{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T04:00:09Z","timestamp":1791864009202,"version":"4.3.4"},"reference-count":52,"publisher":"Optica Publishing Group","issue":"14","license":[{"start":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T00:00:00Z","timestamp":1782691200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T00:00:00Z","timestamp":1782691200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"crossref","award":["432680300"],"award-info":[{"award-number":["432680300"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/018mejw64","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Forschung, Technologie und Raumfahrt","doi-asserted-by":"crossref","award":["05D25MG1"],"award-info":[{"award-number":["05D25MG1"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/04pz7b180","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Forschung, Technologie und Raumfahrt","doi-asserted-by":"crossref","award":["05K25MG1"],"award-info":[{"award-number":["05K25MG1"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/04pz7b180","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002347","name":"Bundesministerium f\u00fcr Forschung, Technologie und Raumfahrt","doi-asserted-by":"crossref","award":["05M26MGA"],"award-info":[{"award-number":["05M26MGA"]}],"id":[{"id":"10.13039\/501100002347","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/04pz7b180","id-type":"ROR","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100022731","name":"Max Planck School of Photonics","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100022731","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/05emy3e34","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2026,7,13]]},"abstract":"<jats:p>X-ray near-field holography has proven to be a powerful 2D and 3D imaging technique with applications ranging from biomedical research to material sciences. To reconstruct meaningful and quantitative images from the measured intensities, however, it relies on computational phase retrieval, which in many cases assumes the phase-shift and attenuation coefficient of the sample to be proportional. Here, we demonstrate an efficient phase retrieval algorithm that does not rely on this homogeneous-object assumption and is a generalization of the well-established contrast transfer function (CTF) approach. We then investigate its stability and present an experimental study comparing the proposed algorithm with established methods. The algorithm shows superior reconstruction quality compared to the established CTF-based method at a similar computational cost. Our analysis provides a deeper fundamental understanding of the homogeneous-object assumption, and the proposed algorithm will help improve the image quality for near-field holography in biomedical applications.<\/jats:p>","DOI":"10.1364\/oe.596620","type":"journal-article","created":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T14:00:10Z","timestamp":1781100010000},"page":"25065","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Phase retrieval beyond the homogeneous object assumption for X-ray in-line holographic imaging"],"prefix":"10.1364","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4447-7882","authenticated-orcid":true,"given":"Jens","family":"Lucht","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01y9bpm73","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5058-7215","authenticated-orcid":true,"given":"Leon M.","family":"Lohse","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01y9bpm73","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5408-2780","authenticated-orcid":true,"given":"Thorsten","family":"Hohage","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01y9bpm73","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4636-0813","authenticated-orcid":true,"given":"Tim","family":"Salditt","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/01y9bpm73","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,6,29]]},"reference":[{"key":"oe-34-14-25065-R2","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1038\/s43586-021-00015-4","type":"journal-article","volume":"1","author":"Withers","year":"2021","journal-title":"Nat. Rev. Methods Primers"},{"key":"oe-34-14-25065-R3","doi-asserted-by":"publisher","first-page":"6296","DOI":"10.1364\/OPEX.13.006296","type":"journal-article","volume":"13","author":"Weitkamp","year":"2005","journal-title":"Opt. Express"},{"key":"oe-34-14-25065-R4","doi-asserted-by":"publisher","first-page":"60","DOI":"10.3390\/jimaging4050060","type":"journal-article","volume":"4","author":"Zdora","year":"2018","journal-title":"J. Imaging"},{"key":"oe-34-14-25065-R5","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1038\/s41586-024-07615-6","type":"journal-article","volume":"632","author":"Aidukas","year":"2024","journal-title":"Nature"},{"key":"oe-34-14-25065-R8","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1107\/S160057752300944X","type":"journal-article","volume":"31","author":"Albers","year":"2024","journal-title":"J. Synchrotron Radiat."