It is shown that the ultimate resolution is not limited by the bandwidth of the microscope but by the bandwidth (i.e., the scattering power) of the object. In the case of a crystal oriented along a zone axis, the scattering is enhanced by the channeling of the electrons. However, if the object is aperiodic along the beam direction, the bandwidth is much more reduced. A particular challenge are the amorphous objects. For amorphous materials, the natural bandwidth is that of the single atom and of the order of 1 Å−1, which can be reached with the present generation of medium voltage microscopes without aberration correctors. A clear distinction is made between resolving a structure and refining, that is, between resolution and precision. In the case of an amorphous structure, the natural bandwidth also puts a limit on the number of atom coordinates that can be refined quantitatively. As a consequence, amorphous structures cannot be determined from one projection, but only by using atomic resolution tomography. Finally a theory of experiment design is presented that can be used to predict the optimal experimental setting or the best instrumental improvement. Using this approach it is suggested that the study of amorphous objects should be done at low accelerating voltage with correction of both spherical and chromatic aberration.