Parallax in angular sensitive powder diffraction tomography

While a few methods for the determination of depth-resolved strain distributions each with inherent limitations are available, tomographic reconstruction has been applied to this problem in only a limited sense. One of the challenges was the potential impact of geometric parallax, which constitutes a non-negligible lateral offset of diffraction information arising from different sample depths at the detector. Here, the effect of parallax was investigated and two main results have emerged. First, the impact of parallax was found to be additive to other offset contributions, which implies a straightforward correction. Second, for tomographic scans utilizing a full 360{\deg} rotation parallax has been found to have no impact on reconstructions of angular information.

Ptychographic reconstruction with wavefront initialization

X-ray ptychography is a cutting edge imaging technique providing ultra-high spatial resolutions. In ptychography, phase retrieval, i.e., the recovery of a complex valued signal from intensity-only measurements, is enabled by exploiting a redundancy of information contained in diffraction patterns measured with overlapping illuminations. For samples that are considerably larger than the probe we show that during the iteration the bulk information has to propagate from the sample edges to the center. This constitutes an inherent limitation of reconstruction speed for algorithms that use a flat initialization. Here, we experimentally demonstrate that a considerable improvement of computational speed can be achieved by utilizing a low resolution sample wavefront retrieved from measured diffraction patterns as initialization. In addition, we show that this approach avoids phase singularity artifacts due to strong phase gradients. Wavefront initialization is computationally fast and compatible with non-bulky samples. Therefore, the presented approach is readily adaptable with established ptychographic reconstruction algorithms implying a wide spread use.

Accelerated iterative tomographic reconstruction with x-ray edge illumination

Compared to standard tomographic reconstruction, iterative approaches offer the possibility to account for extraneous experimental influences, which allows for a suppression of related artifacts. However, the inclusion of corresponding parameters in the iterative forward model typically leads to longer computation times. Here, we demonstrate experimentally for phase sensitive X-ray imaging based on the edge illumination principle that inadequately sampled illumination curves result in ring artifacts in tomographic reconstructions. We take advantage of appropriately sampled illumination curves instead, which enables us to eliminate the corresponding parameter from the forward model and substantially increase computational speed. In addition, we demonstrate a 30\% improvement in spatial resolution of the iterative approach compared with the standard non-iterative single shot approach. Further, we report on several significant improvements in our numerical implementation of the iterative approach, which we make available online with this publication. Finally, we show that the combination of both experimental and algorithmic advancement lead to a total speed increase by one order of magnitude and an improved contrast to noise ratio in the reconstructions.