X-ray Scattering Techniques for Coherent Imaging in Reflection Geometry, Measurement of Mutual Intensity, and Symmetry Determination in Disordered Materials

The advent of highly-coherent x-ray light sources, such as those now available world-wide in modern third-generation synchrotrons and increasingly available in free-electron lasers, is driving the need for improved analytical and experimental techniques which exploit the coherency of the generated light. As the light illuminating a sample approaches full coherence, a simple Fourier transform describes the diffraction pattern generated by the scattered light in the far field; because the Fourier transform of an object is unique, coherent scattering can directly probe local structure in the scattering object instead of bulk properties. In this dissertation, we exploit the coherence of Advanced Light Source beamline 12.0.2 to build three types of novel coherent scattering microscopes. First, we extend the techniques of coherent diffractive imaging and Fourier transform holography, which uses iterative computational methods to invert oversampled coherent speckle patterns, into reflection geometry. This proof-of-principle experiment demonstrates a method by which reflection Bragg peaks, such as those from the orbitally-ordered phase of complex metal oxides, might eventually be imaged. Second, we apply a similar imaging method to the x-ray beam itself to directly image the mutual coherence function with only a single diffraction pattern. This technique supersedes the double-slit experiments commonly seen in the scattering literature to measure the mutual intensity function by using a set of apertures which effectively contains all possible double slit geometries. Third, we show how to evaluate the speckle patterns taken from a labyrinthine domain pattern for "hidden" rotational symmetries. For this measurement, we modify the iterative algorithms used to invert speckle patterns to generate a large number of domain configurations with the same incoherent scattering profile as the candidate pattern and then use these simulations as the basis for a statistical inference of the degree of ordering in the domain configuration. We propose extending this measurement to position-resolved speckle patterns, creating a symmetry-sensitive microscope. The three new techniques described herein may be employed at current and future light sources