Shape Similarity of Aberrations in terms of Azimuthal Symmetry
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The wavefront shapes of some aberrations are very similar to each other in terms of azimuthal symmetry. For instance, aberrations C1,2, C3,2 and C5,2 have essentially the same shape. The similar aberrations are marked in the same colors in Table 3665, which also can be seen in Figure 3665. The groups with similar aberrations will distort the incoming electron beam in a very similar way. The difference between those similar aberrations is the angle-dependence, for instance, at low angles (θ) the lower-order aberrations dominate.

Table 3665. 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 [3]; 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

Figure 3665 shows the aberration coefficients from 0th to 5th order.

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