This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.
A specific tilt angle of the electron beam can be found such that the image coma becomes negligible for a chosen point in the TEM specimen. In this case, the position of the unscattered (transmitted) electron beam, focused in the back focal plane of the objective lens, lies on the optical axis. More accurately speaking, one refers to this axis as the coma-free axis for the given point in the specimen, but one normally refers to the axis defined by coma-free alignment as being optical axis.
In the case of TEM thin film, reflected relrods are formed. When the specimen or the electron beam is tilted, the spot position in the diffraction pattern moves because the Ewald sphere moves relative to the reciprocal lattice.
Spatial coherency originates from the fact that the illumination is never perfectly parallel and is actually slightly convergent at the best imaging condition, which can be described as having a distribution of different illumination tilts. The effect of illumination tilting on the phase contrast transfer function (PCTF) is to cause a phase shift about the y-axis and, in the same way as for the temporal coherency, the PCTF is averaged over this tilt distribution.
Note that we need to realize that tilting illumination also changes the defocus, astigmatisms (e.g. twofold and threefold astigmatisms), and the original aberrations (e.g. spherical aberration).
The off-axial coma must be eliminated in order to provide a large field of view. The optical arrangement that satisfies these requirements is called aplanatic condition. In this case, the imaging characteristics do not vary for small angular beam tilts or with the position of the scatters, in the specimen, in the vicinity of the optic axis. Furthermore, a small misalignment of the direction of the incident electron beam introduces wave aberrations and thus affects the quality of the images [ 2,3] so that coma-free alignment is essential for HRTEM.
Later on, Haider et al.  corrected the aberrations in TEM imaging mode successfully. Figure 3913 shows an example of diffractogram tableaus of the aligned TEM under both uncorrected and corrected conditions. The figures taken under the uncorrected condition demonstrates that the electron beam tilt about the coma-free pivot point introduces primarily a defocus and an axial twofold astigmatism. The strength of these aberrations does not depend on the azimuthal direction of incident beam due to the rotational symmetry of the aligned TEM. After the aberration correction all diffractograms in the tableau exhibit approximately the same appearance revealing the properties of an aplanatic lens. In this case the illumination tilt does neither introduce defocus nor two-fold astigmatism confirming the correction of spherical aberration.
Figure 3913. Diffractograms obtained in an aligned microscope without (a) and with (b) correction of the spherical aberration. τ stands for tilt angles.
 Maximilian Haider, Harald Rose, Stephan Uhlemann, Bernd Kabius and
Knut Urban, Towards 0.1 nm resolution with the first
spherically corrected transmission electron
microscope, Journal ofElectron Microscopy 47(5): 395-405 (1998).
 K. Ishizuka and S. Iijima, Proc. 39th EMSA Annual Meeting,
Atlanta (1981) 96.
 D.J. Smith. W.O. Saxton, M.A. O’Keefe, G.J. Wood and
W.M. Stobbs. Ultramicroscopy I1 (1983) 263.