Abstract
The X-ray dark-field signal can be measured with a grating-based Talbot-Lau interferometer. It measures small angle scattering of micrometer-sized oriented structures. Interestingly, the signal is a function not only of the material, but also of the relative orientation of the sample, the X-ray beam direction, and the direction of the interferometer sensitivity. This property is very interesting for potential tomographically reconstructing structures below the imaging resolution. However, tomographic reconstruction itself is a substantial challenge. A key step of the reconstruction algorithm is the inversion of a forward projection model. In this work, we propose a very general 3-D projection model. We derive the projection model under the assumption that the observed scatter distribution has a Gaussian shape. We theoretically show the consistency of our model with existing, more constrained 2-D models. Furthermore, we experimentally show the compatibility of our model with simulations and real dark-field measurements. We believe that this 3-D projection model is an important step towards more flexible trajectories and, by extension, dark-field imaging protocols that are much better applicable in practice.
Highlights
The probably most studied acquisition system for X-ray phase-contrast imaging is the Talbot-Lau grating interferometer
We propose a X-ray dark-field imaging projection model
It explicitly calculates structural quantities in 3-D using the direction of the fiber, the ray direction and the sensitivity direction. This is the first true 3-D dark-field model. We believe that this model is a powerful tool for further development of X-ray dark-field imaging
Summary
The probably most studied acquisition system for X-ray phase-contrast imaging is the Talbot-Lau grating interferometer. For the angle-dependent dark-field signal, several 2-D projection models were proposed, which are discussed briefly in the following. They conclude that the dark-field signal can be represented as the line integral along the beam direction over the anisotropic scattering components. We propose a fully three-dimensional X-ray dark-field projection model.
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