Aberration-corrected transmission electron microscopy (AC-TEM) is the general term for using electron microscopes where electro optical components are introduced to reduce the aberrations that would otherwise reduce the resolution of images. Historically electron microscopes had quite severe aberrations, and until about the start of the 21st century the resolution was quite limited, at best able to image the atomic structure of materials so long as the atoms were far enough apart. Theoretical methods of correcting the aberrations existed for some time, but could not be implemented in practice. Around the turn of the century the electron optical components were coupled with computer control of the lenses and their alignment; this was the breakthrough which led to significant improvements both in resolution and the clarity of the images. As of 2024 correction of geometric aberrations is standard in many commercial electron microscopes. They are extensively used in many different areas of science.

Scherzer's theorem is a theorem in the field of electron microscopy. It states that there is a limit of resolution for electronic lenses because of unavoidable aberrations.

German physicist Otto Scherzer found in 1936 that the electromagnetic lenses, which are used in electron microscopes to focus the electron beam, entail unavoidable imaging errors. These aberrations are of spherical and chromatic nature, that is, the spherical aberration coefficient C_s and the chromatic aberration coefficient C_c are always positive.

Scherzer solved the system of Laplace equations for electromagnetic potentials assuming the following conditions:

He showed that under these conditions the aberrations that emerge degrade the resolution of an electron microscope up to one hundred times the wavelength of the electron. He concluded that the aberrations cannot be fixed with a combination of rotationally symmetrical lenses.

In his original paper, Scherzer summarized: "Chromatic and spherical aberration are unavoidable errors of the space charge-free electron lens. In principle, distortion (strain and twist) and (all types of) coma can be eliminated. Due to the inevitability of spherical aberration, there is a practical, but not a fundamental, limit to the resolving power of the electron microscope."

The resolution limit provided by Scherzer's theorem can be overcome by breaking one of the above-mentioned three conditions. Giving up rotational symmetry in electronic lenses helps in correcting spherical aberrations. A correction of the chromatic aberration can be achieved with time-dependent, i.e. non-static, electromagnetic fields (for example in particle accelerators).

The benefit of the scanning transmission electron microscope (STEM) and its potentional for high-resolution imaging had been investigated by Albert Crewe. He investigated the need for a brighter electron source in the microscope, positing that cold field emission guns would be feasible. Through this and other iterations, Crewe was able to improve the resolution of the STEM from 30 Ångstroms (Å) down to 2.5 Å. Crewe's work made it possible to visualize individual atoms for the first time.