  While transmission electron microscopes (TEM) can achieve a much higher
resolution than optical microscopes, they face challenges of damage to samples
during the high energy processes involved. Here, we explore using computational
ghost imaging techniques in electron microscopy to reduce the total required
intensity. The technological lack of the equivalent high-resolution, optical
spatial light modulator for electrons means that a different approach needs to
be pursued. To this end, we show a beam shaping technique based on the use of a
distribution of electrically charged metal needles to structure the beam,
alongside a novel reconstruction method to handle the resulting highly
non-orthogonal patterns. Second, we illustrate the application of this ghost
imaging approach in electron microscopy. To test the full extent of the
capabilities of this technique, we realised an analogous optical setup method.
In both regimes, the ability to reduce the amount of total illumination
intensity is evident in comparison to raster scanning.
