X-ray sources are developing rapidly and their coherent output is growing correspondingly. The increased coherent flux from modern X-ray sources is being matched with an associated development in experimental methods. This article reviews the literature describing the ideas that utilize the increased brilliance from modern X-ray sources. It explores how ideas in coherent X-ray science are leading to developments in other areas, and vice versa. The article describes measurements of coherence properties and uses this discussion as a base from which to describe partially coherent diffraction and X-ray phase-contrast imaging, with applications in materials science, engineering and medicine. Coherent diffraction imaging methods are reviewed along with associated experiments in materials science. Proposals for experiments to be performed with the new X-ray free-electron lasers are briefly discussed. The literature on X-ray photon-correlation spectroscopy is described and the features it has in common with other coherent X-ray methods are identified. Many of the ideas used in the coherent X-ray literature have their origins in the optical and electron communities and these connections are explored. A review of the areas in which ideas from coherent X-ray methods are contributing to methods for the neutron, electron and optical communities is presented.

Coherent methods in the X-ray sciences

A wide range of interferometric techniques recover phase information that is
mathematically wrapped on the interval (-π,π] . Obtaining the
true unwrapped phase is a longstanding problem. We present an algorithm that solves
the phase unwrapping problem, using a combination of Fourier techniques. The
execution time for our algorithm is equivalent to the computation time required for
performing eight fast Fourier transforms and is stable against noise and residues
present in the wrapped phase. We have extended the algorithm to handle data of
arbitrary size. We expect the state of the art of existing interferometric
applications, including the possibility for real-time phase recovery, to benefit
from our algorithm.

Fast phase unwrapping algorithm for interferometric applications.

Author(s): Streubel, R; Fischer, P; Kronast, F; Kravchuk, VP; Sheka, DD; Gaididei, Y; Schmidt, OG; Makarov, D | Abstract: Extending planar two-dimensional structures into the three-dimensional space has become a general trend in multiple disciplines, including electronics, photonics, plasmonics and magnetics. This approach provides means to modify conventional or to launch novel functionalities by tailoring the geometry of an object, e.g. its local curvature. In a generic electronic system, curvature results in the appearance of scalar and vector geometric potentials inducing anisotropic and chiral effects. In the specific case of magnetism, even in the simplest case of a curved anisotropic Heisenberg magnet, the curvilinear geometry manifests two exchange-driven interactions, namely effective anisotropy and antisymmetric exchange, i.e. Dzyaloshinskii-Moriya-like interaction. As a consequence, a family of novel curvature-driven effects emerges, which includes magnetochiral effects and topologically induced magnetization patterning, resulting in theoretically predicted unlimited domain wall velocities, chirality symmetry breaking and Cherenkov-like effects for magnons. The broad range of altered physical properties makes these curved architectures appealing in view of fundamental research on e.g. skyrmionic systems, magnonic crystals or exotic spin configurations. In addition to these rich physics, the application potential of three-dimensionally shaped objects is currently being explored as magnetic field sensorics for magnetofluidic applications, spin-wave filters, advanced magneto-encephalography devices for diagnosis of epilepsy or for energy-efficient racetrack memory devices. These recent developments ranging from theoretical predictions over fabrication of three-dimensionally curved magnetic thin films, hollow cylinders or wires, to their characterization using integral means as well as the development of advanced tomography approaches are in the focus of this review.

Magnetism in curved geometries

We propose an extension to Nomarski differential interference contrast microscopy that enables isotropic linear phase imaging. The method combines phase shifting, two directions of shear and Fourier-space integration using a modified spiral phase transform. We simulated the method using a phantom object with spatially varying amplitude and phase. Simulated results show good agreement between the final phase image and the object phase, and demonstrate resistance to imaging noise.

https://nontrivialzeros.net/KGL_Papers/49_spiral-dic-JMicosp_2004.pdf

V.V. Volkov

Papers

A new symmetrized solution for phase retrieval using the transport of intensity equation