The correction of the aberrations of electron lenses is the long story of many seemingly fruitless efforts to improve the resolution of electron microscopes by compensating for aberrations of round electron lenses over a period of 50 years. The problem started in 1936 when Scherzer demonstrated that the chromatic and spherical aberrations of rotationally symmetric electron lenses are unavoidable. Moreover, the coefficients of these aberrations cannot be made sufficiently small. As a result, the resolution limit of standard electron microscopes equals about one hundred times the wavelength of the electrons, whereas modern light microscopes have reached a resolution limit somewhat smaller than the wavelength. In 1947, Scherzer found an ingenious way for enabling aberration correction. He demonstrated in a famous article that it is in theory possible to eliminate chromatic and spherical aberrations by lifting any one of the constraints of his theorem, either by abandoning rotational symmetry or by introducing time-varying fields, or space charges. Moreover, he proposed a multipole corrector compensating for the spherical aberration of the objective lens.
On the existence of marginally trapped tubes in spacetimes with local rotational symmetry
