Abstract text (incl. figure legends and references)
While electron microscopy has reached incredible spatial and energy resolution thanks to sophisticated and bulky electron-optics, a new, somehow orthogonal, research field has emerged based on the idea of giving near-arbitrary transformation to the electron beam before or after its interaction with the sample.
By controlling the electron wavefunction we can improve the measurement sensibility, the spatial resolution, measure new quantities in microscopy, reduce the required dose in experiments, optimise the amount of information that can be extracted by a single electron.
The mathematical instruments supporting this research are the concepts like unitary wave transformation, single pixel imaging, and conformal mapping. The experimental keys are new hardware like electron holograms, miniaturised electrostatic optical elements, electron light interaction and new automatization of hardware control by the innovative use of neural networks.
I will dedicate part of the talk to describe these technical progresses: even not reaching the complexity of the largest innovation in electron optics like spherical aberration correction, they are introducing a little revolution in the way we conceive measurements.
I will conclude summarising the results on the OAM-sorter and the prospective of computational and real ghost imaging, but also a few further ideas for the future.
I acknowledge here the help of all my colleagues and co-workers in my group of CNR Istituto Nanoscienze Modena and in Università di Modena e Reggio Emilia, and all co-workers in QSORT, MINEON and SMART –ELECTRON project. A special thank is due to Prof. Rafal E.Dunin-Borkowski. This work has received funding from the European Union"s Horizon 2020 Research and Innovation Programme under grant agreements 766970 (QSORT), 964591 (SMART-electron) and 101035013 (MINEON).