Enhanced single-shot inversion of the diffraction phase problem with the diffusion model

Enhanced single-shot inversion of the diffraction phase problem with the diffusion model | 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 Enhanced single-shot inversion of the diffraction phase problem with the diffusion model Seungjun Lee, Xi Yu, Yuewei Lin, Shinjae Yoo, Ian Robinson This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8779318/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract We present an advance in computational solution of the crystallographic “phase problem”. The diffraction data used in Bragg Coherent Diffraction Imaging experiments are “oversampled” because there are many more measurement points than unknown pixel values. Their inversion in the presence of noise often leads to multiple solutions. Here we reexamine diffraction data measured previously on thin films of superconducting La1.93Sr0.07CuO4 material on its (103) Bragg peak with bursts of single pulses of X-ray Free Electron Laser radiation. We demonstrate that the diffusion model is able to filter these solutions sufficiently to give reproducible images. The images show nanometer-sized regions of material phase-shifted with respect to each other. These are expected from the use of the Atomic Layer Epitaxy methods used to prepare the samples. Physical sciences/Materials science Physical sciences/Optics and photonics Physical sciences/Physics Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 20 Apr, 2026 Reviewers agreed at journal 27 Mar, 2026 Reviewers agreed at journal 26 Mar, 2026 Reviewers invited by journal 24 Mar, 2026 Submission checks completed at journal 24 Mar, 2026 First submitted to journal 24 Mar, 2026 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-8779318","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":612264137,"identity":"27a664f2-b165-4cb7-bf29-3298bfe319cf","order_by":0,"name":"Seungjun Lee","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAtklEQVRIiWNgGAWjYDACdiBOqLBJADOIA8xA/OBMWgKYQbQWxodth0nQIt/MfPBBYtv5PHNmBuYXH9uI0GJwmC3ZIOHc7WLLZgY2y5lEaWHmMZNIKLuduOEwA5sxzxmiHMb//UcC2zkStDAc5mFjSGg7ANLC/JinghiHHWYzlkg4k1xscJixjXEGMVrk25sffvxRYZdncLz58IcPBsQ4DAEY2yRI0wAEzB9I1jIKRsEoGAUjAgAAXtU2ECTMCTcAAAAASUVORK5CYII=","orcid":"","institution":"Brookhaven National Laboratory","correspondingAuthor":true,"prefix":"","firstName":"Seungjun","middleName":"","lastName":"Lee","suffix":""},{"id":612264139,"identity":"564416a3-70b5-4048-87f2-a2383621388a","order_by":1,"name":"Xi Yu","email":"","orcid":"","institution":"Brookhaven National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Xi","middleName":"","lastName":"Yu","suffix":""},{"id":612264140,"identity":"cb2f95f4-8133-42a0-a037-fbf1dc4a04f3","order_by":2,"name":"Yuewei Lin","email":"","orcid":"","institution":"Brookhaven National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Yuewei","middleName":"","lastName":"Lin","suffix":""},{"id":612264141,"identity":"3c1e8b05-0a5e-4e42-9030-657d6130b4fb","order_by":3,"name":"Shinjae Yoo","email":"","orcid":"","institution":"Brookhaven National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Shinjae","middleName":"","lastName":"Yoo","suffix":""},{"id":612264142,"identity":"696319ea-5822-4c03-b099-5b6e6cca4ba5","order_by":4,"name":"Ian Robinson","email":"","orcid":"","institution":"Brookhaven National Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Ian","middleName":"","lastName":"Robinson","suffix":""}],"badges":[],"createdAt":"2026-02-03 18:54:02","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8779318/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8779318/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105567012,"identity":"7833b999-092c-4c28-b3ad-dbadf705550e","added_by":"auto","created_at":"2026-03-27 12:58:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1624223,"visible":true,"origin":"","legend":"","description":"","filename":"Diffusion4Xray.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8779318/v1_covered_88eefaca-1990-4962-85a8-28954bd46b78.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Enhanced single-shot inversion of the diffraction phase problem with the diffusion model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-computational-materials","isNatureJournal":false,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"npjcompumats","sideBox":"Learn more about [npj Computational Materials](http://www.nature.com/npjcompumats/)","snPcode":"41524","submissionUrl":"https://mts-npjcompumats.nature.com/","title":"npj Computational Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8779318/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8779318/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We present an advance in computational solution of the crystallographic “phase problem”. 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