Correction of Aberrations—Past, Present and Future

The performance of static rotationally symmetric electron lenses is limited by unavoidable chromatic and spherical aberrations. In 1936, Scherzer demonstrated that the integrands of the integral expressions for the coefficients of these aberrations can be written as a sum of positive quadratic terms [1]. Hence these coefficients can never change sign. This important result is called the Scherzer theorem, the only theorem existing in electron optics. Employing variational methods, Tretner determined the field of magnetic and electrostatic round lenses, which yields the smallest spherical aberration coefficient for particular constraints [2]. Unfortunately, these coefficients are still too large for realistic boundaries to enable sub-Ångsrtöm resolution at medium voltages of about 200 to 300 kV. Therefore, the only possibility to directly reach this limit is the correction of the troublesome aberrations. It was again Scherzer who showed different procedures for cancelling these aberrations [3]. The most promising is the incorporation of a corrector consisting of multipole elements or of a tetrode mirror in the case of low voltages. Although the mirror is rotationally symmetric, a non-rotationally symmetric beam splitter is needed to separate the incident beam from the reflected beam.