To adapt electron tomography for the specific study of specimen morphology, a novel reconstruction algorithm is proposed which treats strong intensity gradients in images as arising from the projected edges of surfaces. Images portraying scattering interfaces arising from absorption, elastic, or Fresnel diffraction processes are used to identify edge maps that define the abscissa of projected surface tangents. Differential geometry is used to calculate the shape of these surfaces by considering smooth variations of measured tangent abscissa to infer local tangent intersections. The approach outlined here is not restricted to convex shapes and is designed for cases where morphology is more important than retrieval of the three-dimensional scattering density. The proposed algorithm is tested on simulated data, experimental benchmark specimens of MgO nanoparticles and is then applied to a nanosized atom probe tip, for which the approach here was specifically developed.
Petersen, T., & Ringer, S. (2009). Electron tomography using a geometric surface-tangent algorithm: Application to atom probe specimen morphology. Journal of Applied Physics, 105(10), 103518-1 - 103518-9. https://doi.org/10.1063/1.3129310