Circumventing Scherzer’s Theorem: Large Numerical Aperture Objective Lenses for Pulsed Electron Microscopy

Scherzer’s theorem states that all static round magnetic and electro-static electron lenses possess positive spherical aberration [1]. As a result, in recent years, much effort has been invested in techniques to correct for the spatial aberrations (Cs) of objective lenses in high resolution electron microscopy. For pulsed electron sources, such as those required for ultrafast transmission electron microscopy (UTEM), an alternative strategy for Cs aberration correction is possible through the use of the dynamic lensing properties of RF cavities [2] that, when operated in the appropriate oscillation mode, can possess negative spherical aberration [3]. For single-shot imaging UTEM, which requires ~ 10 8 electrons/pulse, simulations indicate that a large numerical aperture (NA > 0.1) objective lens will also be required to mitigate against deleterious space-charge effects [4] – effectively by minimizing the time electrons experience a high charge density. Here, we present a theoretical analysis of the possibility of using the focusing properties of RF cavities to compensate for the spherical aberration of large NA objective lenses for pulsed electron microscopy.