},{"key":"oe-34-14-25065-R10","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1140\/epjp\/s13360-024-05489-1","type":"journal-article","volume":"139","author":"Longo","year":"2024","journal-title":"Eur. Phys. J. Plus"},{"key":"oe-34-14-25065-R11","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1107\/S1600577515007742","type":"journal-article","volume":"22","author":"Salditt","year":"2015","journal-title":"J. Synchrotron Radiat."},{"key":"oe-34-14-25065-R12","article-title":"Graded multilayers for figured kirkpatrick-baez mirrors on the new esrf end station id16a","author":"MoraweMorawe","year":"2015"},{"key":"oe-34-14-25065-R13","doi-asserted-by":"publisher","first-page":"818","DOI":"10.1364\/OPTICA.420060","type":"journal-article","volume":"8","author":"Soltau","year":"2021","journal-title":"Optica"},{"key":"oe-34-14-25065-R14","doi-asserted-by":"publisher","first-page":"2758","DOI":"10.1364\/AO.21.002758","type":"journal-article","volume":"21","author":"Fienup","year":"1982","journal-title":"Appl. Opt."},{"key":"oe-34-14-25065-R15","doi-asserted-by":"publisher","first-page":"011301","DOI":"10.1063\/1.2403783","type":"journal-article","volume":"78","author":"Marchesini","year":"2007","journal-title":"Rev. Sci. Instrum."},{"key":"oe-34-14-25065-R16","volume":"6","author":"Paganin","year":"2006"},{"key":"oe-34-14-25065-R17","doi-asserted-by":"publisher","first-page":"298","DOI":"10.1107\/S1600577525011567","type":"journal-article","volume":"33","author":"Salditt","year":"2026","journal-title":"J. Synchrotron Radiat."},{"key":"oe-34-14-25065-R18","doi-asserted-by":"publisher","first-page":"103026","DOI":"10.1088\/1367-2630\/13\/10\/103026","type":"journal-article","volume":"13","author":"Osterhoff","year":"2011","journal-title":"New J. Phys."},{"key":"oe-34-14-25065-R19","doi-asserted-by":"publisher","first-page":"054306","DOI":"10.1063\/1.2435943","type":"journal-article","volume":"101","author":"Jarre","year":"2007","journal-title":"J. Appl. Phys."},{"key":"oe-34-14-25065-R20","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1046\/j.1365-2818.2002.01010.x","type":"journal-article","volume":"206","author":"Paganin","year":"2002","journal-title":"J. Microsc."},{"key":"oe-34-14-25065-R21","doi-asserted-by":"publisher","first-page":"890","DOI":"10.1364\/JOSAA.26.000890","type":"journal-article","volume":"26","author":"Witte","year":"2009","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-34-14-25065-R22","doi-asserted-by":"publisher","first-page":"e19783","DOI":"10.1002\/advs.202519783","type":"journal-article","volume":"13","author":"John","year":"2026","journal-title":"Adv. Sci."},{"key":"oe-34-14-25065-R23","first-page":"237","type":"journal-article","volume":"35","author":"Gerchberg","year":"1972","journal-title":"Optik"},{"key":"oe-34-14-25065-R24","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1088\/0266-5611\/21\/1\/004","type":"journal-article","volume":"21","author":"Luke","year":"2005","journal-title":"Inverse Problems"},{"key":"oe-34-14-25065-R25","doi-asserted-by":"publisher","first-page":"041109","DOI":"10.1063\/1.5029927","type":"journal-article","volume":"113","author":"Hagemann","year":"2018","journal-title":"Appl. Phys. Lett."},{"key":"oe-34-14-25065-R26","doi-asserted-by":"publisher","first-page":"22809","DOI":"10.1364\/OE.19.022809","type":"journal-article","volume":"19","author":"Davidoiu","year":"2011","journal-title":"Opt. Express"},{"key":"oe-34-14-25065-R27","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1364\/OPTICA.447021","type":"journal-article","volume":"9","author":"Wittwer","year":"2022","journal-title":"Optica"},{"key":"oe-34-14-25065-R28","doi-asserted-by":"publisher","first-page":"32871","DOI":"10.1364\/OE.462368","type":"journal-article","volume":"30","author":"Huhn","year":"2022","journal-title":"Opt. Express"},{"key":"oe-34-14-25065-R29","doi-asserted-by":"publisher","first-page":"10801","DOI":"10.1364\/OE.514641","type":"journal-article","volume":"32","author":"Dora","year":"2024","journal-title":"Opt. Express"},{"key":"oe-34-14-25065-R30","doi-asserted-by":"publisher","first-page":"35832","DOI":"10.1364\/OE.569216","type":"journal-article","volume":"33","author":"Yang","year":"2025","journal-title":"Opt. Express"},{"key":"oe-34-14-25065-R32","doi-asserted-by":"publisher","first-page":"794","DOI":"10.1107\/S1600577526003188","type":"journal-article","volume":"33","author":"Kim","year":"2026","journal-title":"J. Synchrotron Radiat."},{"key":"oe-34-14-25065-R33","doi-asserted-by":"publisher","first-page":"2912","DOI":"10.1063\/1.125225","type":"journal-article","volume":"75","author":"Cloetens","year":"1999","journal-title":"Appl. Phys. Lett."},{"key":"oe-34-14-25065-R34","doi-asserted-by":"publisher","first-page":"5159","DOI":"10.1364\/OL.530330","type":"journal-article","volume":"49","author":"Farag\u00f3","year":"2024","journal-title":"Opt. Lett."