Recent developments in tomographic small‐angle X‐ray scattering

Abstract

Small‐angle X‐ray scattering (SAXS) has become a standard tool for the investigation of nano‐structured materials with applications in many fields of science. Scanning tomography adds three‐dimensional information to the method. We investigate the validity of the tomographic model in SAXS tomography. We identify the requirement of local rotational invariance of the SAXS cross section and discuss the role of coherence in the framework of SAXS tomography. A tomography experiment performed on nanoporous glass is described as a practical example of the method. SAXS tomography reveals the density and nanostructure on a virtual section through a piece of nanoporous sodium borosilicate glass.

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

“…To measure three-dimensional samples without sectioning, scanning SAXS has to be combined with computed tomography (CT) techniques. If the scattering is invariant with respect to sample rotation (Feldkamp et al, 2009), measurements taken at different angles for one rotation axis are enough and a standard reconstruction algorithm, such as filtered back-projection or simultaneous algebraic reconstruction technique (SART), can be used. Rotational invariance applies for isotropically scattering samples, i.e.…”

“…Rotational invariance applies for isotropically scattering samples, i.e. with no preferred orientation of the nanostructure or for unidirectional orientation of the nanostructure parallel to the rotation axis (Schroer et al, 2006;Feldkamp et al, 2009;Jensen et al, 2011). Skjønsfjell et al (2016) have shown that, with strict assumptions on the sample, the orientation distribution can be retrieved from measurements using a single rotation axis by fitting a model of the X-ray scattering to the experimental SAXS pattern.…”

X-ray dark-field imaging modeling

“…This model can work with popular acquisition modes for x-ray small-angle scattering signal, such as pencil beam imaging [7,8], fan beam scanning [9,10], and x-ray Talbot-Lau interferometry [11]. Our numerical simulation and phantom experiments have shown that the proposed darkfield tomographic imaging method can reconstruct highquality small-angle scattering images with superior contrast resolution relative to its conventional attenuation-based CT counterpart.…”

“…1(a-b). We also performed a comparison with the conventional model of dark-field tomographic imaging, which states that the measured small-angle scattering patterns normalized by the transmitted intensity is a line integral of smallangle scattering coefficient [7][8][9][10], that is,…”

“…A pencil beam-scanning mode can accurately acquire small-angle scattering signal [7][8], and a fan-beam scanning modality with multiline detectors was used to improve scanning efficiency [9][10]. Recently, an x-ray grating interferometric technique was developed to extract high quality differential phase images and dark-field images using a phase-stepping scan method [11].…”