Multimodal Intrinsic Speckle-Tracking (MIST) to extract rapidly-varying diffuse X-ray scatter

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 figure

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, $\beta$, 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 tabl