Lens aberrations and the practical limit of resolution

Like their glass analogues, magnetic lenses suffer from such defects as coma, distortion, astigmatism, and chromatic and spherical aberration. 

The last three are particularly important because they determine the resolution of the objective lens and, hence, of the electron microscope. 

Astigmatism is due to asymmetry of the magnetic field about the axis of the lens. Fortunately, this aberration can be corrected by means of Astig-mator, which superimposes an additional magnetic field (whose strength and direction can be controlled by the microscopist) across the gap in the pole piece of the lens. 

Spherical aberration in the objective lens is particularly important, and there is no convenient way of correcting it. It arises because the outer zones of the lens focus more strongly than the zones closer to the axis. As with chromatic aberration, this produces a disk of confusion of radius Ars, which is given by 

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