Finite difference methods for stationary and time-dependent X-ray propagation

Off-axis multilayer zone plate with 16 nm × 28 nm focus for high-resolution X-ray beam induced current imaging

Using multilayer zone plates (MZPs) as two-dimensional optics, focal spot sizes of less than 10 nm can be achieved, as we show here with a focus of 8.4 nm × 9.6 nm, but the need for order-sorting apertures prohibits practical working distances. To overcome this issue, here an off-axis illumination of a circular MZP is introduced to trade off between working distance and focal spot size. By this, the working distance between order-sorting aperture and sample can be more than doubled. Exploiting a 2D focus of 16 nm × 28 nm, real-space 2D mapping of local electric fields and charge carrier recombination using X-ray beam induced current in a single InP nanowire is demonstrated. Simulations show that a dedicated off-axis MZP can reach sub-10 nm focusing combined with reasonable working distances and low background, which could be used for in operando imaging of composition, carrier collection and strain in nanostructured devices.

Observation of electron-induced characteristic x-ray and bremsstrahlung radiation from a waveguide cavity

We demonstrate x-ray generation based on direct emission of spontaneous x-rays into waveguide modes. Photons are generated by electron impact onto a structured anode target, which is formed as an x-ray waveguide or waveguide array. Both emission of characteristic radiation and bremsstrahlung are affected by the changes in mode density induced by the waveguide structure. We investigate how the excited modal pattern depends on the positions of the metal atoms and the distance of the focused electron beam with respect to the waveguide exit side. We compare the results to synchrotron-excited fluorescence. We then discuss how x-ray generation in waveguides can be used to increase the brilliance and directional emission of tabletop x-ray sources, with a corresponding increase in the spatial coherence. On the basis of the Purcell effect, we lastly show that the gain of emission into waveguide modes is governed by the quality factor of the waveguide.

Comparison of distributed memory algorithms for X-ray wave propagation in inhomogeneous media

Calculations of X-ray wave propagation in large objects are needed for modeling diffractive X-ray optics and for optimization-based approaches to image reconstruction for objects that extend beyond the depth of focus. We describe three methods for calculating wave propagation with large arrays on parallel computing systems with distributed memory: (1) a full-array Fresnel multislice approach, (2) a tiling-based short-distance Fresnel multislice approach, and (3) a finite difference approach. We find that the first approach suffers from internode communication delays when the transverse array size becomes large, while the second and third approaches have similar scaling to large array size problems (with the second approach offering about three times the compute speed).

Three dimensions, two microscopes, one code: Automatic differentiation for x-ray nanotomography beyond the depth of focus limit

Conventional tomographic reconstruction algorithms assume that one has obtained pure projection images, involving no within-specimen diffraction effects nor multiple scattering. Advances in x-ray nanotomography are leading toward the violation of these assumptions, by combining the high penetration power of x-rays, which enables thick specimens to be imaged, with improved spatial resolution that decreases the depth of focus of the imaging system. We describe a reconstruction method where multiple scattering and diffraction effects in thick samples are modeled by multislice propagation and the 3D object function is retrieved through iterative optimization. We show that the same proposed method works for both full-field microscopy and for coherent scanning techniques like ptychography. Our implementation uses the optimization toolbox and the automatic differentiation capability of the open-source deep learning package TensorFlow, demonstrating a straightforward way to solve optimization problems in computational imaging with flexibility and portability.