Alvarez varifocal X-ray lens.

Visible light optical elements such as lenses and mirrors have counterparts for X-rays. In the visible regime, a variable focusing power can be achieved by an Alvarez lens which consists of a pair of inline planar refractors with a cubic thickness profile. When the two refractors are laterally displaced in opposite directions, the parabolic component of the wavefront is changed resulting in a longitudinal displacement of the focus. This paper reports an implementation of this concept for X-rays using two planar microfabricated refractive elements. The Alvarez X-ray lens can vary the focal distance of an elliptical X-ray mirror or a planar compound X-ray lens over several millimetres. The study presents the first demonstration of an Alvarez X-ray lens which adaptively corrects defocus and astigmatism aberrations of X-ray optics. In addition, the Alvarez X-ray lens eliminates coma aberration in an elliptical mirror, to the lowest order, when combining the lens with an adjustment of the pitch angle of the mirror.

Multi-resolution Correlative Ultrastructural and Chemical Analysis of Carious Enamel by Scanning Microscopy and Tomographic Imaging.

Caries, a major global disease associated with dental enamel demineralization, remains insufficiently understood to devise effective prevention or minimally invasive treatment. Understanding the ultrastructural changes in enamel is hampered by a lack of nanoscale characterization of the chemical spatial distributions within the dental tissue. This leads to the requirement to develop techniques based on various characterization methods. The purpose of the present study is to demonstrate the strength of analytic methods using a correlative technique on a single sample of human dental enamel as a specific case study to test the accuracy of techniques to compare regions in enamel. The science of the different techniques is integrated to genuinely study the enamel. The hierarchical structures within carious tissue were mapped using the combination of focused ion beam scanning electron microscopy with synchrotron X-ray tomography. The chemical changes were studied using scanning X-ray fluorescence (XRF) and X-ray wide-angle and small-angle scattering using a beam size below 80 nm for ångström and nanometer length scales. The analysis of XRF intensity gradients revealed subtle variations of Ca intensity in carious samples in comparison with those of normal mature enamel. In addition, the pathways for enamel rod demineralization were studied using X-ray ptychography. The results show the chemical and structural modification in carious enamel with differing locations. These results reinforce the need for multi-modal approaches to nanoscale analysis in complex hierarchically structured materials to interpret the changes of materials. The approach establishes a meticulous correlative characterization platform for the analysis of biomineralized tissues at the nanoscale, which adds confidence in the interpretation of the results and time-saving imaging techniques. The protocol demonstrated here using the dental tissue sample can be applied to other samples for statistical study and the investigation of nanoscale structural changes. The information gathered from the combination of methods could not be obtained with traditional individual techniques.

Two-dimensional wavefront characterization of adaptable corrective optics and Kirkpatrick-Baez mirror system using ptychography.

Aberrations introduced during fabrication degrade the performance of X-ray optics and their ability to achieve diffraction limited focusing. Corrective optics can counteract these errors by introducing wavefront perturbations prior to the optic which cancel out the distortions. Here we demonstrate two-dimensional wavefront correction of an aberrated Kirkpatrick-Baez mirror pair using adaptable refractive structures. The resulting two-dimensional wavefront is measured using hard X-ray ptychography to recover the complex probe wavefield with high spatial resolution and model the optical performance under coherent conditions. The optical performance including the beam caustic, focal profile and wavefront error is examined before and after correction with both mirrors found to be diffraction limited after correcting. The results will be applicable to a wide variety of high numerical aperture X-ray optics aiming to achieve diffraction limited focussing using low emittance sources.

Finite Element Modelling and Experimental Validation of the Enamel Demineralisation Process at the Rod Level.

