{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T23:59:56Z","timestamp":1790726396822,"version":"4.1.0"},"reference-count":33,"publisher":"Optica Publishing Group","issue":"20","license":[{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:00:00Z","timestamp":1790640000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"Japan Science and Technology Agency","award":["JPMJSP2119"],"award-info":[{"award-number":["JPMJSP2119"]}],"id":[{"id":"https:\/\/ror.org\/00097mb19","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2026,10,5]]},"abstract":"<jats:p>Phase-only hologram (POH) generation remains a fundamental challenge in holographic displays because of the inherent difficulty in encoding complex amplitudes using phase-only modulation. Existing methods often suffer from the speckle noise introduced by random phase modulation, high computational costs, or reduced spatial resolution caused by zero padding. In this study, we propose a differentiable Fourier-plane random phase mask (RPM) learning framework for high-fidelity POH generation. The Fourier-plane RPM was parameterized as a learnable phase modulation element and optimized within an end-to-end differentiable encoding-reconstruction model. By directly learning the RPM distribution under the phase-only constraint, the proposed method enables accurate holographic reconstruction without zero padding while requiring only a few optimization iterations. Furthermore, a low-resolution parameterization strategy and a multi-sample optimization scheme were introduced to improve generalization and prevent image-specific overfitting. Consequently, the learned RPM exhibited globally stationary statistical properties and could be reused for different target images. Numerical simulations and optical experiments demonstrate that the proposed method enables high-fidelity holographic reconstruction without zero padding while maintaining robust performance under practical optical conditions. The proposed method provides a new route for an efficient and generalizable framework for POH generation in holographic display applications.<\/jats:p>","DOI":"10.1364\/oe.611499","type":"journal-article","created":{"date-parts":[[2026,8,27]],"date-time":"2026-08-27T15:00:08Z","timestamp":1787842808000},"page":"38021","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Differentiable optimization of Fourier-plane phase mask for high-fidelity phase-only holography"],"prefix":"10.1364","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-6449-4104","authenticated-orcid":true,"given":"Jianglian","family":"Wang","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02e16g702","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuuki","family":"Tokunaga","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02e16g702","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Atsushi","family":"Okamoto","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02e16g702","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"key":"oe-34-20-38021-R1","doi-asserted-by":"publisher","first-page":"H87","DOI":"10.1364\/AO.50.000H87","type":"journal-article","volume":"50","author":"Hong","year":"2011","journal-title":"Appl. Opt."},{"key":"oe-34-20-38021-R2","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1167\/8.3.33","type":"journal-article","volume":"8","author":"Hoffman","year":"2008","journal-title":"J. Vis."},{"key":"oe-34-20-38021-R3","doi-asserted-by":"publisher","first-page":"2300641","DOI":"10.1002\/lpor.202300641","type":"journal-article","volume":"18","author":"Liu","year":"2024","journal-title":"Laser Photonics Rev."},{"key":"oe-34-20-38021-R4","doi-asserted-by":"publisher","first-page":"45406","DOI":"10.1364\/OE.538649","type":"journal-article","volume":"32","author":"Fang","year":"2024","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R5","doi-asserted-by":"publisher","first-page":"5674","DOI":"10.1364\/AO.591781","type":"journal-article","volume":"65","author":"Chen","year":"2026","journal-title":"Appl. Opt."},{"key":"oe-34-20-38021-R6","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1038\/s41377-022-00894-6","type":"journal-article","volume":"11","author":"Shi","year":"2022","journal-title":"Light: Sci. Appl."},{"key":"oe-34-20-38021-R7","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1038\/s41377-024-01446-w","type":"journal-article","volume":"13","author":"Sui","year":"2024","journal-title":"Light: Sci. Appl."},{"key":"oe-34-20-38021-R8","first-page":"237","type":"journal-article","volume":"35","author":"Gerchberg","year":"1972","journal-title":"Optik"},{"key":"oe-34-20-38021-R9","doi-asserted-by":"publisher","first-page":"1058","DOI":"10.1364\/JOSAA.5.001058","type":"journal-article","volume":"5","author":"Wyrowski","year":"1988","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-34-20-38021-R10","doi-asserted-by":"publisher","first-page":"1412","DOI":"10.1364\/OE.413723","type":"journal-article","volume":"29","author":"Wu","year":"2021","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R11","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1364\/OL.43.000731","type":"journal-article","volume":"43","author":"Zea","year":"2018","journal-title":"Opt. Lett."