A computational geometry framework for the optimisation of atom probe reconstructions

• An atom probe reconstruction can be iteratively improved by using shape constraints.
• An atom probe reconstruction can be inverted using barycentric coordinate transforms.
• Hulls for atom probe datasets can be obtained from 2D detector outlines that are co-reconstructed with the data.
• Ion trajectory compressions caused by instrument-specific residual fields in the drift tube can be corrected.

In this paper, we present pathways for improving the reconstruction of atom probe data on a coarse (>10 nm) scale, based on computational geometry. We introduce a way to iteratively improve an atom probe reconstruction by adjusting it, so that certain known shape criteria are fulfilled. This is achieved by creating an implicit approximation of the reconstruction through a barycentric coordinate transform. We demonstrate the application of these techniques to the compensation of trajectory aberrations and the iterative improvement of the reconstruction of a dataset containing a grain boundary. We also present a method for obtaining a hull of the dataset in both detector and reconstruction space. This maximises data utilisation, and can be used to compensate for ion trajectory aberrations caused by residual fields in the ion flight path through a ‘master curve’ and correct for overall shape deviations in the data.