3D nano-tomography using coherent X-rays

X-rays allow to non-destructively investigate biological, chemical or physical processes at thenano-scale. Their high penetration depth in matter allows to investigate samples even in-side sample environments, which would be difficult with complementary methods such astransmission electron microscopy (TEM). The microscopy technique ptychography has beenestablished in X-ray imaging in recent years. Utilizing the short wavelengths of X-rays, resolu-tions of about10 nmand below have been achieved in the reconstructed projection images.
However, projections provide no information about the spatial distribution of features alongthe beam axis. Knowing the structure of materials and objects in three spatial dimensions is keyto understanding their properties and function. Hence, two-dimensional ptychography has beenextended to three spatial dimensions based on tomographic methods known from radiographsand computed tomography (CT) resulting in a method called ptychographic X-ray computedtomography (PXCT). Using PXCT quantitative three-dimensional maps of the complex indexof refraction of the sample can be reconstructed, which yield quantitative information on thelocal electron density. Such PXCT measurements are very time intensive to perform, verycomputing intensive to reconstruct and are based on several limiting approximations.
In this work, a detailed description of PXCT and its limitations is given. From that startingpoint, a coupled ptychographic tomography (CPT) algorithm, improving on the PXCT algo-rithm in terms of alignment and sampling requirements, is presented and tested on experimentaldata. Moreover, a resonant PXCT experiment is performed at the Ga-Kabsorption edge, al-lowing for additional elemental and chemical information inside the reconstructed volume. Af-terwards, the shared limit of both the PXCT algorithm and the CPT algorithm, the thin-sampleapproximation, is addressed by presenting a multi-slice approach utilizing the propagation ofthe X-ray beam in the sample. In total three different experiments, performed at the hard X-ray nanoprobe endstation at beamline P06 at the PETRA III synchrotron radiation source, arepresented in this work.