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.

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.

This study reports the characterisation of human dental enamel caries using synchrotron nanoscale correlative ptychography and spectroscopic mapping in combination with scanning electron microscopy. A lamella ̴2.4 µm thick was extracted from a carious enamel region of a tooth using focused ion beam-scanning electron microscopy and transferred to two synchrotron beamlines to perform hard X-ray nano-fluorescence spectroscopy simultaneously with differential phase contrast mapping at a beam size of 55 × 45 nm. Soft X-ray ptychography data was then reconstructed with a pixel size of 8 nm. The two dimensional variation in chemistry and structure of carious enamel was revealed at the nanoscale, namely, the organisation of hydroxyapatite nano-crystals within enamel rods was imaged together with the inter-rod region. Correlative use of electron and X-ray scanning microscopies for the same sample allowed visualisation of the connection between structure and composition as presented in a compound image where colour indicates the relative calcium concentration in the sample, as indicated by the calcium Kα fluorescence intensity and grey scale shows the nanostructure. This highlights the importance of advanced correlative imaging to investigate the complex structure-composition relationships in nanomaterials of natural or artificial origin.

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.

Enamel caries is a highly prevalent worldwide disease that involves the demineralisation of the outer tooth structure. In this study, we report the analysis of artificially demineralised human enamel sections (‘slices’) etched using lactic acid (2% v/v) in comparison with healthy enamel using correlative techniques of optical and electron microscopy, as well as scanning diffraction. Demineralisation of the enamel was characterised at the micron to sub-micron scale. The structure of the healthy enamel was investigated using Focused Ion Beam - Scanning Electron Microscopy (FIB-SEM) and compared with an etched sample to reveal their structural differences. Additional chemical analysis using energy-dispersive X-ray spectroscopy (EDS) was performed and a decrease in the Ca/P atomic % ratio was found in etched samples in comparison with healthy enamel, suggesting greater loss of calcium compared with phosphorus. Synchrotron wide-angle X-ray scattering (WAXS) was performed on the samples to reveal the differences in the diffraction patterns before and after etching in terms of lattice structure and preferred orientation (texture). Texture maps were extracted from diffraction analysis at 500 nm spatial resolution. These maps were correlated with the dimension of the enamel structure. The multi-scale correlative approach provided insights into the demineralisation-induced enamel structure alteration at a resolution approaching 500 nm.

Ptychography is a scanning coherent diffraction imaging technique that provides high-resolution imaging and complete spatial information of the complex probe and object transmission function. The wavefront error caused by aberrated optics has previously been recovered using ptychography when a highly coherent source is used, but has not been demonstrated with partial coherence due to the multi-modal probe required. Here, we demonstrate that partial coherence can be accounted for in ptychographic reconstructions using the multi-modal approach and assuming that decoherence arises from either the probe or the object. This equivalence recovers coherent (or single state) reconstructions of both the probe and the object even in the presence of partial coherence. We demonstrate this experimentally by using hard x-ray ptychography with a partially coherent source to image a Siemens star test object and to also recover the wavefront error from an aberrated beryllium compound refractive lens. The source properties and resolving capabilities are analyzed, and the wavefront error results are compared with another at-wavelength metrology technique. Our work demonstrates the capability of ptychography to provide high-resolution imaging and optics characterization even in the presence of partial coherence.

