When the lens presents different focal lengths depending on the planes that the electrons pass, astigmatism occurs. In other words, astigmatism exists when a lens magnetic field is not symmetrical in strength but stronger in one plane than in the other. This out-of-roundness of the magnetic field may be caused by dirt on pole-pieces, apertures, and/or specimen holders.
For instance, in Figure 1983, the electrons passing plane A are focused at point PA, while those passing plane B are focused at point PB.
Figure 1983. Schematic illustration of astigmatism.
In this case, the radius (ΔrA) of the circle of least confusion is given by,
ΔfA -- The maximum difference in focal length.
Astigmatism in condenser lens is important because it reduces the coherence of the electron beam, while astigmatism in objective lens is important because it induces a serious degradation of spatial resolution.
In TEM a stigmator is used to compensate for the fixed threefold astigmatism of the objective lens .
 Wang, Y.C., Fitzgerald, A., Nelson, E.C., Song, C., O’Keefe,
M.A.& Kisielowski, C. (1999). Effect of correction of the 3-fold
astigmatism on HREM lattice imaging with information below
100 pm. In Proceedings of the 57th Annual Microscopy Society of
America Meeting, pp. 822–823. New York: Springer-Verlag.