From the optical defect point of view, the projector lenses introduce primarily image distortion. Fortunately, the distortion can be eliminated by properly exciting the constituent lenses of the projector system.
At HRTEM magnifications in TEMs, the image distortion can be verified by measuring the lattice spacings of a symmetric lattice in different lattice orientations. There are no distortions if the lattice spacings are equivalent in all orientations.
Due to the inaccuracy of eye judgment and/or the error from the digitalized user interface (UI) of the microscope software, to obtain the highest precision in quantifying spot spacings of crystals, we normally measure a distance between higher order spots, and then divide it by n+1 (here, n is the number of spots between the two higher order spots). However, this method can induce errors if the Ewald sphere cuts the spot at an angle, or if there is a slight distortion of the diffraction pattern caused by the projector lens of the microscope. Therefore, it is important to know the systematic errors of the TEM and software by measuring diffraction patterns of “ideal” crystals.