Aberrations of the cathode objective lens up to fifth order

In this paper we discuss a topic that was close to Prof. Gertrude Rempfer s interests for many years. On this occasion of her 100th birthday, we remember and honor Gertrude for her many outstanding contributions, and for the inspiring example that she set. We derive theoretical expressions for the aberration coefficients of the uniform electrostatic field up to 5th order and compare these with raytracing calculations for the cathode lens used in Low Energy Electron Microscopy and Photo Electron Emission Microscopy experiments. These higher order aberration coefficients are of interest for aberration corrected experiments in which chromatic (C(c)) and spherical (C₃) aberrations of the microscope are set to zero. The theoretical predictions are in good agreement with the results of raytracing. Calculations of image resolution using the Contrast Transfer Function method show that sub-nanometer resolution is achievable in an aberration corrected LEEM system.