Z-contrast STEM 3D information by Abel transform in rotational symmetric systems

image tomography of clusters, in transmission electron microscopy, is a recent and highly interesting field of study for its capability to explore the 3-dimensional shape and the structure of nanoparticles. Z-contrast imaging is an ideal technique, for nanometre scale tomography, and could give also 3-dimensional information on the variation in the chemical composition within the particles. Unfortunately, 3-dimensional reconstruction, with high-resolution information, requires time-consuming series of high-resolution images and long data analysis times. Here, it is shown how 3D reconstructions can be obtained from a single high resolution Z-contrast image, if the particle under study has a rotational symmetry. In this case, the reconstruction can be performed by using a procedure based on the Abel's integral. Here, the method is explained and applied to simulated and experimental images of core-shell nanocrystals, showing the capability of detecting compositional variation as distinct from particle thickness variation.