X-ray diffraction computed tomography

If the sample contains small and randomly oriented crystals, then it generates smooth powder diffraction "rings" when using a 2D area detector.

The latter can be performed using also a letterbox, cone and parallel X-ray beam and yields 2D or 3D images corresponding to maps of the crystallites or "grains" present in the sample and their properties, such as stress or strain.

In a perfect scenario for any pencil-beam scanning tomographic method, the measured angles should match the number of translation steps multiplied by π/2, adhering to the Nyquist sampling theorem.

In most studies, the predominant data reconstruction approach is the 'reverse analysis' introduced by Bleuet et al.[9] where each sinogram is treated independently yielding a new CT image.

There are strategies to remove or significantly all of these artefacts: Analyzing the local diffraction patterns can range from basic single-peak sequential batch fitting to a comprehensive one-step full-profile analysis, known as 'Rietveld-CT' (Wragg et al., 2015 [15]).

Another approach which is also computational expensive is the DLSR which performs the tomographic data reconstruction and peak fitting in a single step.