Scherzer's theorem

[1] In his original paper, Scherzer summarized: "Chromatic and spherical aberration are unavoidable errors of the space charge-free electron lens.

Due to the inevitability of spherical aberration, there is a practical, but not a fundamental, limit to the resolving power of the electron microscope.

"[1] 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.

[5][6] A correction of the chromatic aberration can be achieved with time-dependent (i.e., non-static) electromagnetic fields (for example in particle accelerators).