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

52 Chapter 2
P
(a)
P
(b)
y
y
x
x
+V 1
-V 1
-V 1
+V 1
F y F F x
Figure 2-15. (a) Rays leaving an axial image point, focused by a lens (with axial astigmatism)
into ellipses centered around Fx and Fy or into a circle of radius R at some intermediate plane.
(b) Use of an electrostatic stigmator to correct for the axial astigmatism of an electron lens.
Axial astigmatism also occurs in the human eye, when there is a lack of
axial symmetry. It can be corrected by wearing lenses whose focal length
differs with azimuthal direction by an amount just sufficient to compensate
for the azimuthal variation in focusing power of the eyeball. In electron
optics, the device that corrects for astigmatism is called a stigmator and it
takes the form of a weak quadrupole lens.
An electrostatic quadrupole consists of four electrodes, in the form of
short conducting rods aligned parallel to the z-axis and located at equal
distances along the +x, -x, +y, and –y directions; see Fig. 2-15b. A power
supply generating a voltage –V1 is connected to the two rods that lie in the xz
plane and electrons traveling in that plane are repelled toward the axis,
resulting in a positive focusing power (convex-lens effect). A potential +V1
is applied to the other pair, which therefore attract electrons traveling in the
y-z plane and provide a negative focusing power in that plane. By combining
the stigmator with an astigmatic lens and choosing V1 appropriately, the
focal length of the system in the x-z and y-z planes can be made equal; the
two foci Fx and Fy are brought together to a single point and the axial
astigmatism is eliminated, as in Fig. 2-15b.
F
z
z