},{"key":"oe-34-14-25065-R35","doi-asserted-by":"publisher","first-page":"710","DOI":"10.1364\/OE.21.000710","type":"journal-article","volume":"21","author":"Kostenko","year":"2013","journal-title":"Opt. Express"},{"key":"oe-34-14-25065-R36","doi-asserted-by":"publisher","first-page":"1133","DOI":"10.1364\/OL.42.001133","type":"journal-article","volume":"42","author":"Villanueva-Perez","year":"2017","journal-title":"Opt. Lett."},{"key":"oe-34-14-25065-R37","doi-asserted-by":"publisher","first-page":"5389","DOI":"10.1364\/OL.469174","type":"journal-article","volume":"47","author":"Mom","year":"2022","journal-title":"Opt. Lett."},{"key":"oe-34-14-25065-R38","author":"Goodman","year":"2007"},{"key":"oe-34-14-25065-R39","doi-asserted-by":"publisher","first-page":"2960","DOI":"10.1364\/OPEX.12.002960","type":"journal-article","volume":"12","author":"Turner","year":"2004","journal-title":"Opt. Express"},{"key":"oe-34-14-25065-R40","doi-asserted-by":"publisher","first-page":"073705","DOI":"10.1063\/1.1960797","type":"journal-article","volume":"76","author":"Zabler","year":"2005","journal-title":"Rev. Sci. Instrum."},{"key":"oe-34-14-25065-R41","doi-asserted-by":"publisher","first-page":"11110","DOI":"10.1364\/OE.26.011110","type":"journal-article","volume":"26","author":"Yu","year":"2018","journal-title":"Opt. Express"},{"key":"oe-34-14-25065-R42","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1561\/2200000016","type":"journal-article","volume":"3","author":"Boyd","year":"2011","journal-title":"Foundations and Trends in Machine Learning"},{"key":"oe-34-14-25065-R43","author":"Beck","year":"2017"},{"key":"oe-34-14-25065-R44","author":"Bauschke","year":"2017"},{"key":"oe-34-14-25065-R45","first-page":"185","author":"Combettes","year":"2011"},{"key":"oe-34-14-25065-R46","doi-asserted-by":"publisher","first-page":"1588","DOI":"10.1137\/120896219","type":"journal-article","volume":"7","author":"Goldstein","year":"2014","journal-title":"SIAM J. Imaging Sci."},{"key":"oe-34-14-25065-R47","doi-asserted-by":"publisher","first-page":"384","DOI":"10.1137\/16M1086170","type":"journal-article","volume":"77","author":"Maretzke","year":"2017","journal-title":"SIAM J. Appl. Math."},{"key":"oe-34-14-25065-R48","doi-asserted-by":"publisher","first-page":"065003","DOI":"10.1088\/0266-5611\/31\/6\/065003","type":"journal-article","volume":"31","author":"Maretzke","year":"2015","journal-title":"Inverse Problems"},{"key":"oe-34-14-25065-R49","doi-asserted-by":"publisher","first-page":"2428","DOI":"10.1109\/TIP.2010.2048608","type":"journal-article","volume":"19","author":"Langer","year":"2010","journal-title":"IEEE Trans. on Image Process."},{"key":"oe-34-14-25065-R50","author":"Salditt","year":"2020"},{"key":"oe-34-14-25065-R51","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1107\/S160057752001557X","type":"journal-article","volume":"28","author":"Hagemann","year":"2021","journal-title":"J. Synchrotron Radiat."},{"key":"oe-34-14-25065-R52","doi-asserted-by":"publisher","first-page":"776","DOI":"10.1016\/j.sab.2011.09.011","type":"journal-article","volume":"66","author":"Schoonjans","year":"2011","journal-title":"Spectrochim. Acta, Part B"},{"key":"oe-34-14-25065-R53","doi-asserted-by":"publisher","first-page":"2191","DOI":"10.1090\/S0025-5718-10-02359-8","type":"journal-article","volume":"79","author":"Jin","year":"2010","journal-title":"Math. Comp."},{"key":"oe-34-14-25065-R54","doi-asserted-by":"publisher","first-page":"6490","DOI":"10.1364\/OE.24.006490","type":"journal-article","volume":"24","author":"Maretzke","year":"2016","journal-title":"Opt. Express"},{"key":"oe-34-14-25065-R55","doi-asserted-by":"publisher","first-page":"1586","DOI":"10.1107\/S1600577525008550","type":"journal-article","volume":"32","author":"Lucht","year":"2025","journal-title":"J. Synchrotron Radiat."},{"key":"oe-34-14-25065-R56","doi-asserted-by":"publisher","first-page":"600","DOI":"10.1109\/TIP.2003.819861","type":"journal-article","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. on Image Process."},{"key":"oe-34-14-25065-R57","doi-asserted-by":"publisher","author":"Lucht","year":"2026","DOI":"10.25625\/FCN6AQ","type":"dataset"}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-34-14-25065&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T17:54:51Z","timestamp":1782755691000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-34-14-25065"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,29]]},"references-count":52,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.596620","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,29]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.596620","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"27 February 2026","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"9 June 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"29 June 2026","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2026 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement","name":"copyright","label":"Copyright"}]}}