Influence of loss function and electron dose on ptychography of 2D materials using the Wirtinger flow.

Iterative phase retrieval is based on minimising a loss function as a measure of the consistency of an initial guess and underlying experimental data. Under ideal experimental conditions, real data contains Poissonian noise due to counting statistics. In this work, we use the Wirtinger Flow concept in combination with four common loss functions, being the L1 loss, the mean-squared error (MSE), the amplitude loss and the Poisson loss. Since only the latter reflects the counting statistics as an asymmetric Poisson distribution correctly, our simulation study focuses on two main cases. Firstly, high-dose momentum-resolved scanning transmission electron microscopy (STEM) of an MoS2 monolayer is considered for phase retrieval. In this case, it is found that the four losses perform differently with respect to chemical sensitivity and frequency transfer, which we interprete in terms of the substantially different signal level in the bright and dark field part of diffraction patterns. Remedies are discussed using further simulations, addressing the use of virtual ring detectors for the dark field, or restricting loss calculation to the bright field. Secondly, a dose series is presented down to 100 electrons per diffraction pattern. It is found that all losses yield qualitatively reasonable structural data in the phase, whereas only MSE and Poisson loss range at the correct amplitude level. Chemical contrast is, in general, reliably obtained using the Poisson concept, which also provides the most continuous spatial frequency transfer as to the reconstructed object transmission function.

Dynamical scattering in ice-embedded proteins in conventional and scanning transmission electron microscopy.

Structure determination of biological macromolecules using cryogenic electron microscopy is based on applying the phase object (PO) assumption and the weak phase object (WPO) approximation to reconstruct the 3D potential density of the molecule. To enhance the understanding of image formation of protein complexes embedded in glass-like ice in a transmission electron microscope, this study addresses multiple scattering in tobacco mosaic virus (TMV) specimens. This includes the propagation inside the molecule while also accounting for the effect of structural noise. The atoms in biological macromolecules are light but are distributed over several nanometres. Commonly, PO and WPO approximations are used in most simulations and reconstruction models. Therefore, dynamical multislice simulations of TMV specimens embedded in glass-like ice were performed based on fully atomistic molecular-dynamics simulations. In the first part, the impact of multiple scattering is studied using different numbers of slices. In the second part, different sample thicknesses of the ice-embedded TMV are considered in terms of additional ice layers. It is found that single-slice models yield full frequency transfer up to a resolution of 2.5 Å, followed by attenuation up to 1.4 Å. Three slices are sufficient to reach an information transfer up to 1.0 Å. In the third part, ptychographic reconstructions based on scanning transmission electron microscopy (STEM) and single-slice models are compared with conventional TEM simulations. The ptychographic reconstructions do not need the deliberate introduction of aberrations, are capable of post-acquisition aberration correction and promise benefits for information transfer, especially at resolutions beyond 1.8 Å.

Single-particle cryo-EM structures from iDPC-STEM at near-atomic resolution.

In electron cryomicroscopy (cryo-EM), molecular images of vitrified biological samples are obtained by conventional transmission microscopy (CTEM) using large underfocuses and subsequently computationally combined into a high-resolution three-dimensional structure. Here, we apply scanning transmission electron microscopy (STEM) using the integrated differential phase contrast mode also known as iDPC-STEM to two cryo-EM test specimens, keyhole limpet hemocyanin (KLH) and tobacco mosaic virus (TMV). The micrographs show complete contrast transfer to high resolution and enable the cryo-EM structure determination for KLH at 6.5 Å resolution, as well as for TMV at 3.5 Å resolution using single-particle reconstruction methods, which share identical features with maps obtained by CTEM of a previously acquired same-sized TMV data set. These data show that STEM imaging in general, and in particular the iDPC-STEM approach, can be applied to vitrified single-particle specimens to determine near-atomic resolution cryo-EM structures of biological macromolecules.