Rafal E. Dunin-Borkowski, Jan Caron, Patrick Diehle, Fengshan Zheng, Vadim Migunov and András Kovács

Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons and Peter Grünberg Institute, Forschungszentrum Jülich, 52425 Jülich, Germanys

Off-axis electron holography is a powerful technique, which can be used to record the phase shift of an electron wave that has passed through an electron-transparent specimen in a transmission electron microscope. The phase shift is sensitive to local variations in electromagnetic potential, which are in turn dependent on nanoscale properties of a specimen of interest, such as magnetization or charge density.

We have developed a model-based iterative reconstruction technique, which can be used to retrieve the projected in-plane magnetization distribution from the magnetic contribution to a recorded phase image, or alternatively the three-dimensional magnetization distribution from a set of at least two tilt series of magnetic phase images [1]. The technique is based on the optimized implementation of a forward model, which maps a given magnetization distribution onto one or more phase images. The ill-posed problem is tackled by first replacing the original problem by a least squares minimization, which is augmented by regularization techniques to find a unique solution for the reconstructed magnetization distribution. We are also using the same model-based approach for reconstructing the projected or three-dimensional charge density distributions inside specimens from phase images. Just as for reconstructing magnetic moments, this approach allows the incorporation of a priori information, such as the shape of the object (i.e.,  the region in which charge can be located), as well as the use of a confidence mask to exclude regions containing artefacts from the analysis. Examples will be presented from the characterisation of magnetic moments in nanoscale grains and charge density distributions in electrically biased needle-shaped specimens [2].

[1] J. Caron, Model-Based Reconstruction of Magnetisation Distributions in Nanostructures from Electron Optical Phase Images, Ph.D. thesis, RWTH Aachen University, 2017. http://juser.fz-juelich.de/record/851773.

[2] The authors thank M Beleggia, G Pozzi, Z-A Li, J Ungermann, M Riese and M Farle for contributions to this work.