This paper presents a deep learning algorithm for tomographic reconstruction (GANrec). The algorithm uses a generative adversarial network (GAN) to solve the inverse of the Radon transform directly. It works for independent sinograms without additional training steps. The GAN has been developed to fit the input sinogram with the model sinogram generated from the predicted reconstruction. Good quality reconstructions can be obtained during the minimization of the fitting errors. The reconstruction is a self‐training procedure based on the physics model, instead of on training data. The algorithm showed significant improvements in the reconstruction accuracy, especially for missing‐wedge tomography acquired at less than 180° rotational range. It was also validated by reconstructing a missing‐wedge X‐ray ptychographic tomography (PXCT) data set of a macroporous zeolite particle, for which only 51 projections over 70° could be collected. The GANrec recovered the 3D pore structure with reasonable quality for further analysis. This reconstruction concept can work universally for most of the ill‐posed inverse problems if the forward model is well defined, such as phase retrieval of in‐line phase‐contrast imaging.

Three-dimensional (3D) x-ray microscopy by ptychographic tomography requires elaborate numerical reconstructions. We describe a coupled ptychography-tomography reconstruction algorithm and apply it to an experimental ptychographic x-ray computed tomography data set of a catalyst particle. Compared to the traditional sequential algorithm, in which ptychographic projections are reconstructed to serve as input for subsequent tomographic reconstruction, the coupled ptychography-tomography algorithm reconstructs the 3D volume with higher spatial resolution over a larger field of view. Coupling the data from different projections improves the overall reconstruction, and the ptychographic sampling in individual projections can be coarsened beyond the point of overlap between neighboring scan points, still leading to stable reconstructions.

Ptychographic X-ray imaging at the highest spatial resolution requires an optimal experimental environment, providing a high coherent flux, excellent mechanical stability and a low background in the measured data. This requires, for example, a stable performance of all optical components along the entire beam path, high temperature stability, a robust sample and optics tracking system, and a scatter-free environment. This contribution summarizes the efforts along these lines to transform the nanoprobe station on beamline P06 (PETRA III) into the ptychographic nano-analytical microscope (PtyNAMi).

Ptychographic X-ray microscopy is an ideal tool to observe chemical processes under in situ conditions. Chemical reactors, however, are often thicker than the depth of field, limiting the lateral spatial resolution in projection images. To overcome this limit and reach higher lateral spatial resolution, wave propagation within the sample environment has to be taken into account. Here, we demonstrate this effect recording a ptychographic projection of copper(I) oxide nanocubes grown on two sides of a polyimide foil. Reconstructing the nanocubes using the conventional ptychographic model shows the limitation in the achieved resolution due to the thickness of the foil. Whereas, utilizing a multi-slice approach unambiguously separates two sharper reconstructions of nanocubes on both sides of the foil. Moreover, we illustrate how ptychographic multi-slice reconstructions are crucial for high-quality imaging of chemical processes by ex situ studying copper(I) oxide nanocubes grown on the walls of a liquid cell.

Inhomogeneities and defects often limit the overall performance of thin-film solar cells. Therefore, sophisticated microscopy approaches are sought to characterize performance and defects at the nanoscale. Here, we demonstrate, for the first time, the simultaneous assessment of composition, structure, and performance in four-fold multi-modality. Using scanning X-ray microscopy of a Cu(In,Ga)Se2 (CIGS) solar cell, we measured the elemental distribution of the key absorber elements, the electrical and optical response, and the phase shift of the coherent X-rays with nanoscale resolution. We found structural features in the absorber layer—interpreted as voids—that correlate with poor electrical performance and point towards defects that limit the overall solar cell efficiency.

The interaction of an object with a coherent probe often encodes its properties in a complex-valued function, which is then detected in an intensity-only measurement. Phase retrieval methods commonly infer this complex-valued function from the intensity. However, the decoding of the object from the complex-valued function often involves some ambiguity in the phase, e.g., when the phase shift in the object exceeds 2 π . Here, we present a phase retrieval framework to directly recover the amplitude and phase of the object. This refractive framework is straightforward to integrate into existing algorithms. As examples, we introduce refractive algorithms for ptychography and near-field holography and demonstrate this method using measured data.

Modern subtractive and additive manufacturing techniques present new avenues for X-ray optics with complex shapes and patterns. Refractive phase plates acting as glasses for X-ray optics have been fabricated, and spherical aberration in refractive X-ray lenses made from beryllium has been successfully corrected. A diamond phase plate made by femtosecond laser ablation was found to improve the Strehl ratio of a lens stack with a numerical aperture (NA) of 0.88 × 10−3 at 8.2 keV from 0.1 to 0.7. A polymer phase plate made by additive printing achieved an increase in the Strehl ratio of a lens stack at 35 keV with NA of 0.18 × 10−3 from 0.15 to 0.89, demonstrating diffraction-limited nanofocusing at high X-ray energies.

List of author contributions 22 HK had the idea of doing µXANES on plant samples in tomographic mode and 23 supervised the study. Ana Mijovilovich made the Geopixe fits, the XANES analysis, and 24 wrote the first draft of the manuscript, which was revised by all other authors. Ana 25 Mijovilovich, DB, GF, KS, JG and HK did the measurements at the synchrotron. Archana 26 Mishra did the metal treatments of the plants. Ana Mijovilovich, Archana Mishra and 27 HK prepared the plant samples for the µXANES measurements. EA prepared most of 28 the model compounds, the others were done by Ana Mijovilovich and HK. DB did the 29 tomographic reconstructions. 2