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X-ray dark-field imaging visualises scattering from sample microstructure, and has found application in medical and security contexts. While most X-ray dark-field imaging techniques rely on masks, gratings, or crystals, recent work on the Fokker--Planck model of diffusive imaging has enabled dark-field imaging in the propagation-based geometry. Images captured at multiple propagation distances or X-ray energies can be used to reconstruct dark-field from propagation-based images but have previously required multiple exposures. Here, we show single-exposure dark-field imaging by exploiting the harmonic content in a monochromatised synchrotron beam and utilising an energy-discriminating photon-counting detector to capture dual-energy propagation-based images. The method is validated by filming time-varying samples, showing the advantage of the dark-field contrast in analysing dynamic evolution. We measure and adjust for the impact of detector charge-sharing on the images. This work opens the way for low-dose and dynamic dark-field X-ray imaging without the need for a high-stability set-up and precision optics., Comment: 9 pages, 7 figures

A key contribution to X-ray dark-field (XDF) is X-ray diffusion by sample structures smaller than the imaging system's spatial resolution. However, some XDF techniques report that resolvable sample edges also generate XDF. Speckle-based X-ray imaging (SBXI) extracts XDF by analyzing sample-imposed changes to a reference speckle pattern's visibility. We present an algorithm for SBXI (a variant of our Multimodal Intrinsic Speckle-Tracking (MIST) algorithm) capable of separating these two distinct XDF contrast mechanisms. The algorithm uses the 'devolving' X-ray Imaging Fokker-Planck equation as its forward model and then solves the associated multimodal inverse problem, to retrieve sample attenuation, phase, and XDF. Previous MIST variants were based on the evolving Fokker-Planck equation, which considers how a reference-speckle image is modified by introducing a sample. The devolving perspective instead considers how the image collected in the presence of the sample and speckle membrane optically flows in reverse, to generate the reference-speckle image when the sample is removed from the system. We compare single- and multiple-exposure multimodal retrieval algorithms from the two Fokker-Planck perspectives. We demonstrate that the devolving perspective can distinguish between two physically different XDF contrast mechanisms; unresolved microstructure- and sharp-edge-induced XDF. This was verified by applying the retrieval algorithms to two experimental data sets. We anticipate that this work will be useful in: Yielding a pair of complementary XDF images that separate sharp-edge diffuse scatter from unresolved microstructure diffuse scatter. XDF computed tomography, where the strong edge XDF can lead to tainting streaking artefacts. Sample preparation, as samples will not need to be embedded since the strong XDF edge signal seen between the sample and air can be separated out., Comment: 21 pages and 7 figures

Dark-field X-ray imaging is a novel modality which visualises scattering from unresolved microstructure. Most dark-field imaging techniques rely on crystals or structured illumination, but recent work has shown that dark-field effects are observable in straightforward propagation-based imaging (PBI). Based on the single-material X-ray Fokker--Planck equation with an a priori dark-field energy dependence, we propose an algorithm to extract phase and dark-field effects from dual-energy PBI images. We successfully apply the dark-field retrieval algorithm to simulated and experimental dual-energy data, and show that by accounting for dark-field effects, projected thickness reconstruction is improved compared to the classic Paganin algorithm. With the emergence of spectral detectors, the method could enable single-exposure dark-field imaging of dynamic and living samples., Comment: 21 pages, 17 figures

Speckle-based phase-contrast X-ray imaging (SB-PCXI) can reconstruct high-resolution images of weakly-attenuating materials that would otherwise be indistinguishable in conventional attenuation-based imaging. The experimental setup of SB-PCXI requires only a sufficiently coherent source and spatially random mask, positioned between the source and detector. The technique can extract sample information at length scales smaller than the imaging system's spatial resolution; this enables multimodal signal reconstruction. ``Multimodal Intrinsic Speckle-Tracking'' (MIST) is a rapid and deterministic formalism derived from the paraxial-optics form of the Fokker-Planck equation. MIST simultaneously extracts attenuation, refraction, and small-angle scattering (diffusive-dark-field) signals from a sample and is more computationally efficient compared to alternative speckle-tracking approaches. Hitherto, variants of MIST have assumed the diffusive-dark-field signal to be spatially slowly varying. Although successful, these approaches have been unable to well-describe unresolved sample microstructure whose statistical form is not spatially slowly varying. Here, we extend the MIST formalism such that there is no such restriction, in terms of a sample's rotationally-isotropic diffusive-dark-field signal. We reconstruct multimodal signals of two samples, each with distinct X-ray attenuation and scattering properties. The reconstructed diffusive-dark-field signals have superior image quality compared to our previous approaches which assume the diffusive-dark-field to be a slowly varying function of transverse position. Our generalisation may assist increased adoption of SB-PCXI in applications such as engineering and biomedical disciplines, forestry, and palaeontology, and is anticipated to aid the development of speckle-based diffusive-dark-field tensor tomography., Comment: 18 pages, 7 figures

