Figure 3338a shows the simulated intensity distribution patterns of 200 keV-electron probes at 100 nm of B₂ (second-order axial coma), 100 nm of A₂ (three-fold axial astigmatism), 1 µm of S₃ (axial star aberration of the 3rd order), and 2 µm of A₃ (four-fold axial astigmatism).

Figure 3338a. Simulated intensity distribution patterns of 200 keV-electron probes: (a) B₂ = 100 nm, (b) A₂ = 100 nm, (c) S₃ = 1 µm, and (d) A₃ = 2 µm. In this simulation, the defocus C₁ was set to -3 nm, the imaginary parts of the aberrations to zero, and the illumination semi-angle to 30 mrad. [1]

For STEM mode, Figure 3338b shows the change of Ronchigram taken at overfocus of 50 nm during correction of 3^rd order star aberration (S₃). The characteristic feature of the aberration marked by white broken lines disappeared after the aberration correction.

Figure 3338b. Change of Ronchigram taken at overfocus of 50 nm during correction of 3^rd order star aberration (S₃). Adapted from [2]

For TEM mode, Figure 3338c shows the schematic comparison of Zemlin (diffractogram)-tableau characteristics for the axial aberrations up to third orders. First-order aberration (e.g. defocus and twofold astigmatism, A₁) shows the elliptical distortion even without electron beam tilting because the impact of first-order aberrations does not depend on the tilt angle. For the aberrations of higher orders (n≥2), such as second-order axial coma B₂, three-fold astigmatism A₂, third-order spherical aberration C₃ (>0), third-order star aberration S₃ and four-fold astigmatism A₃, there is no elliptical distortion observable for the un-tilted case. In these cases, only at illumination tilts the characteristic distortion due to the aberrations becomes discernible. Note that the higher-order aberrations have equal symmetries to the ones in Figure 3338c as discussed in page3740.

[1] Simulation of Rolf Erni.
[2] H. Akima, Y. Hirayama and T. Yoshida, Automated Alignment Cs Correction System for STEM (II): Installation of Reinforcement Learning, www.microscopy.org, 2011 .