Joint Ptychographic Tomography—From Frozen Hydrated Proteins to Magnetic Vector Potentials

An electron beam passing through a thin sample acquires phase shifts due to sample interactions, including electrostatic and magnetic scattering contributions. Reconstructing three-dimensional scattering sources from two-dimensional phase-less diffraction intensities is a high-dimensional non-convex inverse problem. Iterative electron ptychography is a phase-retrieval technique which attempts to solve this inverse problem using the redundant information in a set of converged-beam diffraction intensities with sufficient real-space illumination overlap [1,2], e.g., using defocused-probe 4DSTEM measurements.<br/><br/>Conversely, single particle analysis (SPA) of frozen-hydrated proteins using cryogenic electron microscopy (cryo-EM) enables the three-dimensional structure determination of biomolecules with ångström resolution. Despite the remarkable advances enabled by cryo-EM SPA, the technique requires extensive data acquisition and processing and suffers from size limitations. Recently, considerable efforts have been employed to apply phase-contrast STEM methods, including electron ptychography, to study biological structures [3,4,5]. Cryogenic electron ptychography has recently been used to obtain sub-nanometer resolution of apoferritin samples using a relatively small number (~11,000) of high signal-to-noise particle reconstructions [6]. This “serial” approach, where one uses the 4D diffraction datasets to reconstruct 2D projection images which are then subsequently used to reconstruct a 3D volume using standard cryo-EM methods, is however, not maximally dose efficient.<br/><br/>In this talk, I will propose an alternative technique we term “joint” ptychographic tomography, where the 3D volume is reconstructed directly from the 4D data. This has multiple advantages of 2D projection-based techniques: first, nonlinearities arising from multiple scattering in the sample can be accurately modeled; second, it enables 3D regularization directly which can more effectively fill-in information from missing projection directions; and finally, it can more accurately capture amplitude and phase variations of the scattering potential. Finally, I will demonstrate how orthogonal tilt-series of diffraction intensities can also be used to directly solve for the three-dimensional nature of vector magnetic scattering sources, to enable antiferromagnetic imaging at atomic resolution [7].<br/><br/>[1] J Rodenburg, A Maiden, Springer Handbook of Microscopy, (2019), doi: 10.1007/978-3-030-00069<br/>[2] G. Varnavides et al. arXiv:2309.05250 (2023), https://arxiv.org/abs/2309.05250<br/>[3] L Zhou, J Song, J Kim, et al. Nature Communications (2020), doi: 10.1038/s41467-020-16391-6<br/>[4] I Lazic, M Wirix, M Leidl, et al. Nature Methods (2022), doi: 10.1038/s41592-022-01586-0<br/>[5] Y Yu, K. SPoth, M. Colleta, et al. BioRxiV (2024), doi: 10.1101/2024.04.22.590491<br/>[6] B Küçükoğlu, I Mohammed, RC Guerrero-Ferreira, et al. bioRxiV (2024), doi: 10.1101/2024.02.12.579607<br/>[7] G. Varnavides et al. Microscopy and Microanalysis 29, (2023), doi: 10.1093/micmic/ozad067.128