Electron Gun
Creating an SEM was proven to be too difficult. The electron gun with a magnetic lens is a simplification of the project.
Idea
There are two parts to this project. The first would be to create the electron source which seems to be done with the use of a Lenard/Crookes tube [1]. Secondly, we would want to focus this electron beam into a spot with the use of a homemade magnetic lens (probably a solenoid of some form). We could perhaps perform a measurement of the focal length with respect to the magnetic field strength of the lens.