  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 $\r{A}$ngstr\"om
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$\r{A}$, proving that it should be
possible to correct spherical aberration well past the 1\AA~ limit using a
programmable phase plate consisting of an array of electrostatic phase shifting
elements.
