3D nano-tomography using coherent X-rays

X-rays allow to non-destructively investigate biological, chemical or physical processes at the nano-scale. Their high penetration depth in matter allows to investigate samples even inside sample environments, which would be difficult with complementary methods such as transmission electron microscopy (TEM). The microscopy technique ptychography has been established in X-ray imaging in recent years. Utilizing the short wavelengths of X-rays, resolutions of about 10 nm and below have been achieved in the reconstructed projection images.
However, projections provide no information about the spatial distribution of features along the beam axis. Knowing the structure of materials and objects in three spatial dimensions is key to understanding their properties and function. Hence, two-dimensional ptychography has been extended to three spatial dimensions based on tomographic methods known from radiographs and computed tomography (CT) resulting in a method called ptychographic X-ray computed tomography (PXCT). Using PXCT quantitative three-dimensional maps of the complex index of refraction of the sample can be reconstructed, which yield quantitative information on the local electron density. Such PXCT measurements are very time intensive to perform, very computing 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 starting point, a coupled ptychographic tomography (CPT) algorithm, improving on the PXCT algorithm in terms of alignment and sampling requirements, is presented and tested on experimental data. Moreover, a resonant PXCT experiment is performed at the Ga-K absorption edge, allowing for additional elemental and chemical information inside the reconstructed volume. Afterwards, the shared limit of both the PXCT algorithm and the CPT algorithm, the thin-sample approximation, is addressed by presenting a multi-slice approach utilizing the propagation of the 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, are presented in this work.