27 Technical RepoRT Refractive Optics for Modifying X-Ray Wavefronts DaviD LaunDy,1 Thomas moxham,1,2 vishaL Dhamgaye,3 hossein KhosroabaDi,1 oLiver Fox,1 anD KawaL sawhney1 1Diamond Light Source, Didcot, UK 2Department of Engineering Science, University of Oxford, Oxford, UK 3Synchrotron Utilisation Section, Raja Ramanna Centre for Advanced Technology, Indore, India Introduction Diamond Light Source (DLS) is the UK synchrotron light source with over 30 beamlines, many operating in the X-ray part of the spectrum. The facility has an Optics Group with active research in areas such as modelling of beamlines, development of X-ray optics, and X-ray beam characterization using techniques such as X-ray wavefront measurements. Many optics developments have benefited from using the DLS test beamline, B16 [1], a versatile dipole magnet beamline, for developing techniques and for optics test experiments. A recent project has been the development of microfabricated refractive structures for modifying the X-ray wavefront to extend and improve the performance of beamline optics. At a synchrotron radiation source, X-radiation is emitted by relativistic electrons in the storage ring passing through regions with high magnetic fields. The electromagnetic (em) radiation field emitted by different electrons in the source is uncorrelated and if the spatial distribution of the source is sufficiently large, perfect X-ray focusing optics will produce a direct image of the electrons in the source. With the latest generation of SR facilities—the so-called 4th generation—the electron spatial distribution at the source is small (of order 10 μm rms in both horizontal and vertical directions) and the radiation field at beamline optics becomes highly correlated in the transverse direction. At a focal plane, where these correlated fields overlap, the intensity distribution is determined by interference and for "ideal" focusing optics, interference at the center of the focus is entirely constructive and the focus size is determined by the diffraction limit. In this highly correlated regime, a useful concept is that of the wavefront of the em field [2]. The wavefront is a surface given by the locus of the point at which the phase of the em field is constant. For slowly varying field amplitude and a wavefront that is locally smooth, the wavefront propagates along its normal direction. The wavefront error can be defined as the displacement along the wavefront normal of the actual from the ideal wavefront. In Cartesian coordinates x y ( , , ) z with the z axis pointing along the optical axis, the wavefront error can be expressed as a function of the two transverse coordinates w x y ( , ) . Wavefront error is generated as the em wave encounters optical elements in the beamline such as, for example, monochromators, X-ray mirrors, refractive lenses, and X-ray windows and is given by the variation in the accumulated X-ray path-length. In the case of reflecting optics, the wavefront error is directly related to the figure error h x y ( , ) as shown in Figure 1, by θ = w x y h x y x y ( , ) 2 ( , ) sin( ( , )) (1) where θ x y ( , ) is the local incidence angle on the mirror. For refractive optics, the wavefront error is given by the path-length change δ = w x y E t x y ( , ) ( ) ( , ) where δ E ( ) is the X-ray energy-dependent real part decrement of the refractive index and t x y ( , ) is the error in the thickness profile of the refractor. For a constant amplitude monochromatic beam, the complex em field can be obtained directly from the wavefront error up to a constant phase factor by π λ = i w x y E E 0 exp[ 2 ( , ) / ] where λ is the wavelength of the radiation. The field obtained can be propagated to

We report major advances in the analysis of synchrotron 3D datasets acquired from human healthy and carious dental enamel. Synchrotron tomographic data for three human carious samples and a non-carious reference tooth sample were collected with the voxel size of 325 nm for a total volume of 815.4 x 815.4 x 685.4 mu m(3). The results were compared with conventional X-ray tomography, optical microscopy, and focused ion beam-scanning electron microscopy. Clear contrast was seen within demineralised enamel due to reduced mineral content using synchrotron tomography in comparison with conventional tomography. The features were found to correspond with the rod and inter-rod structures within prismatic enamel. 2D and 3D image segmentation allowed statistical quantification of important structural characteristics (such as the aspect ratio and the cross-sectional area of voids, as well as the demineralised volume fraction as a function of lesion depth). Whilst overall carious enamel predominantly displayed a Type 1 etching pattern (preferential demineralisation of enamel rods), a transition between Type 2 (preferential inter-rod demineralisation) and Type 1 was identified within the same lesion for the first time. This study does not provide extensive results on the different lesions studied, but illustrate a new method and its potential application.

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.

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.

Residual stresses in thin films and multi-layered coatings fabricated by physical vapour deposition largely affect their mechanical and thermal reliability during operation in numerous fields of applications. By changing the argon working pressure in between each multilayer planar DC magnetron sputter deposition step, it is possible to control the residual stress distribution within coatings. A combination of FIB-DIC ring-core strain analysis, synchrotron XRD analysis based on the sin(2)(Psi) method and micro-cantilever deflection analysis is used to reconstruct the in-plane stress state of multilayer coatings at different deposition pressures, with a residual stress depth profile resolution of 50 nm. A clear transition from compressive to tensile residual stresses is observed with an increase of working pressure, with pronounced stress peaks near the substrate-coating interface. These peak stresses resolved by FIB-DIC ring-core analysis exceed the average XRD stress measurements significantly, thus providing a reasonable explanation for multilayer failure. Experimental results are presented and comprehensively discussed in the context of deposition conditions for different thin film applications.

