<p> 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.</p><p> 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.</p><p> 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.</p>

<p> Optical microscopy is one of the oldest and most important imaging techniques; however, its far-field resolution is diffraction-limited. In this dissertation, we proposed and developed a novel method of optical microscopy with super-resolution by using high-index dielectric microspheres immersed in liquid and placed on the surface of the structures under study. We used barium titanate glass microspheres with diameters of D~2-220 &mu;m and refractive indices <i> n</i>&sim;1.9-2.1 to discern minimal feature sizes &sim;&lambda;/4 (down to &sim;&lambda;/7) of various photonic and plasmonic nanostructures, where &lambda; is the illumination wavelength. We studied the magnification, field of view, and resolving power, in detail, as a function of sphere sizes.</p><p> We studied optical coupling, transport, focusing, and polarization properties of linear arrays of dielectric spheres. We showed that in arrays of spheres with refractive index n=<rad><rcd>3</rcd></rad>, a special type of rays with transverse magnetic (TM) polarization incident on the spheres under the Brewster&#129;'s angle form periodically focused modes with radial polarization and <i> 2D</i> period, where <i> D</i> is the diameter of the spheres. We showed that the formation of periodically focused modes in arrays of dielectric spheres gives a physical explanation for beam focusing and extraordinarily small attenuation of light in such chains. We showed that the light propagation in such arrays is strongly polarization-dependent, indicating that such arrays can be used as filters of beams with radial polarization. The effect of forming progressively smaller focused beams was experimentally observed in chains of sapphire spheres in agreement with the theory.</p><p> We studied optical coupling,transport, focusing, and polarization properties of linear arrays of dielectric spheres. We showed that in arrays of spheres with refractive index n=&#129;&atilde;3, a special type of rays with transverse magnetic (TM) polarization incident on the spheres under the Brewster&#129;'s angle form periodically focused modes with radial polarization and 2D period, where D is the diameter of the spheres. We showed that the formation of periodically focused modes in arrays of dielectric spheres gives a physical explanation for beam focusing and extraordinarily small attenuation of light in such chains. We showed that the light propagation in such arrays is strongly polarization-dependent, indicating that such arrays can be used as filters of beams with radial polarization. The effect of forming progressively smaller focused beams was experimentally observed in chains of sapphire spheres in agreement with the theory.</p>