Physical Principles of Electron Microscopy: An Introduction to TEM ...

Electron Optics 47
procedure that is permissible in both light and electron optics, resulting in
Fig. 2-12b. By adding extra dashed rays as shown, Fig. 2-12b illustrates how
electrons emitted from two points a distance 2rs apart are focused into two
magnified disks of confusion in the image (shown on the left) of radius Mrs
and separation 2Mrs. Although these disks touch at their periphery, the
image would still be recognizable as representing two separate point-like
objects in the specimen. If the separation between the object points is now
reduced to rs, the disks overlap substantially, as in Fig. 2-12c. For a further
reduction in spacing, the two separate point objects would no longer be
distinguishable from the image, and so we take rs as the spherical-aberration
limit to the point resolution of a TEM objective lens. This approximates to
the Rayleigh criterion (Section 1.1); the current-density distribution in the
image consists of two overlapping peaks with about 15% dip between them.
Spherical aberration occurs in TEM lenses after the objective but is much
less important. This situation arises from the fact that each lens reduces the
maximum angle of electrons (relative to the optic axis) by a factor equal to
its magnification (as illustrated in Fig 2.12b), while the spherical-aberration
blurring depends on the third power of this angle, according to Eq. (2.14).
2Mr s
Mr s
G
(a)
(b)
(c)
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u
M ~ f/u > 1
Figure 2-12. (a) Ray diagram similar to Fig. 2-11, with the object distance u large but finite.
(b) Equivalent diagram with the rays reversed, showing two image disks of confusion arising
from object points whose separation is 2rs. (c) Same diagram but with object-point separation
reduced to r s so that the two points are barely resolved in the image (Rayleigh criterion).
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2r s
2r s
r s