Numerical aperture

Chemistry

Materials science

Cathode ray

Artificial intelligence

Physics

Ptychography

Aperture (computer memory)

Crystallography

Electron

Optics

Diffraction

Acoustics

Quantum mechanics

Computer science

Resolution (logic)

Image resolution

Wavelength

Angstrom

Nature

Aberration-corrected optics have made electron microscopy at atomic resolution a widespread and often essential tool for characterizing nanoscale structures. Image resolution has traditionally been improved by increasing the numerical aperture of the lens (α) and the beam energy, with the state-of-the-art at 300 kiloelectronvolts just entering the deep sub-ångström (that is, less than 0.5 ångström) regime. Two-dimensional (2D) materials are imaged at lower beam energies to avoid displacement damage from large momenta transfers, limiting spatial resolution to about 1 ångström. Here, by combining an electron microscope pixel-array detector with the dynamic range necessary to record the complete distribution of transmitted electrons and full-field ptychography to recover phase information from the full phase space, we increase the spatial resolution well beyond the traditional numerical-aperture-limited resolution. At a beam energy of 80 kiloelectronvolts, our ptychographic reconstruction improves the image contrast of single-atom defects in MoS2 substantially, reaching an information limit close to 5α, which corresponds to an Abbe diffraction-limited resolution of 0.39 ångström, at the electron dose and imaging conditions for which conventional imaging methods reach only 0.98 ångström. Combining an electron microscope pixel-array detector that collects the entire distribution of scattered electrons with full-field ptychography greatly improves image resolution and contrast compared to traditional techniques, even at low beam energies.

Electron ptychography of 2D materials to deep sub-ångström resolution