This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.

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Under axial illumination conditions it is not possible to measure all aberration coefficients. In this case, only the defocus and the twofold astigmatism can be determined by the defocusbased techniques. The other aberration coefficients, e.g. spherical aberration, need to be provided by the microscope manufacturer or to be determined by different methods. However, those aberration coefficients, such as the axial coma and the threefold astigmatism, cannot be ignored at high spatial resolutions approaching 0.1 nm. Therefore, the measurements of the other aberration coefficients should be done by other methods such as tilting the illumination. Note that we need to realize that tilting illumination also changes the defocus, astigmatism, and the original aberrations.
Figure 3676a shows the simulated intensity distribution patterns of 200 keVelectron probes at 100 nm of B_{2} (secondorder axial coma), 100 nm of A_{2} (threefold axial astigmatism), 1 µm of S_{3} (axial star aberration of the 3rd order), and 2 µm of A_{3} (fourfold axial astigmatism).
Figure 3676a. Simulated intensity distribution patterns of 200 keVelectron probes: (a) B_{2} = 100 nm, (b) A_{2} = 100 nm, (c) S_{3} = 1 µm, and (d) A_{3} = 2 µm. In this simulation, the defocus C_{1} was set to 3 nm, the imaginary parts of the aberrations to zero, and the illumination semiangle to 30 mrad. [1]
Figure 3676b shows the schematic comparison of Zemlin (diffractogram)tableau characteristics for the axial aberrations up to third orders. Firstorder aberration (e.g. defocus and twofold astigmatism, A_{1}) shows the elliptical distortion even without electron beam tilting because the impact of firstorder aberrations does not depend on the tilt angle. For the aberrations of higher orders (n≥2), such as secondorder axial coma B_{2}, threefold astigmatism A_{2}, thirdorder spherical aberration C_{3} (>0), thirdorder star aberration S_{3} and fourfold astigmatism A_{3}, there is no elliptical distortion observable for the untilted case. In these cases, only at illumination tilts the characteristic distortion due to the aberrations becomes discernible. Note that the higherorder aberrations have equal symmetries to the ones in Figure 3676b as discussed in page3740.
Figure 3676b. Schematic representation of Zemlin (diffractogram)tableau characteristics for the axial aberrations up to third order.
[1] Simulation of Rolf Erni.
