Purpose: To investigate how an intrinsic speckle-tracking approach to speckle-based X-ray imaging can be used to extract an object's effective dark-field signal, which is capable of providing object information in three dimensions. Approach:The effective dark-field 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. We here 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 dark-field signal, was numerically stabilised using a "weighted determinants" approach.Results: Effective dark-field projection images are presented, as well as the dark-field tomographic reconstructions of the wood sample. Dark-field tomography was performed using a filtered-back projection reconstruction algorithm. The dark-field 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 dark-field signal at a low sample exposure and with a simple experimental set-up. The obtained dark-field reconstructions have image quality comparable to alternative X-ray dark-field techniques.

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.

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 X-ray imaging. The experimental setup of SB-PCXI requires only a sufficiently coherent X-ray 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 this restriction is removed, 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—as measured by the naturalness image quality evaluator, signal-to-noise ratio, and azimuthally averaged power-spectrum—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.

has made contributions to the development and application of novel theoretical and computational approaches to 2D, 3D and 4D image reconstruction and structure characterisation in application to X-ray imaging and diffraction. These approaches were successfully used in experiments at numerous laboratory and synchrotron radiation sources (Photon Factory, Japan; SPring-8, Japan; ELETTRA, Italy; ESRF, France; Australian Synchrotron). In particular, Dr Pavlov has developed new theoretical approaches in diffraction tomography, deterministic coherent diffractive imaging, phase-contrast imaging/tomography and extended the statistical dynamical X-ray diffraction theory to multilayer structures and nanostructures.