The Limits of Resolution and Dose for Aberration-Corrected Electron Tomography

TL;DR

This paper establishes theoretical limits and practical methods for achieving unprecedented 3D resolution in aberration-corrected electron tomography, surpassing traditional constraints like the Crowther limit for large specimens.

Contribution

It provides a theoretical framework and demonstrates that aberration-corrected electron tomography can achieve atomic resolution in large 3D specimens, breaking previous resolution limits.

Findings

Aberration-corrected tomography surpasses the Crowther limit under certain tilt conditions.

Atomic 3D imaging is feasible for objects larger than 20nm using modest tilting.

The dose can be effectively fractionated across tilts without loss of resolution.

Abstract

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