A new method is developed for three-dimensional (3D) reconstruction of multi-material objects using propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval via the contrast transfer function (CTF) formalism. The approach differs from conventional PB-CT algorithms that apply phase retrieval on individual two-dimensional (2D) projections. Instead, this method involves performing phase retrieval to the CT-reconstructed volume in 3D. The CTF formalism is further extended to the cases of partially-coherent illumination and strongly absorbing samples. Simulated results demonstrate that the proposed post-reconstruction CTF method provides fast and stable phase retrieval, producing results equivalent to conventional pre-reconstruction 2D CTF phase retrieval. Moreover, it is shown that application can be highly localised to isolated objects of interest, without a significant loss of quality, thus leading to increased computational efficiency. Combined with the extended validity of the CTF to greater propagation distances, this method provides additional advantages over approaches based on the transport-of-intensity equation., Comment: 11 pages, 5 figures

Propagation-based phase-contrast X-ray imaging (PB-PCXI) generates image contrast by utilizing sample-imposed phase-shifts. This has proven useful when imaging weakly-attenuating samples, as conventional attenuation-based imaging does not always provide adequate contrast. We present a PB-PCXI algorithm capable of extracting the X-ray attenuation, $\beta$, and refraction, $\delta$, components of the complex refractive index of distinct materials within an unknown sample. The method involves curve-fitting an error-function-based model to a phase-retrieved interface in a PB-PCXI tomographic reconstruction, which is obtained when Paganin-type phase-retrieval is applied with incorrect values of $\delta$ and $\beta$. The fit parameters can then be used to calculate true $\delta$ and $\beta$ values for composite materials. This approach requires no a priori sample information, making it broadly applicable. Our PB-PCXI reconstruction is single distance, requiring only one exposure per tomographic angle, which is important for radiosensitive samples. We apply this approach to a breast-tissue sample, recovering the refraction component, $\delta$, with 0.6 - 2.4\% accuracy compared to theoretical values., Comment: 8 pages, 4 figures and 1 table

When a macroscopic-sized non-crystalline sample is illuminated using coherent x-ray radiation, a bifurcation of photon energy flow may occur. The coarse-grained complex refractive index of the sample may be considered to attenuate and refract the incident coherent beam, leading to a coherent component of the transmitted beam. Spatially-unresolved sample microstructure, associated with the fine-grained components of the complex refractive index, introduces a diffuse component to the transmitted beam. This diffuse photon-scattering channel may be viewed in terms of position-dependent fans of ultra-small-angle x-ray scatter. These position-dependent fans, at the exit surface of the object, may under certain circumstances be approximated as having a locally-elliptical shape. By using an anisotropic-diffusion Fokker-Planck approach to model this bifurcated x-ray energy flow, we show how all three components (attenuation, refraction and locally-elliptical diffuse scatter) may be recovered. This is done via x-ray speckle tracking, in which the sample is illuminated with spatially-random x-ray fields generated by coherent illumination of a spatially-random membrane. The theory is developed, and then successfully applied to experimental x-ray data., Comment: To be published in Physical Review A; accepted version with minor revisions compared to the previous version

We develop X-ray Multi-modal Intrinsic-Speckle-Tracking (MIST), a form of X-ray speckle-tracking that is able to recover both the position-dependent phase shift and the position-dependent small-angle X-ray scattering (SAXS) signal of a phase object. MIST is based on combining a Fokker-Planck description of paraxial X-ray optics, with an optical-flow formalism for X-ray speckle-tracking. Only two images need to be taken in the presence of the sample, corresponding to two different transverse positions of the speckle-generating membrane, in order to recover both the refractive and local-SAXS properties of the sample. Like the optical-flow X-ray phase-retrieval method which it generalises, the MIST method implicitly rather than explicitly tracks both the transverse motion and the diffusion of speckles that is induced by the presence of a sample. Application to X-ray synchrotron data shows the method to be efficient, rapid and stable.

