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

Abstract

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.

Paraxial diffusion-field retrieval

“…techniques employed in the previously cited references may incorporate aspects of our I 2 inverse problem, to relate visibility reduction ν (and its associated diffusion coefficient D) to sample-related properties such as . A similar remark applies to using the I 2 methods of the present paper, for the Fokker-Planck implicit 29 approach to x-ray speckle tracking [16,104,134,135], since the latter approach is also couched in terms of a diffusion field (cf. Sec.…”

“…Similarly, let P noise (k R ) denote the rotationally averaged intensity power spectrum of the noise that will be present in a given measured image of the sample. Assume the powerlaw noise model [137][138][139] P noise (k R ) ∼ A noise (k R ) β , A noise > 0, 0 < β < γ, (135) where A noise is a measure of the total power contained in the noise, and the positive exponent β is smaller than γ because we assume the noise to decay more slowly than the signal at high radial spatial frequency. As sketched in Fig.…”

Multimodal intrinsic speckle-tracking (MIST) to extract images of rapidly-varying diffuse X-ray dark-field

“…Several studies have verified the broad applicability and importance of DF imaging 34 , 47 , 48 , with a significant focus on biomedical clinical applications 49 , e.g., using DF imaging for early-stage diagnosis of lung diseases such as fibrosis 50 , 51 , pneumothorax 52 , emphysema 53 , and breast cancer 26 . Our improved MIST approach might provide an alternative experimentally versatile, low-dose imaging technique that can reconstruct high-resolution multimodal signals in two- and three-dimensions, with CT achieved as shown with the earlier variant of MIST 42 .…”

Fast implicit diffusive dark-field retrieval for single-exposure, single-mask x-ray imaging

“…, respectively. The dimensionless transmission function t 0 quantifies the attenuation properties of the object, yielding a flux loss in the reference pattern [32,33]. D is the dimensionless diffusive function [38]…”

“…This algorithm was later extended by Pavlov et al [29] and Quénot et al [30] to include sample attenuation effects. The idea was taken further by Pavlov et al [31,32] and Alloo et al [33], to recover a diffusive dark-field signal. As a starting point, their approach utilized the Fokker-Planck generalization [34,35] of the transport-of-intensity equation of paraxial wave optics [36], adapted to random mask-based imaging.…”