2 Correcting aberration
Spherical aberration in a lens prevents the rays from all meeting at the same focal point, which causes images to become blurred. The deviation of a ray (or an electron in the case of an electron microscope) is proportional to the cube of the radius of the ray from the optic axis, and the deflection is always in the direction towards the optic axis (top). An electromagnetic octupole (middle) can correct this along two perpendicular axes, but in between these directions electrons are deflected towards the optic axis - thereby adding to spherical aberration in these directions. This can be corrected by first passing the beam through a quadrupole (bottom), which stretches and squashes the beam into a "line crossover" that is only affected by the desired divergent field of the octupole. To correct the aberration in the perpendicular direction, the beam emerging from the octupole is then passed through a second quadrupole-octupole combination rotated at 90 °.