{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T17:07:09Z","timestamp":1789146429040,"version":"build-2803163510"},"reference-count":50,"publisher":"Optica Publishing Group","issue":"15","license":[{"start":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T00:00:00Z","timestamp":1776729600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T00:00:00Z","timestamp":1776729600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Appl. Opt."],"published-print":{"date-parts":[[2026,5,20]]},"abstract":"<jats:p>Coded diffraction enables the reconstruction of complex fields from\n\t\t\t\t\tphase-less sensor images. Such reconstruction is possible with\n\t\t\t\t\tdiffractive encoders; however, the reconstruction quality depends\n\t\t\t\t\tsignificantly on the object\u2013encoder pair and structure, as well as the\n\t\t\t\t\tsampling of the intensity-only sensor-plane images. Here, we derive\n\t\t\t\t\tthe Fisher information content of the image phase gradient when\n\t\t\t\t\tadditional information is captured from a single topological phase\n\t\t\t\t\tsingularity. This diffractive mask provides sensor-plane patterns that\n\t\t\t\t\tdepend on the unencoded phase gradient. We numerically validate the\n\t\t\t\t\tmachine-learned phase-gradient retrieval with simple neural networks.\n\t\t\t\t\tOur results identify issues of sampling and the traceability of\n\t\t\t\t\tphase-gradient information in the Fourier-plane diffractive encoder\n\t\t\t\t\tscheme and point to information-guided strategies for hybrid\n\t\t\t\t\tcomputing.<\/jats:p>","DOI":"10.1364\/ao.589275","type":"journal-article","created":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T14:00:06Z","timestamp":1774965606000},"page":"G96","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Phase-gradient information from vortex encoders"],"prefix":"10.1364","volume":"65","author":[{"given":"Abigail","family":"Perry","sequence":"first","affiliation":[{"name":"University of California Riverside"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0652-4214","authenticated-orcid":true,"given":"Luat T.","family":"Vuong","sequence":"additional","affiliation":[{"name":"University of California Riverside"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,4,21]]},"reference":[{"key":"ao-65-15-G96-R1","doi-asserted-by":"publisher","first-page":"D31","DOI":"10.1364\/JOSAA.36.000D31","type":"journal-article","volume":"36","author":"Latychevskaia","year":"2019","journal-title":"J. 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Inf.\n\t\t\t\t\tTheory"},{"key":"ao-65-15-G96-R18","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1038\/s41566-025-01657-6","type":"journal-article","volume":"19","author":"Starshynov","year":"2025","journal-title":"Nat. Photonics"},{"key":"ao-65-15-G96-R19","doi-asserted-by":"publisher","first-page":"18824","DOI":"10.1364\/OE.489492","type":"journal-article","volume":"31","author":"Li","year":"2023","journal-title":"Opt. Express"},{"key":"ao-65-15-G96-R20","doi-asserted-by":"publisher","first-page":"231103","DOI":"10.1063\/1.4937122","type":"journal-article","volume":"107","author":"Seaberg","year":"2015","journal-title":"Appl. Phys.\n\t\t\t\t\tLett."},{"key":"ao-65-15-G96-R21","doi-asserted-by":"publisher","first-page":"106808","DOI":"10.1016\/j.optlaseng.2021.106808","type":"journal-article","volume":"149","author":"Ye","year":"2022","journal-title":"Opt. 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Neural Netw."},{"key":"ao-65-15-G96-R43","volume-title":"Fundamentals of Statistical Signal\n\t\t\t\t\tProcessing: Estimation Theory","author":"Kay","year":"1993"},{"key":"ao-65-15-G96-R44","doi-asserted-by":"crossref","DOI":"10.1364\/ISA.2021.IW3H.4","article-title":"Compressed sensing and shape\n\t\t\t\t\textraction with vortex singularities","volume-title":"OSA\n\t\t\t\t\tImaging and Applied Optics Congress (3D, COSI, DH, ISA,\n\t\t\t\t\tpcAOP)","author":"Vuong","year":"2021"},{"key":"ao-65-15-G96-R45","doi-asserted-by":"publisher","first-page":"135850I","DOI":"10.1117\/12.3066337","type":"journal-article","volume":"13585","author":"Perry","year":"2025","journal-title":"Proc. SPIE"},{"key":"ao-65-15-G96-R46","doi-asserted-by":"publisher","first-page":"1420","DOI":"10.1364\/OL.590553","type":"journal-article","volume":"51","author":"Wu","year":"2026","journal-title":"Opt.\n\t\t\t\t\tLett."},{"key":"ao-65-15-G96-R47","doi-asserted-by":"publisher","first-page":"1924","DOI":"10.1364\/OL.34.001924","type":"journal-article","volume":"34","author":"Mehta","year":"2009","journal-title":"Opt.\n\t\t\t\t\tLett."},{"key":"ao-65-15-G96-R48","doi-asserted-by":"publisher","first-page":"4813","DOI":"10.1364\/OL.38.004813","type":"journal-article","volume":"38","author":"Mat\u00edas Di Martino","year":"2013","journal-title":"Opt.\n\t\t\t\t\tLett."},{"key":"ao-65-15-G96-R49","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1038\/s41567-020-01137-4","type":"journal-article","volume":"17","author":"Bouchet","year":"2021","journal-title":"Nat.\n\t\t\t\t\tPhys."},{"key":"ao-65-15-G96-R50","unstructured":"Perry A. , \u201c VortexInformation ,\u201d GitHub , 2025 , github.com\/altaiperry\/VortexInformation ."}],"container-title":["Applied Optics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=ao-65-15-G96&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,11]],"date-time":"2026-09-11T16:09:37Z","timestamp":1789142977000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=ao-65-15-G96"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,21]]},"references-count":50,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/ao.589275","relation":{},"ISSN":["1559-128X","2155-3165"],"issn-type":[{"value":"1559-128X","type":"print"},{"value":"2155-3165","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,21]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/AO.589275","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":"5 January 2026","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"31 March 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"21 April 2026","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2026 Optica Publishing Group. All rights, including\n\t\t\t\t\tfor text and data mining (TDM), Artificial Intelligence (AI) training,\n\t\t\t\t\tand similar technologies, are reserved.","name":"copyright","label":"Copyright"}]}}