PhaseT∃M: 3D Imaging at 1.6 Å Resolution via Electron Cryo-Tomography with Nonlinear Phase Retrieval

PhaseT∃M: 3D Imaging at 1.6 Å Resolution via Electron Cryo-Tomography with Nonlinear Phase Retrieval | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article PhaseT∃M: 3D Imaging at 1.6 Å Resolution via Electron Cryo-Tomography with Nonlinear Phase Retrieval Juhyeok Lee, Samuel Song, Min Cho, Georgios Varnavides, Stephanie Ribet, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6531498/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 17 Dec, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Abstract Electron cryo-tomography (cryo-ET) enables 3D imaging of complex, radiation-sensitive structures with molecular detail. However, image contrast from the interference of scattered electrons is nonlinear with atomic density and multiple scattering further complicates interpretation. These effects degrade resolution, particularly in conventional reconstruction algorithms, which assume linearity. Particle averaging can reduce such issues but is unsuitable for heterogeneous or dynamic samples ubiquitous in biology, chemistry, and materials sciences. Here, we develop a phase retrieval-based cryo-ET method, PhaseT∃M. We experimentally demonstrate its application to a ~7 nm Co3O4 nanoparticle on ~30 nm carbon substrate, achieving a maximum resolution of 1.6 Å, surpassing conventional limits using standard cryo-TEM equipment. PhaseT∃M uses a multislice model for multiple scattering and Bayesian optimization for alignment and computational aberration correction, with a positivity constraint to recover 'missing wedge' information. Applied directly to biological particles, it enhances resolution and reduces artifacts, establishing a new standard for routine 3D imaging of complex, radiation-sensitive materials. Physical sciences/Physics/Techniques and instrumentation/Microscopy/Transmission electron microscopy Physical sciences/Physics/Techniques and instrumentation/Microscopy/Cryoelectron microscopy Physical sciences/Materials science/Nanoscale materials/Nanoparticles Full Text Additional Declarations There is NO Competing Interest. Supplementary Files HRTEMtomosupplementaryInformationv6.pdf Supplementary Information Cite Share Download PDF Status: Published Journal Publication published 17 Dec, 2025 Read the published version in Nature Communications → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6531498","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":452662526,"identity":"652b999a-120a-484b-a8ff-6f0d5ed41481","order_by":0,"name":"Juhyeok 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