Image aberrations of axially symmetric imaging systems with off-axial rays: Three-dimensionally imaging electron microscopes (part III)

Abstract

Abstract Off-axial ray paths in axially symmetric imaging systems may be used to realize electron-optical tilting for three-dimensional imaging in electron microscopy. It is shown that, for off-axial imaging of an object region near to the rotational axis, the axial symmetry yields relations between the aberration constants thus considerably reducing the number of independent constants. Consequently the number of lens parameters necessary to achieve a desired iage quality is likewise reduced. For rays neighbouring the pencil axis, expansions of the image coordinates and of the mixed eikonal are given in terms of invariants about the rotational axis. From these, the relations can easily be deduced. Using the relations the claim is confirmed that published systems are completely corrected for a aperture aberrations up to the third (or fourth) order and for first order chromatic aberration, and that Scherzer's theorem (which states that the third-order spherical and the first-order chromatic aberrations cannot be avoided in usual round lenses) is not valid for off-axial imaging.