Progress in structure recovery from low dose exposures: Mixed molecular adsorption, exploitation of symmetry and reconstruction from the minimum signal level

TL;DR

This paper presents a maximum likelihood method for reconstructing molecular structures from extremely low dose imaging data, leveraging symmetry and multiple copies to achieve atomic resolution without particle alignment.

Contribution

It introduces a novel maximum likelihood approach that reconstructs structures from low dose data without particle identification or alignment, exploiting symmetry for improved resolution.

Findings

Achieves atomic resolution from doses as low as 5 e⁻/Ų

Method is limited only by count statistics, requiring three counts per entity

Works effectively with real experimental data and aberrations

Abstract

We investigate the recovery of structures from large-area, low dose exposures that distribute the dose over many identical copies of an object. The reconstruction is done via a maximum likelihood approach that does neither require to identify nor align the individual particles. We also simulate small molecular adsorbates on graphene and demonstrate the retrieval of images with atomic resolution from \add{large area and} extremely low dose raw data. Doses as low as 5 $e^{-}/$\AA$^{2}$ are sufficient if all symmetries (translations, rotations and mirrors) of the supporting membrane are exploited to retrieve the structure of individual adsorbed molecules. We compare different optimization schemes, consider mixed molecules and adsorption sites, and requirements on the amount of data. We further demonstrate that the maximum likelihood approach is only count limited by requiring at least three independent counts per entity.Finally, we demonstrate that the approach works with real experimental data and in presence of aberrations.