Electron lens

An electron lens uses an electric field or magnetic field to make trajectories from an object point converge towards an image point. It has no glass for the Electrons to pass through. In a paraxial approximation, an effective focal length permits the same first-order image geometry used for a thin lens; finite beam angles, energy spread and misalignment limit this approximation.

A magnetic electron lens uses a solenoid around the beam axis; iron pole pieces concentrate its magnetic field.^[ref] A strictly axial trajectory in a perfectly uniform axial magnetic field experiences no Lorentz force, since $\mathbf{v}\times \mathbf{B}=0$. Near the entrance, a radial field component turns an advancing Electron azimuthally; the resulting sideways velocity in the axial magnetic field also produces a radial Lorentz force. This couples image rotation and focusing. Real trajectories bend smoothly, whereas a thin lens diagram compresses that bending into one effective plane.