Imaging properties of hemispherical electrostatic energy analyzers for high resolution momentum microscopy

Highlights: • The imaging properties of hemispherical electron analyzers for electron microscopy are discussed. • Nonisochromaticity of the hemispherical imaging energy filter is described, and can be corrected numerically. • Electron refraction at the entrance- and exit-slits cancels out the sphere aberration in the image. • A new imaging double pass analyzer can be realized with a largely increased transmission and improved energy resolution. • The double pass configuration is of particular advantage for momentum microscopy with ultimate energy an wave vector resolution. -- Abstract: Hemispherical deflection analyzers are the most widely used energy filters for state-of-the-art electron spectroscopy. Due to the high spherical symmetry, they are also well suited as imaging energy filters for electron microscopy. Here, we review the imaging properties of hemispherical deflection analyzers with emphasis on the application for cathode lens microscopy. In particular, it turns out that aberrations, in general limiting the image resolution, cancel out at the entrance and exit of the analyzer. This finding allows more compact imaging energy filters for momentum microscopy or photoelectron emission microscopy. For instance, high resolution imaging is possible, using only a single hemisphere. Conversely, a double pass hemispherical analyzer can double the energy dispersion, which means it can double the energy resolution at certain transmission, or can multiply the transmission at certain energy resolution.