Obstacles and optimisation in weak-beam dark-field tomography of defects

Weak-beam dark field tomography of dislocations has so far been done in a heuristic way with little theoretical analysis of how to optimise the technique. In this paper a more quantitative analysis of the limits of WBDF tomography is summarised. It can be shown that the object reconstructed from WBDF images by a conventional tomography algorithm is the locus of dislocation images laid down as central slices at the appropriate tilt angles, as would be intuitively expected. By comparison with projections of the displacement field, a reconstruction from dark-field images gives a better indication of the dislocation's path than a projection of the displacement field itself. Reconstruction is performed on a simulated tilt series of stacking fault images; the resulting structure follows the correct plane but is a 3D array of rods, not a flat plane. This is produced by the 'movement' of dynamical fringes in the stacking fault images as the sample is tilted and is an example of WBDF images being suboptimal for tomography. Finally, the influence of misalignment between the tilt axis and systematic row is modelled, and is shown to degrade the reconstruction, especially in the out-of-plane direction. This misalignment changes the excitation error with tilt, which introduces another variable to the reconstruction process and breaks the requirement that the images be a straight-ray projection of a monotonic function of the required parameter.