Iterative Phase Retrieval Methods for Weakly Scattering Signals: Transfer of Information and Efficient Regularization

BIO Web of Conferences 129, 04015 (2024) EMC 2024 https://doi.org/10.1051/bioconf/202412904015 Iterative Phase Retrieval Methods for Weakly Scattering Signals: Transfer of Information and Efficient Regularization Georgios Varnavides1,2, Dr Stephanie Ribet2, Mr Reed Yalisove2,3, Dr Mary Scott2,3, Dr Colin Ophus2 1Miller Institute for Basic Research in Science, University of California, Berkeley, USA, 2National Center for Electron Microscopy, Lawrence Berkeley Laboratory, Berkeley, USA, 3Department of Materials Science and Engineering, University of California, Berkeley, USA When a converged electron probe is scanned across a thin sample, it acquires phase-shifts due to sample interactions which scatter the incident electron wavefunction. Reconstructing these various scattering sources from phaseless measurements of the intensity at far-field detectors is a highdimensional, non-convex, inverse scattering 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], e.g., using defocused-probe 4DSTEM measurements [2]. We have recently introduced a general computational framework, implemented in the open-source analysis toolkit py4DSTEM [3], to reconstruct common coherent scattering sources using physically inspired forward and adjoint operators as-well as a suite of regularization constraints robust against common experimental artifacts. Here, we present recent experimental results using the ptychographic framework on a number of materials-science samples, including atomic defects in few-layer hBN, post-acquisition aberration correction on Au nanoparticles, few-layer twisted SrTiO3 moirés, and strain measurements in upconverting core-shell nanoparticles [4], as-well as biological samples, including single-particle analysis of frozen hydrated proteins at sub-nanometer resolution [5]. Moreover, we present simulated results on how the depth-resolution of these phase-retrieval methods can be extended by solving a joint inverse problem for orthogonal tilt-series directly to obtain the three-dimensional nature of scalar and vector scattering sources such as electrostatic (Figure 1a) and magnetic vector potentials (Figure 1b), respectively [3]. In contrast to "serial" ptychographic-tomography, where one performs 2D ptychographic reconstructions for each tilt projection before reconstructing the 3D object using standard tomographic methods, "joint" ptychographic tomography leverages the ability of multislice-ptychography to capture non-linear propagation, together with three-dimensional regularizations, to recover some information inside the "missing-wedge" due to sample-geometry limitations. © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (https://creativecommons.org/licenses/by/4.0/). BIO Web of Conferences 129, 04015 (2024) EMC 2024 https://doi.org/10.1051/bioconf/202412904015 Finally, we discuss the transfer of information of iterative electron ptychography and derive various analytical expressions and numerical results for a white-noise model. We compare the results against other common iterative phase retrieval methods, notably differential phase contrast and tiltcorrected BF-STEM [3], to arrive at experiment design recommendations as a function of electron fluence and defocus (Figure 1c). Phase-retrieval methods in STEM offer particular promise due to their remarkable dose-efficiency, enabling the observation of otherwise imperceptible signals, such as fields inside materials, and of radiationsensitive materials, such as hybrid organic materials and biological samples. Graphic: Keywords: phase-retrieval, ptychography, tomography, single-particle analysis Reference: [1] J Rodenburg, A Maiden, Springer Handbook of Microscopy, (2019), doi: 10.1007/978-3-030-00069 [2] C Ophus, Microscopy and Microanalysis, 25 (2019), doi: 10.1017/S1431927619000497 [3] G Varnavides, S Ribet et al. arXiv:2309.05250 (2023), doi: 10.48550/arXiv.2309.05250 [4] S Ribet, G Varnavides et al. arXiv:2402.10084 (2024), doi: 10.48550/arXiv.2402.10084 [5] B Küçükoğlu et al., bioRxiv (2024) doi: 10.1101/2024.02.12.579607 2  (...truncated)