Bone is a natural hierarchical composite tissue incorporating hard mineral nano-crystals of hydroxyapatite (HAp) and organic binding material containing elastic collagen fibers. In the study, we investigated the structure and deformation of ovine bone by the combination of high-energy synchrotron X-ray tomographic imaging and scattering. X-ray experiments were performed prior to and under three-point bending loading by using a specially developed in situ load cell constructed from aluminium alloy frame, fast-drying epoxy resin for sample fixation, and a titanium bolt for contact loading. Firstly, multiple radiographic projection images were acquired and tomographic reconstruction was performed using SAVU software, following segmentation using Avizo. Secondly, Wide Angle X-ray Scattering (WAXS) and Small Angle X-ray Scattering (SAXS) 2D scattering patterns were collected from HAp and collagen. Both sample shape and deformation affect the observed scattering. Novel combined tomographic and diffraction analysis presented below paves the way for advanced characterization of complex shape samples using the Dual Imaging and Diffraction (DIAD) paradigm.

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.

Operando synchrotron XRD and in situ ptycho-tomography of single NMC811 particle revealed the correlation between lattice strain and degradation.

The weak refraction of X-rays allows refracting optical elements to be fabricated that perturb the X-ray phase at the picometre level. This allows fine correction of the X-ray wavefront from imperfect optical elements. Adaptable refractive correcting optics are a new concept of refractive optics that produce a wavefront correction that can be varied in size and form [1] allowing an dynamic correction of X-ray wavefront following mirror or lens focusing optics. Precise measurements and simulation at Diamond Light Source of the wavefront of a spatially coherent X-ray beam focused by an elliptical mirror, demonstrate that after optimisation, focusing close to the theoretical diffraction limit is achieved. [1] David Laundy, Vishal Dhamgaye, Thomas Moxham and Kawal Sawhney, Adaptable refractive correctors for X-ray optics. Optica 6 (12), 1484-1490.2019. DOI: 10.1364/OPTICA.6.001484

Deformation analysis in engineering materials and components is a subject of ongoing enquiry due to its importance for obtaining reliable prediction of strength and durability of structures and assemblies. Whilst optical methods deliver information about surface displacements, X-ray scattering methods have the capability to provide efficient assessment of crystal lattice distortion in the bulk of the component. The height digital image correlation (hDIC) technique is an alternative to conventional digital image correlation that uses the out-of-plane surface height variations for the identification of triaxial deformations. In this study, the hDIC technique was used for the determination of displacements in an aluminium specimen after 3-point bending process that creates a complex deformation state that includes both axial displacements and rotations. The surface of the specimen was prepared for the analysis by electric discharge machining (EDM) technique that has minimal effect on material properties and produces random height profile well-suited for the aim of this study. Surface height variations were measured using deep focus microscopy and used instead of pixel intensity for correlation in the DIC process. The distribution of total of elastic and plastic strains were also calculated by the evolutionary eigenstrain model using 2D X-ray diffraction patterns processed according to the polar transformation method. The agreement between hDIC and polar X-Ray diffraction analyses allowed reliable cross-validation between these two techniques.

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-S TM 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.

Shallow cracks are often observed in dental enamel, however do not normally lead to deep fractures. Previous work has highlighted the toughening mechanisms that operate in enamel during crack propagation, but very little is known about the deformation and stress fields arising around the propagating cracks during realistic loading conditions. This work aims to elucidate how the stresses are distributed within human dental enamel when a pre-existing crack is subjected to opening and surface contact with in situ indentation. We present a synchrotron-based insitu analysis coupled with a linear elastic finite element method simulation. The experimental reconstructed stress fields identified a prominent residual stress within the enamel, accompanied by a visible pattern that appeared clearly associated with its underlying microstructure. The numerical modelling of the stress field and discerning of surface contact and crack opening caused by the indentation was subsequently possible, even if in this study the influence of the anisotropy induced by the presence of features at a smaller scale was neglected. The implications of these findings and directions for future research are discussed.

Advances in x-radiation sources put greater demands on x-ray optics. Fabrication errors in optical elements lead to deformation of the radiation wavefront, which prevents diffraction-limited imaging of the source. A new adaptable x-ray phase compensator using refracting elements has been developed, fabricated, and tested. The compensator makes a sinusoidal correction to the x-ray wavefront with variable amplitude, period, and phase. The adaptable compensator was used to correct two planar compound refractive lenses and a Kirkpatrick–Baez mirror system on an x-ray beamline. Wavefront measurements showed a reduction in the rms wavefront error by a factor of seven for the lenses and three for the mirror system, reducing rms wavefront errors down to of order $ \lambda /100 $λ/100. This concept could be used with optics on existing x-ray beamlines to enable diffraction-limited focusing.