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.
Spatial resolution in standard phase-contrast X-ray imaging is limited by the finite number and size of detector pixels. As a result, this limits the size of features that can be seen directly in projection images or tomographic reconstructions. Dark-field imaging allows information regarding such features to be obtained, as the reconstructed image is a measure of the position-dependent small-angle X-ray scattering of incident rays from the unresolved microstructure. In this paper we utilize an intrinsic speckle-tracking-based X-ray imaging technique to obtain the effective dark-field signal from a wood sample. This effective dark-field signal is 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 assume 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, is numerically stabilised using a “weighted determinants” approach. Effective dark-field projection images are presented, as well as the dark-field tomographic reconstructions obtained using Fokker-Planck implicit speckle-tracking.
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