Image simulation in projection-type electron microscopy for understanding experimental images under non-optimal conditions

Microscope images are acquired under a wide range of optical conditions-regardless of whether optical alignment is complete-when using projection-type electron microscopes such as transmission, low-energy, photoemission, and mirror electron microscopes. Although paraxial rays and aberration coefficients are often calculated to describe electron optical conditions, image simulations are rarely conducted. Therefore, interpreting images under non-optimal experimental setups, such as misaligned apertures or off-center electron beams, can be challenging for users and electron-optics designers. To address this issue, we developed a fast and simple image-simulation method that is based on paraxial rays and aberration coefficients. As a demonstration, we simulated three types of image effects: field-of-view loss due to displacement of an angular limitation aperture along the optical axis, shadow-contrast formation caused by the angular limitation aperture, and change in images due to lens wobbling. The simulated images well reproduce those commonly observed in daily experiments. The proposed method provides a more intuitive and quantitative understanding of image formation under non-optimal conditions and can serve as a useful tool for both experimentalists and designers in the field of electron optics.