Coherent methods in the X-ray sciences

Abstract

X-ray sources are developing rapidly and their coherent output is growing extremely rapidly. The increased coherent flux from modern X-ray sources is being matched with an associated rapid development in experimental methods. This article reviews the literature describing the ideas that utilise the increased brilliance from modern Xray 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 its 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.

High-resolution three-dimensional structural microscopy by single-angle Bragg ptychography

“…This algorithm features concepts utilized in other reconstructionbased microscopy methods, namely ptychography and tomography. In order to put our 3DBPP method in context, we briefly cover the essential concepts of Bragg coherent diffraction imaging, ptychography, and tomography that relate to our new approach.X-ray microscopy of nano-and microscale crystals using coherent Bragg diffraction imaging allows three dimensional internal strain fields to be quantitatively measured [1,2]. In its first implementation, Bragg coherent diffraction imaging involved illuminating a sub-micron-sized isolated crystal with a much larger coherent x-ray beam and measuring the diffracted intensity with an area detector [3].…”

Coherent X-ray diffractive imaging on the single-cell-level of microbial samples

“…Good introductions can be found in text book literature such as [6,223] and reviews [216,243,297] and [198], where the reader nds a treatment of the crystallographic phase problem. The reader who is interested in practical introductions with an emphasis on the experimental side is referred to the doctoral theses [95,108,267,293].…”

“…For instance, Weierstall and co-workes [321] require that (cf. also [216]) 72) where ∆ denotes the smallest length scale that can be resolved in a given experiment. Using the small angle approximation sin(θ) ≈ θ ≈ tan(θ) and the scattering geometry as depicted in gure 1.9, one also obtains the following relation (cf.…”

“…The reader who is interested in phase-retrieval with an emphasis also on partial coherence is referred to the following review articles [216,243].…”

Diffraction imaging: The limits of partial coherence

“…One relatively recent development is Coherent Diffraction Imaging (CDI) 1 , in which a far-field coherent diffraction pattern is inverted to produce a high resolution image that contains both amplitude and phase information. It is anticipated that X-ray CDI will continue to become an important imaging method for imaging samples with a resolution in the range of one to ten nanometres 2,3 . CDI has been applied in material science [4][5][6] and biology 7-12 successfully.…”