},{"key":"oe-34-20-38021-R12","doi-asserted-by":"publisher","first-page":"23680","DOI":"10.1364\/OE.21.023680","type":"journal-article","volume":"21","author":"Tsang","year":"2013","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R13","doi-asserted-by":"publisher","first-page":"3874","DOI":"10.1364\/AO.17.003874","type":"journal-article","volume":"17","author":"Hsueh","year":"1978","journal-title":"Appl. Opt."},{"key":"oe-34-20-38021-R14","doi-asserted-by":"publisher","first-page":"30368","DOI":"10.1364\/OE.24.030368","type":"journal-article","volume":"24","author":"Qi","year":"2016","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R15","doi-asserted-by":"publisher","first-page":"20577","DOI":"10.1364\/OE.21.020577","type":"journal-article","volume":"21","author":"Li","year":"2013","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R16","doi-asserted-by":"publisher","first-page":"5115","DOI":"10.1364\/OL.529878","type":"journal-article","volume":"49","author":"Martinez-Carranza","year":"2024","journal-title":"Opt. Lett."},{"key":"oe-34-20-38021-R17","doi-asserted-by":"publisher","first-page":"2597","DOI":"10.1364\/OE.414299","type":"journal-article","volume":"29","author":"Sui","year":"2021","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R18","doi-asserted-by":"publisher","first-page":"8427","DOI":"10.1364\/AO.36.008427","type":"journal-article","volume":"36","author":"Mendlovic","year":"1997","journal-title":"Appl. Opt."},{"key":"oe-34-20-38021-R19","doi-asserted-by":"publisher","first-page":"30552","DOI":"10.1364\/OE.463462","type":"journal-article","volume":"30","author":"Sui","year":"2022","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R20","doi-asserted-by":"publisher","first-page":"31142","DOI":"10.1364\/OE.499595","type":"journal-article","volume":"31","author":"Wang","year":"2023","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R21","doi-asserted-by":"publisher","first-page":"7413","DOI":"10.1364\/OE.483590","type":"journal-article","volume":"31","author":"Wang","year":"2023","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R22","doi-asserted-by":"publisher","first-page":"15089","DOI":"10.1364\/OE.425077","type":"journal-article","volume":"29","author":"Chen","year":"2021","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3355089.3356539","type":"journal-article","volume":"38","author":"Chakravarthula","year":"2019","journal-title":"ACM Trans. Graph."},{"key":"oe-34-20-38021-R24","doi-asserted-by":"publisher","first-page":"3859","DOI":"10.1364\/AO.57.003859","type":"journal-article","volume":"57","author":"Horisaki","year":"2018","journal-title":"Appl. Opt."},{"key":"oe-34-20-38021-R25","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/3414685.3417802","type":"journal-article","volume":"39","author":"Peng","year":"2020","journal-title":"ACM Trans. Graph."},{"key":"oe-34-20-38021-R26","doi-asserted-by":"publisher","first-page":"27373","DOI":"10.1364\/OE.418803","type":"journal-article","volume":"29","author":"Liu","year":"2021","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R27","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1038\/s41586-020-03152-0","type":"journal-article","volume":"591","author":"Shi","year":"2021","journal-title":"Nature"},{"key":"oe-34-20-38021-R28","doi-asserted-by":"publisher","first-page":"112507","DOI":"10.1016\/j.isci.2025.112507","type":"journal-article","volume":"28","author":"Yu","year":"2025","journal-title":"iScience"},{"key":"oe-34-20-38021-R29","doi-asserted-by":"publisher","first-page":"3968","DOI":"10.1364\/OE.22.003968","type":"journal-article","volume":"22","author":"Shibukawa","year":"2014","journal-title":"Opt. Express"},{"key":"oe-34-20-38021-R30","doi-asserted-by":"publisher","first-page":"6877","DOI":"10.1364\/AO.52.006877","type":"journal-article","volume":"52","author":"Lingel","year":"2013","journal-title":"Appl. Opt."},{"key":"oe-34-20-38021-R31","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1038\/s41565-026-02128-x","type":"journal-article","volume":"21","author":"Fan","year":"2026","journal-title":"Nat. Nanotechnol."},{"key":"oe-34-20-38021-R32","doi-asserted-by":"publisher","first-page":"132852","DOI":"10.1016\/j.optcom.2025.132852","type":"journal-article","volume":"604","author":"Wang","year":"2026","journal-title":"Opt. Commun."},{"key":"oe-34-20-38021-R34","doi-asserted-by":"publisher","first-page":"1740","DOI":"10.1364\/OL.39.001740","type":"journal-article","volume":"39","author":"Mendoza-Yero","year":"2014","journal-title":"Opt. Lett."}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-34-20-38021","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-34-20-38021&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T23:04:45Z","timestamp":1790723085000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-34-20-38021"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,29]]},"references-count":33,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.611499","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,29]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.611499","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":"15 July 2026","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"27 August 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"29 September 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"}]}}