Tomographic reconstruction with a generative adversarial network

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

Evolution of Hierarchically Porous Nickel Alumina Catalysts Studied by X‐Ray Ptychography

The synthesis of hierarchically porous materials usually requires complex experimental procedures, often based around extensive trial and error approaches. One common synthesis strategy is the sol–gel method, although the relation between synthesis parameters, material structure and function has not been widely explored. Here, in situ 2D hard X‐ray ptychography (XRP) and 3D ptychographic X‐ray computed tomography (PXCT) are applied to monitor the development of hierarchical porosity in Ni/Al(2)O(3) and Al(2)O(3) catalysts with connected meso‐ and macropore networks. In situ XRP allows to follow textural changes of a dried gel Ni/Al(2)O(3) sample as a function of temperature during calcination, activation and CO(2) methanation reaction. Complementary PXCT studies on dried gel particles of Ni/Al(2)O(3) and Al(2)O(3) provide quantitative information on pore structure, size distribution, and shape with 3D spatial resolution approaching 50 nm, while identical particles are imaged ex situ before and after calcination. The X‐ray imaging results are correlated with N(2)‐sorption, Hg porosimetry and He pycnometry pore characterization. Hard X‐ray nanotomography is highlighted to derive fine structural details including tortuosity, branching nodes, and closed pores, which are relevant in understanding transport phenomena during chemical reactions. XRP and PXCT are enabling technologies to understand complex synthesis pathways of porous materials

X-ray in-line holography and holotomography at the NanoMAX beamline

Coherent X-ray imaging techniques, such as in-line holography, exploit the high brilliance provided by diffraction-limited storage rings to perform imaging sensitive to the electron density through contrast due to the phase shift, rather than conventional attenuation contrast. Thus, coherent X-ray imaging techniques enable high-sensitivity and low-dose imaging, especially for low-atomic-number (Z) chemical elements and materials with similar attenuation contrast. Here, the first implementation of in-line holography at the NanoMAX beamline is presented, which benefits from the exceptional focusing capabilities and the high brilliance provided by MAX IV, the first operational diffraction-limited storage ring up to approximately 300 eV. It is demonstrated that in-line holography at NanoMAX can provide 2D diffraction-limited images, where the achievable resolution is only limited by the 70 nm focal spot at 13 keV X-ray energy. Also, the 3D capabilities of this instrument are demonstrated by performing holotomography on a chalk sample at a mesoscale resolution of around 155 nm. It is foreseen that in-line holography will broaden the spectra of capabilities of MAX IV by providing fast 2D and 3D electron density images from mesoscale down to nanoscale resolution

PtyNAMi: ptychographic nano-analytical microscope

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

Structure and Composition of Isolated Core-Shell(In,Ga)N/GaNRods Based on Nanofocus X-Ray Diffraction and Scanning Transmission Electron Microscopy

Nanofocus x-ray diffraction is used to investigate the structure and local strain field of an isolated ðIn; GaÞN=GaN core-shell microrod. Because the high spatial resolution of the x-ray beam is only 80 × 90 nm2, we are able to investigate several distinct volumes on one individual side facet. Here, we find a drastic increase in thickness of the outer GaN shell along the rod height. Additionally, we performed highangle annular dark-field scanning-transmission-electron-microscopy measurements on several rods from the same sample showing that (In,Ga)N double-quantum-well and GaN barrier thicknesses also increase strongly along the height. Moreover, plastic relaxation is observed in the top part of the rod. Based on the experimentally obtained structural parameters, we simulate the strain-induced deformation using the finiteelement method, which serves as the input for subsequent kinematic scattering simulations. The simulations reveal a significant increase of elastic in-plane relaxation along the rod height. However, at a certain height, the occurrence of plastic relaxation yields a decrease of the elastic strain. Because of the experimentally obtained structural input for the finite-element simulations, we can exclude unknown structural influences on the strain distribution, and we are able to translate the elastic relaxation into an indium concentration which increases by a factor of 4 from the bottom to the height where plastic relaxation occurs

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

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

Complete alignment of a KB-mirror system guided by ptychography

We demonstrate how the individual mirrors of a high-quality Kirkpatrick-Baez (KB) mirror system can be aligned to each other to create an optimally focused beam, through minimizing aberrations in the phase of the ptychographically reconstructed pupil function. Different sources of misalignment and the distinctive phase artifacts they create are presented via experimental results from the alignment of the KB mirrors at the NanoMAX diffraction endstation. The catalog of aberration artifacts can be used to easily identify which parameter requires further tuning in the alignment of any KB mirror system