Lenses for Electron Microscopy and Microanalysis: Shadowgraph Method of Determining Focal Properties and Aberration Coefficients

The performance characteristics of electron microscopes and probe-forming instruments depend ultimately on the focal properties and aberrations of electron lenses. A practical method of experimentally determining the properties of electron lenses is described. The method utilizes shadows cast by two meshes inserted separately in front of the lens and behind the lens to study the properties of the image of a point source. The image properties are then used to calculate the lens properties. The paraxial values of the focal length and focal distance as well as their spherical and chromatic aberrations are determined. Experimental data and the analysis are presented in the form of a tutorial that has been tested in the classroom. Discussions of the relationship between image properties and lens properties, in particular, focal point aberrations and focal length aberrations, and the various ways aberration coefficients can be defined, are included to clarify concepts in optics that are important for microscopists.