Fig. 1

MEM imaging geometry. The electron beam (blue line) travels along the z-axis. The beam is converging and is focused towards the point \( \left(x=0,\;y=0,\;z=4{L}_{\mathrm{M}}\right) \). The beam passes through an aperture in the grounded anode \( \mathrm{A}\;\left(z=0\right) \) and is deflected slightly as the beam enters the electric field in the region \( 0\le z\le L \), where the cathode \( \mathrm{C} \) is at \( z=L \). This deflection causes the beam to travel parallel to the \( z \)-axis, resulting in parallel illumination of the sample. The electron beam turns around in the vicinity of the turning distance \( z={L}_M=L-\delta \), for some small distance \( \delta \). After interacting with the electric field above the cathode surface (held at a potential of \( V \)) in the vicinity of \( z={L}_M \), the deflected electron beam is reaccelerated away from the cathode and passes back through the anode aperture \( A \) \( \left(z=0\right) \). The microscope is assumed to form an image of the electron positions as they would appear on a virtual image plane at \( z=\Delta f+4{L}_M/3 \). Here, \( \Delta f \) is the defocus distance from the plane \( z=4{L}_M/3 \) and is controlled by the magnetic part of the objective lens. The \( y \)-axis extends out of the page