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

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 large area and extremely low dose raw data. Doses as low as 5 e/Å 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 the presence of aberrations.

A Deep Learning Approach to Identify Local Structures in Atomic‐Resolution Transmission Electron Microscopy Images

“…[33][34][35] Of particular interest is the ability to identify defects, both localized (vacancies, dislocations, etc.) [33][34][35] Of particular interest is the ability to identify defects, both localized (vacancies, dislocations, etc.)…”

Analysis of Point Defects in Graphene Using Low Dose Scanning Transmission Electron Microscopy Imaging and Maximum Likelihood Reconstruction

“…This is very different from the more balanced divacancy populations reported from lower voltage and much higher dose www.advancedsciencenews.com www.pss-b.com aquisition series of one single divacancy [10,11] (note also that in the earlier work in Ref. [13] , where we used conventional, highdose experimental data that was artificially resampled to mimic low-dose conditions, the 555777 and 555567777 defects could be recovered). The set of models follows the pattern from the most simple divacancy to paired divacancies and also a five fold vacancy with a bridging atom.…”

“…The post‐processed signal to noise ratio of −6.9 dB is measured in accordance to Ref. as the contrast of the graphene lattice compared to the noise level. Examples are shown in Figure .…”

“…The experimental images were split into smaller hexagonal pieces (supercells) with 3.35 nm 2 each. This size is chosen to be just large enough to contain our expected defects . Also, the supercells are allowed to overlap by half of their diameter, to ensure that every point defect is captured completely at least once.…”

“…A total of 9 Á 10 4 supercells were extracted from the data. With these supercells and the experimentally obtained PDFs, the likelihood of a basis set of model images to account for the entirity of the measured data can be directly calculated as [12,13] :…”