Round lenses in conventional EMs suffer from spherical aberration as well as off-axial coma. To eliminate the azimuthal or anisotropic coma, the axial magnetic field must change its sign with a dual lens consisting of two spatially separated windings with opposite directions of their currents . The axial chromatic coefficient (Cc) of the coma-free lens is significantly larger (≥ 50%) than that of standard objective lenses. Therefore, in order to obtain sub-Ångstroem resolution it is necessary to greatly minimize the chromatic aberration in coma-free lenses.
The off-axial coma must be eliminated in order to provide a large field of view. The optical arrangement that satisfies these requirements is called aplanatic condition. In this case, the imaging characteristics do not vary for small angular beam tilts or with the position of the scatters, in the specimen, in the vicinity of the optic axis. However, the field astigmatism and the image curvature can diminish the resolution in the region far from the optic axis.
Figure 4237 shows the schematic comparison of Zemlin (diffractogram)-tableau characteristics for the axial aberrations up to third orders. First-order aberration (e.g. defocus and twofold astigmatism, A1) shows the elliptical distortion even without electron beam tilting because the impact of first-order aberrations does not depend on the tilt angle. For the aberrations of higher orders (n≥2), such as second-order axial coma B2, three-fold astigmatism A2, third-order spherical aberration C3 (>0), third-order star aberration S3 and four-fold astigmatism A3, there is no elliptical distortion observable for the un-tilted case. In these cases, only at illumination tilts the characteristic distortion due to the aberrations becomes discernible. Note that the higher-order aberrations have equal symmetries to the ones in Figure 4237 as discussed in page3740.
Figure 4237. Schematic representation of Zemlin (diffractogram)-tableau characteristics for the axial aberrations up to third order.
 H. Rose, Optik 34 (1971) 285.