Non-imaging metasurface design for collimated beam shaping

Metasurfaces provide a versatile platform for realizing ultrathin flat optics for use in a wide variety of optical applications. The design process involves defining or calculating the phase profile of the metasurface that will yield the desired optical output. Here, we present an inverse design method for determining the phase profile for shaping the intensity profile of a collimated incident beam. The model is based on the concept of optimal transport from non-imaging optics and enables a collimated beam with an arbitrary intensity profile to be redistributed to a desired output intensity profile. We derive the model from the generalized law of refraction and numerically solve the resulting differential equation using a finite-difference scheme. Through a variety of examples, we show that our approach accommodates a range of different input and output intensity profiles, and discuss its feasibility as a design platform for non-imaging optics

Phase Resolved Dark-Field X-ray Microscopy

This thesis presents dark-field x-ray microscopy (DFXM) as a tool for characterizing ferroelectric domain structures and investigates new approaches to the data analysis of DFXM images based on methods from computational, coherent microscopy. The underlying theory of DFXM is described and applied to study characteristic diffraction peak splitting due to coherent twinning in perovskite ferroelectrics. This constitutes the first quantitative comparison of DFXM measurements with theoretical predictions based on coherent twinning of ferroelectrics and thereby provides new evidence for the quantitativeness of DFXM.It is shown that using Fourier Ptychography (FP), the phase-profile of the x-ray beam in transmission- and Bragg-scattering experiments can be recovered. This is promising for the study of crystals containing inversion domain boundaries, that are visible to x-ray scattering in the phase of the scattered beam. Furthermore, images of the complex aperture-function of the objective lens can be acquired. The reconstructions do not succeed in improving the resolution of the images compared to the conventional data-analysis which is shown to be identical to a kind of differential phase contrast (DPC).Several experimental challenges are investigated both theoretically and experimentally. This includes thick-lens behavior of the applied CRL objective lenses, multiple x-ray scattering effects in the sample crystal, and partial coherence of the incident x-ray light. The role of these experimental sources of error are discussed both in relation to conventional DFXM as well as FP. Finally, a complete simulation of a DFXM experiment based on the propagation of coherent wave fronts and the Takagi-Taupin approach to dynamical scattering is presented. The simulation is compared to experiment and good agreement is found

Simulations of dislocation contrast in dark-field X-ray microscopy

Dark-field X-ray microscopy (DFXM) is a full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM, an objective lens is placed along the diffracted beam to generate a magnified projection image of the local diffracted volume. This work explores contrast methods and optimizes the DFXM setup specifically for the case of mapping dislocations. Forward projections of detector images are generated using two complementary simulation tools based on geometrical optics and wavefront propagation, respectively. Weak and strong beam contrast and the mapping of strain components are studied. The feasibility of observing dislocations in a wall is elucidated as a function of the distance between neighbouring dislocations and the spatial resolution. Dislocation studies should be feasible with energy band widths of 10-2, of relevance for fourth-generation synchrotron and X-ray free-electron laser sources