to provide a full-fledged solution to process datasets from R-PXST and CBC experiments, respectively. During this PhD thesis, several experiments were performed at PETRA III synchrotron radiation facility and European X-ray free electron laser facility. In these experiments, the capabilities of R-PXST, CBC, and other X-ray imaging techniques have been explored and a number of biological and artificial specimens, such as Lysozyme protein and nano-structured Au, have been studied.The ptychographic X-ray speckle tracking (PXST) technique devised previously in our group plays an indispensable role in measuring the wavefront of the X-ray beam produced by a lens. The measured wavefront aberrations are used to give feedback on the lens manufacturing procedure. Since the PXST method enabled our group to fabricate MLLs with very low aberrations, it started to show its limitations in the ability to robustly reconstruct the wavefront. In the new version of PXST designed by the author of this thesis, we employed machine learning techniques to improve the phase sensitivity and robustness to noise of the speckle tracking technique. We tested the performance of R-PXST and compared it to PXST by recovering known wavefronts in simulated datasets. R-PXST obtained accurate estimates over a wider range of parameters of experimental geometry and with lower photon counts. The wider domain of applicability allows us to further maximise the phase sensitivity of the technique. Due to better error handling ivivpyrost yields an accurate wavefront for the datasets with a high level of noise whereas PXST underestimated the wavefront aberration and failed to recover fine features of the sample.In contrast to other diffraction microscopy techniques and conventional X-ray crystallography, convergent beam diffraction (CBD) allows simultaneous determination of the atomic structure and the microscopic projection profiles of the crystal. Moreover, in a CBD scheme a greater number of more complete Bragg reflections are measured on the detector compared to partial reflections measured in conventional crystallography. On the other hand, since the CBD scheme is fundamentally different from the diffraction of a collimated X-ray beam the analysis of a CBD pattern presents unique and novel challenges addressed in this thesis. We employed the forward modelling of the CBC pattern and parametric regression of the experimental geometry to accurately reconstruct the incident and outcoming wave-vectors and reciprocal lattice points that satisfy the Bragg condition for each Bragg reflection pertaining to the measured pattern. Moreover, a new iterative method based on Poisson regression was put forward to simultaneously reconstruct the projection maps and structure factors of the crystalline sample from the intensity measurements of the diffraction pattern. The devised technique was successfully employed to reconstruct the atomic structure and projection maps from the simulated dataset of a Lysozyme protein crystal. Additionally, the cbclib software was used to process the tilt-series of CBC patterns from a Lysozyme protein crystal measured at the P06 beamline in PETRA III. The reconstructed projection maps were consistent with the known shape of the sample, although the reconstructed structure factors only loosely correlate with the Lysozyme structure obtained from the protein database due to the high level of radiation damage observed during the experiment