In the past years, a significant amount of effort has been directed at the observation and characterisation of caries using experimental techniques. Nevertheless, relatively little progress has been made in numerical modelling of the underlying demineralisation process. The present study is the first attempt to provide a simplified calculation framework for the numerical simulation of the demineralisation process at the length scale of enamel rods and its validation by comparing the data with statistical analysis of experimental results. FEM model was employed to simulate a time-dependent reaction-diffusion equation process in which H ions diffuse and cause demineralisation of the enamel. The local orientation of the hydroxyapatite crystals was taken into account. Experimental analysis of the demineralising front was performed using advanced high-resolution synchrotron X-ray micro-Computed Tomography. Further experimental investigations were conducted by means of SEM and STEM imaging techniques. Besides establishing and validating the new modelling framework, insights into the role of the etchant solution pH level were obtained. Additionally, some light was shed on the origin of different types of etching patterns by simulating the demineralisation process at different etching angles of attack. The implications of this study pave the way for simulations of enamel demineralisation within different complex scenarios and across the range of length scales. Indeed, the framework proposed can incorporate the presence of chemical species other than H ions and their diffusion and reaction leading to dissolution and re-precipitation of hydroxyapatite. It is the authors' hope and aspiration that ultimately this work will help identify new ways of controlling and preventing caries.

Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures.

A refractive phase corrector optics is proposed for the compensation of fabrication error of X-ray optical elements. Here, at-wavelength wavefront measurements of the focused X-ray beam by knife-edge imaging technique, the design of a three-dimensional corrector plate, its fabrication by 3D printing, and use of a corrector to compensate for X-ray lens figure errors are presented. A rotationally invariant corrector was manufactured in the polymer IP-STM using additive manufacturing based on the two-photon polymerization technique. The fabricated corrector was characterized at the B16 Test beamline, Diamond Light Source, UK, showing a reduction in r.m.s. wavefront error of a Be compound refractive Lens (CRL) by a factor of six. The r.m.s. wavefront error is a figure of merit for the wavefront quality but, for X-ray lenses, with significant X-ray absorption, a form of the r.m.s. error with weighting proportional to the transmitted X-ray intensity has been proposed. The knife-edge imaging wavefront-sensing technique was adapted to measure rotationally variant wavefront errors from two different sets of Be CRL consisting of 98 and 24 lenses. The optical aberrations were then quantified using a Zernike polynomial expansion of the 2D wavefront error. The compensation by a rotationally invariant corrector plate was partial as the Be CRL wavefront error distribution was found to vary with polar angle indicating the presence of non-spherical aberration terms. A wavefront correction plate with rotationally anisotropic thickness is proposed to compensate for anisotropy in order to achieve good focusing by CRLs at beamlines operating at diffraction-limited storage rings.

Hard X-ray ptychography for optics characterization using a partially coherent synchrotron source.

Ptychography is a scanning coherent diffraction imaging technique which provides high resolution imaging and complete spatial information of the complex electric field probe and sample transmission function. Its ability to accurately determine the illumination probe has led to its use at modern synchrotrons and free-electron lasers as a wavefront-sensing technique for optics alignment, monitoring and correction. Recent developments in the ptychography reconstruction process now incorporate a modal decomposition of the illuminating probe and relax the restriction of using sources with high spatial coherence. In this article a practical implementation of hard X-ray ptychography from a partially coherent X-ray source with a large number of modes is demonstrated experimentally. A strongly diffracting Siemens star test sample is imaged using the focused beam produced by either a Fresnel zone plate or beryllium compound refractive lens. The recovered probe from each optic is back propagated in order to plot the beam caustic and determine the precise focal size and position. The power distribution of the reconstructed probe modes also allows the quantification of the beams coherence and is compared with the values predicted by a Gaussian-Schell model and the optics exit intensity.

Synchrotron X-ray Scattering Analysis of Nylon-12 Crystallisation Variation Depending on 3D Printing Conditions.

Nylon-12 is an important structural polymer in wide use in the form of fibres and bulk structures. Fused filament fabrication (FFF) is an extrusion-based additive manufacturing (AM) method for rapid prototyping and final product manufacturing of thermoplastic polymer objects. The resultant microstructure of FFF-produced samples is strongly affected by the cooling rates and thermal gradients experienced across the part. The crystallisation behaviour during cooling and solidification influences the micro- and nano-structure, and deserves detailed investigation. A commercial Nylon-12 filament and FFF-produced Nylon-12 parts were studied by differential scanning calorimetry (DSC) and wide-angle X-ray scattering (WAXS) to examine the effect of cooling rates under non-isothermal crystallisation conditions on the microstructure and properties. Slower cooling rates caused more perfect crystallite formation, as well as alteration to the thermal properties.