Current progress in programmable electrostatic phase plates raises questions about their usefulness for specific applications. Here, we explore different designs for such phase plates with the specific goal of correcting spherical aberration in the transmission electron microscope (TEM). We numerically investigate whether a phase plate could provide down to 1 Ångström spatial resolution on a conventional uncorrected TEM. Different design aspects (fill factor, pixel pattern, symmetry) were evaluated to understand their effect on the electron probe size and current density. Some proposed designs show a probe size ($d_{50}$) down to 0.66 Å, proving that it should be possible to correct spherical aberration well past the 1 Å limit using a programmable phase plate consisting of an array of electrostatic phase-shifting elements.

Multi-element electrostatic aperture lens systems are widely used to control electron or charged particle beams in many scientific instruments. By means of applied voltages, these lens systems can be operated for different purposes. In this context, numerous methods have been performed to calculate focal properties of these lenses. In this study, an artificial neural network (ANN) classification method is utilized to determine the focused/unfocused charged particle beam in the image point as a function of lens voltages for multi-element electrostatic aperture lenses. A data set for training and testing of ANN is taken from the SIMION 8.1 simulation program, which is a well known and proven accuracy program in charged particle optics. Mean squared error results of this study indicate that the ANN classification method provides notable performance characteristics for electrostatic aperture zoom lenses.