Constrained X-ray tensor tomography reconstruction

Abstract

Quite recently, a method has been presented to reconstruct X-ray scattering tensors from projections obtained in a grating interferometry setup. The original publications present a rather specialised approach, for instance by suggesting a single SART-based solver. In this work, we propose a novel approach to solving the inverse problem, allowing the use of other algorithms than SART (like conjugate gradient), a faster tensor recovery, and an intuitive visualisation. Furthermore, we introduce constraint enforcement for X-ray tensor tomography (cXTT) and demonstrate that this yields visually smoother results in comparison to the state-of-art approach, similar to regularisation.

Non-Destructive Testing of Archaeological Findings by Grating-Based X-Ray Phase-Contrast and Dark-Field Imaging

“…The method is applicable for the analysis of bones [15][16][17] or the characterisation of fibre alignments in polymers [18][19][20]. An extension of directional dark-field imaging to a 3D analysis of fibre orientations is done by tensor tomography [21][22][23].…”

2D-Omnidirectional Hard-X-Ray Scattering Sensitivity in a Single Shot

“…However, up to now GI has mainly been composed of linear gratings and the dark-field sensitivity is therefore only perpendicular to the grating lines. To obtain multiple-direction dark-field sensitivity, either the sample or the interferometer needs to be rotated [13][14], which is a time-consuming procedure. The usage of 2D gratings can mitigate the issue but can only provide dark-field sensitivity in up to four directions.…”

Six dimensional X-ray Tensor Tomography with a compact laboratory setup

“…A standard XTT dense sampling scheme S comprises several acquisition poses s i S ¼ fs i :¼ ðw; h; /Þ; w 2 f0 ; 20 ; 40 g; h 2 H; / 2 Ug; where H ¼ f0 ; 30 ; 60 ; 90 g; U ¼ f0 ; 2:01 ; …; 360 g. Such an acquisition geometry enables the measurement of the anisotropic dark-field signal from several poses spread over the unit sphere. These dark-field projections are then fed into an iterative reconstruction algorithm, 15 which splits the combined signal measured in all the projections into several auxiliary scattering components, each of which determines the strength of scattering along a unique orientation. The scattering orientations are then scaled with their respective scattering strengths, and a Principal Component Analysis is performed to fit a scattering tensor in each voxel.…”

“…14,15 It is, however, limited by long acquisition times owing to the large number of measurements and the time required for the movement of several motors. Moreover, the Eulerian cradle is a bulky component and poses challenges for a compact setup design.…”

“…Scattering tensors T S ðr i Þ 2 R 3Â3 þ for voxels r i , i ¼ 1,…, I, discretizing the volume of interest (isotropic voxel size 64 lm 3 ), are calculated using the method proposed by Vogel et al 15 and demonstrated in Figure 2; the subscript (here S) indicates the acquisition protocol used to compute the scattering tensors. Figure 4(a) shows the scattering tensors T S (r i ) along with the corresponding structure orientation overlaid on the XCT volume of the sample described above.…”