Limits of Three-Dimensional Resolution and Dose for Aberration-Corrected Electron Tomography

Aberration-corrected electron microscopy can resolve the smallest atomic bond-lengths in nature. However, high-convergence angles that enable spectacular resolution 2D have unknown 3D limits for all but objects ($< \sim$8nm). We show aberration-corrected tomography offers new imaging by measuring several focal planes at each specimen tilt. present a theoretical foundation establishing analytic descriptions resolution, sampling, object size, and dose---with direct analogy to Crowther-Klug criterion. Remarkably, scanning transmission measure complete structure of unbounded sizes up specified cutoff resolution. This breaks established Crowther limit when tilt increments are twice convergence angle or smaller. Unprecedented is achievable across large objects. Atomic (1$\unicode{xC5}$) allowed extended larger than depth-of-focus (e.g. $>$ 20nm) using available microscopes modest tilting ($<$ 3$^\circ$). Furthermore, follows rule dose-fractionation where total dose be divided among tilts defoci.