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. A more quantitative analysis of the limits of weak-beam dark field tomography was summarised here. It could be shown that the object reconstructed from weak-beam dark field images by a conventional tomography algorithm was 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 gave a better indication of the dislocation's path than a projection of the displacement field itself. Reconstruction was performed on a simulated tilt series of stacking fault images; the resulting structure follows the correct plane but was a 3D array of rods, not a flat plane. This was produced by the 'movement' of dynamical fringes in the stacking fault images as the sample was tilted and was an example of weak-beam dark field images being suboptimal for tomography. Finally, the influence of misalignment between the tilt axis and systematic row was modelled, and was 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.

Obstacles and Optimisation in Weak-Beam Dark-Field Tomography of Defects. J.H.Sharp, J.S.Barnard, P.A.Midgley: Journal of Physics - Conference Series, 2010, 241[1], 012007