Six-dimensional real and reciprocal space small-angle X-ray scattering tomography

Abstract

When used in combination with raster scanning, small-angle X-ray scattering (SAXS) has proven to be a valuable imaging technique of the nanoscale, for example of bone, teeth and brain matter. Although two-dimensional projection imaging has been used to characterize various materials successfully, its three-dimensional extension, SAXS computed tomography, poses substantial challenges, which have yet to be overcome. Previous work using SAXS computed tomography was unable to preserve oriented SAXS signals during reconstruction. Here we present a solution to this problem and obtain a complete SAXS computed tomography, which preserves oriented scattering information. By introducing virtual tomography axes, we take advantage of the two-dimensional SAXS information recorded on an area detector and use it to reconstruct the full three-dimensional scattering distribution in reciprocal space for each voxel of the three-dimensional object in real space. The presented method could be of interest for a combined six-dimensional real and reciprocal space characterization of mesoscopic materials with hierarchically structured features with length scales ranging from a few nanometres to a few millimetres--for example, biomaterials such as bone or teeth, or functional materials such as fuel-cell or battery components.

Techniques to assess bone ultrastructure organization: orientation and arrangement of mineralized collagen fibrils

“…By stacking these results from consecutive thin sections, one obtains volumetric information for samples at the millimetre scale, as exemplified for complete trabeculae [67,145], that can also provide insight into important ultrastructure-microstructure relationships [67]. X-ray scattering tomography techniques, including 6D SAXS tomography [162] and SAS tensor tomography [163], provide bone ultrastructure organization information in a tomographic, non-destructive way, at the cost of higher X-ray doses and longer data post-processing times. Nevertheless, X-ray scattering tomography techniques seem to open the way to tomographic investigations that provide ultrastructure orientation information in three dimensions.…”

“…Their use in providing information on ultrastructure organization [161,169], by exploiting ultrastructure orientation-dependent signal modulations [168,293], is expected to rise in the future, as these methods have not been adequately explored to date [169]. In addition, the two recent non-destructive X-ray scattering tomographic methods [162,163] are potential candidates for being applied in vivo, although that would require significant technological advances, mainly in detector technology, in order to reduce the dose deposited in the sample.…”

“…Concerning quantitative ultrastructure organization analysis, three techniques were developed very recently to investigate 3D ultrastructure orientation in a tomographic way, based on the phenomenon of X-ray scattering: X-ray tensor tomography [161], six-dimensional SAXS tomography (6D SAXS tomography) [162] and small-angle scattering tensor tomography (SAS tensor tomography) [163]. The three techniques can retrieve the ultrastructure organization of a volume of material, such as bone, without having to section the sample.…”

“…The orientation reconstruction technique of 3D sSAXS [145] could be applied to whole sample measurements in order to provide such 3D information. Also, the X-ray scattering tomography techniques of SAS tensor tomography [163] and 6D SAXS tomography [162] could be used to provide the ultrastructure organization in situ. However, the biggest limitations of X-ray-based techniques for use in conjunction with in situ experiments are the radiation dose and the time needed to acquire the experimental image data, both of which have an important effect on the mechanical properties of the bone sample rsif.royalsocietypublishing.org J. R. Soc.…”

Small-angle X-ray scattering tensor tomography: model of the three-dimensional reciprocal-space map, reconstruction algorithm and angular sampling requirements

“…For more general anisotropically oriented scatterers, SAXS acquisition using two rotation axes is needed (see Fig. 1b) in order to retrieve the full three-dimensional reciprocal-space map Schaff et al, 2015). Schaff et al (2015) have extended the concept of the rotation invariance (Feldkamp et al, 2009) by the introduction of virtual tomographic axes.…”