The aberration called astigmatism occurs when the electrons in the primary beam are exposed to a non-uniform magnetic field as they spiral round the optic axis. Astigmatism has several causes. It arises because the soft iron pole pieces comprising the electromagnetic lens cannot be fabricated with perfect cylindrical symmetry. The soft iron may also have micro-structural inhomogeneities which cause local variations in the magnetic field strength.
The apertures introduced into the lens may disturb the field if they are not precisely centered around the axis. Furthermore, if the apertures are not clean, contamination causes charge accumulation and deflects the beam in unexpected ways.
There are a variety of factors which contribute to form an astigmatism, which distort the image by an amount rast =βΔf, where Δf is the maximum difference in focus induced by astigmatism.
Fortunately, astigmatism is "easily" corrected using stigmators. These are small octupoles that introduce a compensating field to balance the inhomogeneities causing the astigmatism. Stigmators are present both in the illumination system (condenser lenses) and in the imaging system (objective lens).