Deterministic X-ray Bragg coherent diffraction imaging as a seed for subsequent iterative reconstruction

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 2017 Sci. Rep. 7 1132) 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

Directional dark-field implicit x-ray speckle tracking using an anisotropic-diffusion Fokker-Planck equation

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

Dark-field tomography of an attenuating object using intrinsic x-ray speckle tracking.

Purpose: We investigate how an intrinsic speckle tracking approach to speckle-based x-ray imaging is used to extract an object's effective dark-field (DF) signal, which is capable of providing object information in three dimensions. Approach: The effective DF signal was extracted using a Fokker-Planck type formalism, which models the deformations of illuminating reference beam speckles due to both coherent and diffusive scatter from the sample. Here, we assumed that (a) small-angle scattering fans at the exit surface of the sample are rotationally symmetric and (b) the object has both attenuating and refractive properties. The associated inverse problem of extracting the effective DF signal was numerically stabilized using a "weighted determinants" approach. Results: Effective DF projection images, as well as the DF tomographic reconstructions of the wood sample, are presented. DF tomography was performed using a filtered back projection reconstruction algorithm. The DF tomographic reconstructions of the wood sample provided complementary, and otherwise inaccessible, information to augment the phase contrast reconstructions, which were also computed. Conclusions: An intrinsic speckle tracking approach to speckle-based imaging can tomographically reconstruct an object's DF signal at a low sample exposure and with a simple experimental setup. The obtained DF reconstructions have an image quality comparable to alternative x-ray DF techniques

Tomographic phase and attenuation extraction for a sample composed of unknown materials using x-ray propagation-based phase-contrast imaging

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 β and refraction δ, 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 δ and β. The fit parameters can then be used to calculate true δ and β 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 δ, with 0.6–2.4% accuracy compared with theoretical values