We develop a means for speckle-based phase imaging of the projected thickness of a single-material object, under the assumption of illumination by spatially random time-independent x-ray speckles. These speckles are generated by passing x rays through a suitable spatially random mask. The method makes use of a single image obtained in the presence of the object, which serves to deform the illuminating speckle field relative to a reference speckle field (which only needs to be measured once) obtained in the presence of the mask and the absence of the object. The method implicitly rather than explicitly tracks speckles, and utilizes the transport-of-intensity equation to give a closed-form solution to the inverse problem of determining the complex transmission function of the object. Implementation using x-ray synchrotron data shows the method to be robust and efficient with respect to noise. Applications include x-ray phase--amplitude radiography and tomography, as well as time-dependent imaging of dynamic and radiation-sensitive samples using low-flux sources.

The following paper describes a method for three-dimensional (3D) reconstruction of multi-material objects based on propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval using the homogenous form of the Transport-of-Intensity equation (TIE-Hom). Unlike conventional PB-CT algorithms that perform phase retrieval of individual projections, the described post-reconstruction phase-retrieval method is applied in 3D to a localised region of the CT-reconstructed volume. We demonstrate via numerical simulations the accuracy and noise characteristics of the method under a variety of experimental conditions, comparing it to both conventional absorption tomography and two-dimensional (2D) TIE-Hom phase retrieval applied to projection images. The results indicate that the 3D post-reconstruction method generally achieves a modest improvement in noise suppression over existing PB-CT methods. It is also shown that potentially large computational gains over projection-based phase retrieval for multi-material samples are possible. In particular, constraining phase retrieval to a localised 3D region of interest reduces the overall computational cost and eliminates the need for multiple CT reconstructions and global 2D phase retrieval operations for each material within the sample., Comment: 23 pages, 8 figures

Coherent diffractive imaging (CDI), using both X-rays and electrons, has made extremely rapid progress over the past two decades. The associated reconstruction algorithms are typically iterative, and seeded with a crude first estimate. A deterministic method for Bragg Coherent Diffraction Imaging (Pavlov et al., Sci. Rep. 7, 1132 (2017)) is used as a more refined starting point for a shrink-wrap iterative reconstruction procedure. The appropriate comparison with the autocorrelation function as a starting point is performed. Real-space and Fourier-space error metrics are used to analyse the convergence of the reconstruction procedure for noisy and noise-free simulated data. Our results suggest that the use of deterministic-CDI reconstructions, as a seed for subsequent iterative-CDI refinement, may boost the speed and degree of convergence compared to the cruder seeds that are currently commonly used. We also highlight the utility of monitoring multiple error metrics in the context of iterative refinement., Comment: 12 pages, 4 figures

Novel plasma-clustered deposition technique, called PVD Droplets, as well as its main principles of operation were described. New types of obtained thick, over 20 {\mu}m, functional coatings basing on Ta and Zr have been presented. Results of research in physic-chemical properties of the coating materials are listed including preliminary studies of superconductive properties. Comparative evaluation between of obtained coatings and sample CVD coating was made., Comment: 13 pages, 14 figures

We report the obtaining and primary studies of ~ 250microns thick multi-layer Ti-based protective coating deposited at high cooling rate from substance generated by cathode arc discharge in vacuum. High adhesion to steel substrate was attained through prior Arc plasma generator cleaning and successive Ion Bombardment method. All three arc-generated fractions including mainly droplet, vapour and ions have been utilised to form the coating. Obtained coating features pore-free, least defects and high hardness which, besides N presence, supposed to result from mainly martensitic transformations occurred at the presence of Nitrogen. Two intermediate thin layers of Cu of few microns were achieved to insert within coating presumably to reduce overall elastic modulus of the material., Comment: 6 pages; 6 figures; 1 table