Correction of 3rd Order Star Aberration (S3)
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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. 
For STEM mode, Figure 3338b shows the change of Ronchigram taken at overfocus of 50 nm during correction of 3rd 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 3rd order star aberration (S3). Adapted from 
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.
Figure 3338c. Schematic representation of Zemlin (diffractogram)-tableau characteristics for the axial aberrations up to third order.
 Simulation of Rolf Erni.
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