Ray Path in an Electromagnetic Lens and its Light Optical Analogue

Magnetic lenses influence electrons in a similar way as convex glass lenses do with light. Thus, very similar diagrams can be drawn to describe the respective ray paths. Consequently, the imaginary line through the centers of the lenses in an electron microscopes is called optic axis as well. Furthermore, the lens equation of light optics is also valid in electron optics, and the magnification is defined accordingly:

1/u + 1/v = 1/f

Magnification M = v/u

f: focal length; u: object distance; v: image distance

In electron microscopes, magnetic lenses perform two different tasks:
1. Beam formation (condenser lenses in TEM and SEM)
2. Image formation and magnification (objective, diffraction, intermediate, and projective lenses in TEM).

Lens problems: As in glass lenses, magnetic lenses have spherical (electrons are deflected stronger the more they are off-axis) and chromatic aberrations (electrons of different wavelengths are deflected differently). Moreover, the iron pole pieces are not perfectly circular, and this makes the magnetic field deviating from being rotational symmetric. The astigmatism of the objective lens can distort the image seriously. Thus, the astigmatism must be corrected, and this can fortunately be done by using quadrupole elements, so-called stigmators. These stigmators generate an additional field that compensates the inhomogeneities causing the astigmatism. In light microscopy, the spherical aberration can be compensated by a concave lens. Such lenses are not available for an electromagnetic lens but a carefully designed corrector system containing hexapols can achieve an analogous effect (link).