Chapter/Index: Introduction  A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z  Appendix
So far only two types of aberration correctors have been proposed: The first of Scherzer’s theorem suggested that the rotational symmetry from the round lenses induces unavoidable spherical aberrations (C_{s}). Therefore, to correct the C_{s} one way is to break the symmetry. This has been established by using electromagnetic multipole lenses such as 2 (dipole), 4 (quadrupole), 6 (sextupole), 8 (octupole) poles, and so on, alternating North and South around the optic axis. Based on the Lorentz force solution from the given magnetic field of a multipole lens (2N poles) in free space, the electron trajectory can be extracted. Assuming that the magnetic poles have an ideal shape, the magnetic scalar potential obtained from the Laplace’s equation can be given by [1],  [4313] where the r and θ are polar coordinates, for instance, shown in Figure 3661 for the dipole case. The similarity between Equations 3752f and 4313 indicates that the multipole lens can be used to correct the aberration in the conventional lenses. Based on this principle, multipole lens, especially quadrupole, can be used to directly correct simple astigmatism. Note that in EMs except for alignment deflectors, stigmators, and multipole aberration correctors, all the other conventional optical lenses are cylinder symmetric.
[1] Jackson, J. D. (1999), Classical Electrodynamics, John Wiley & Sons Inc, New York.
[2] H. Rose, Elektronenoptische Aplanate, Optik 34 (1971) 285. [3] Rose H. 1990. Outline of a spherically corrected semiaplanatic mediumvoltage transmission electronmicroscope. Optik 85:19–24
