Manually Correctable Aberrations in EMs
- Practical Electron Microscopy and Database -
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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.


Aberrations at different degrees can be corrected by different manners. Some high order aberrations can only be corrected by implemented, highly automated correctors, while some low order aberrations can still be corrected by skilled operators even though in conventional EMs (they can also be automatically adjusted by software). The angular-dependent aberrations, which the skilled operators can manually separate and correctly adjust as long as their controls are available and are purely separated, are marked in green in Table 3651.

Table 3651. Aberration Coefficient Nomenclature. The aberration coefficients have two
main types of notations, namely Krivanek notation, and Typke and Dierksen notation.
Krivanek notation Typke and Dierksen notation Radial Order Azimuthal Symmetry Nomenclature
Ray Wave (k)
C0,1 A0 0 1 1 Image Shift
C1,2 A1 1 2 2 Two-fold axial astigmatism (or axial astigmatism of the 1st order)
C1,0 C1 1 2 0, ∞ Defocus (overfocus positive, or spherical aberration of the 1st order; Real numbers and describing rotationally symmetric contributions to the wave aberration) (alt: Δf)
C2,3 A2 2 3 3 Three-fold axial astigmatism (or axial astigmatism of the 2nd order)
C2,1 B2 2 3 1 Axial coma
C3,4 A3 4 4 Four-fold axial astigmatism or axial astigmatism of the 3rd order Cs
C3,2 B3   4 2

Twofold astigmatism of Cs (or Third order twofold astigmatism, or Axial star aberration of the 3rd order)

C3,0 C3   4 0, ∞ Third-order spherical aberration (always positive for round lenses [1]; Real numbers and describing rotationally symmetric contributions to the wave aberration) (alt: Cs )
C4,5 A4   5 5 Five-fold axial astigmatism or axial astigmatism of the 4th order
C4,1 B4   5 1 Fourth-order axial coma
C4,3 D4 4 5 3

Fourth order threefold astigmatism (or Three lobe aberration)

C5,6 A5   6 6 Six-fold axial astigmatism or sixfold axial astigmatism of the 5th order
C5,4 R5 5 6 4 Fourfold astigmatism of C5 (or Fifth order rosette aberration)
C5,2 S5 5 6 2

Twofold astigmatism of C5 (or Fifth-order axial star aberration)

C5,0 C5   6 0, ∞ Fifth-order spherical aberration
  D5       Four lobe aberration of the 5th order



[1] O. Scherzer, J. Appl. Phys. 20 (1949) 20.



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