{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T02:54:01Z","timestamp":1787021641288,"version":"build-2736575974"},"reference-count":26,"publisher":"Optica Publishing Group","issue":"24","license":[{"start":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T00:00:00Z","timestamp":1637280000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v1#VOR-OA"},{"start":{"date-parts":[[2021,11,19]],"date-time":"2021-11-19T00:00:00Z","timestamp":1637280000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/100000151","name":"Division of Industrial Innovation and Partnerships","doi-asserted-by":"publisher","award":["1338877"],"award-info":[{"award-number":["1338877"]}],"id":[{"id":"10.13039\/100000151","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000151","name":"Division of Industrial Innovation and Partnerships","doi-asserted-by":"publisher","award":["1338898"],"award-info":[{"award-number":["1338898"]}],"id":[{"id":"10.13039\/100000151","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000151","name":"Division of Industrial Innovation and Partnerships","doi-asserted-by":"publisher","award":["1822026"],"award-info":[{"award-number":["1822026"]}],"id":[{"id":"10.13039\/100000151","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000151","name":"Division of Industrial Innovation and Partnerships","doi-asserted-by":"publisher","award":["1822049"],"award-info":[{"award-number":["1822049"]}],"id":[{"id":"10.13039\/100000151","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2021,11,22]]},"abstract":"<jats:p>Imaging depth of field is shallow in applications with high magnification and high numerical aperture, such as microscopy, resulting in images with in- and out-of-focus regions. Therefore, methods to extend depth of field are of particular interest. Researchers have previously shown the advantages of using freeform components to extend depth of field, with each optical system requiring a specially designed phase plate. In this paper we present a method to enable extended depth-of-field imaging for a range of numerical apertures using freeform phase plates to create variable cubic wavefronts. The concept is similar to an Alvarez lens which creates variable spherical wavefronts through the relative translation of two transmissive elements with XY polynomial surfaces. We discuss design and optimization methods to enable extended depth of field for lenses with different numerical aperture values by considering through-focus variation of the point spread function and compare on- and off-axis performance through multiple metrics.<\/jats:p>","DOI":"10.1364\/oe.439980","type":"journal-article","created":{"date-parts":[[2021,11,10]],"date-time":"2021-11-10T03:30:16Z","timestamp":1636515016000},"page":"40524","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Freeform optics for variable extended depth of field imaging"],"prefix":"10.1364","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4523-4631","authenticated-orcid":true,"given":"Sara","family":"Moein","sequence":"first","affiliation":[{"name":"University of North Carolina at Charlotte"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas J.","family":"Suleski","sequence":"additional","affiliation":[{"name":"University of North Carolina at Charlotte"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2021,11,19]]},"reference":[{"key":"oe-29-24-40524-R1","first-page":"41","author":"Tkaczyk","year":"2010"},{"key":"oe-29-24-40524-R3","doi-asserted-by":"publisher","first-page":"1859","DOI":"10.1364\/AO.34.001859","volume":"34","author":"Dowski","year":"1995","journal-title":"Appl. Opt."},{"key":"oe-29-24-40524-R4","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1364\/OL.26.000875","volume":"26","author":"Chi","year":"2001","journal-title":"Opt. Lett."},{"key":"oe-29-24-40524-R5","doi-asserted-by":"publisher","first-page":"1304","DOI":"10.1080\/09500340903082689","volume":"56","author":"Zhai","year":"2009","journal-title":"J. Mod. Opt."},{"key":"oe-29-24-40524-R6","doi-asserted-by":"publisher","first-page":"2244","DOI":"10.1364\/AO.54.002244","volume":"54","author":"Zahreddine","year":"2015","journal-title":"Appl. Opt."},{"key":"oe-29-24-40524-R7","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1364\/OL.42.000995","volume":"42","author":"Shain","year":"2017","journal-title":"Opt. Lett."},{"key":"oe-29-24-40524-R8","doi-asserted-by":"publisher","first-page":"6895","DOI":"10.1364\/AO.47.006895","volume":"47","author":"Chu","year":"2008","journal-title":"Appl. Opt."},{"key":"oe-29-24-40524-R9","doi-asserted-by":"publisher","first-page":"60900N","DOI":"10.1117\/12.647022","volume":"6090","author":"Abrahamsson","year":"2006","journal-title":"Proc. SPIE"},{"key":"oe-29-24-40524-R11","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1364\/OPTICA.413762","volume":"8","author":"Rolland","year":"2021","journal-title":"Optica"},{"key":"oe-29-24-40524-R12","doi-asserted-by":"publisher","first-page":"8207","DOI":"10.1364\/OE.18.008207","volume":"18","author":"Demenikov","year":"2010","journal-title":"Opt. Express"},{"key":"oe-29-24-40524-R13","doi-asserted-by":"publisher","first-page":"21118","DOI":"10.1364\/OE.17.021118","volume":"17","author":"Muyo","year":"2009","journal-title":"Opt. Express"},{"key":"oe-29-24-40524-R14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1117\/12.487572","volume":"5108","author":"Prasad","year":"2003","journal-title":"Proc. SPIE"},{"key":"oe-29-24-40524-R15","doi-asserted-by":"publisher","first-page":"1878","DOI":"10.1364\/OE.20.001878","volume":"20","author":"Somayaji","year":"2012","journal-title":"Opt. Express"},{"key":"oe-29-24-40524-R16","doi-asserted-by":"publisher","first-page":"2709","DOI":"10.1364\/AO.43.002709","volume":"43","author":"Sherif","year":"2004","journal-title":"Appl. Opt."},{"key":"oe-29-24-40524-R17","doi-asserted-by":"publisher","first-page":"1171","DOI":"10.1364\/OL.33.001171","volume":"33","author":"Zhao","year":"2008","journal-title":"Opt. Lett."},{"key":"oe-29-24-40524-R18","doi-asserted-by":"publisher","first-page":"2100","DOI":"10.1364\/OL.35.002100","volume":"35","author":"Demenikov","year":"2010","journal-title":"Opt. Lett."},{"key":"oe-29-24-40524-R19","doi-asserted-by":"publisher","first-page":"2574","DOI":"10.1364\/OPEX.12.002574","volume":"12","author":"Rege","year":"2004","journal-title":"Opt. Express"},{"key":"oe-29-24-40524-R21","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1364\/AO.38.000086","volume":"38","author":"Palusinski","year":"1999","journal-title":"Appl. Opt."},{"key":"oe-29-24-40524-R22","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1117\/12.354625","volume":"3705","author":"Mitchell","year":"1999","journal-title":"Proc. SPIE"},{"key":"oe-29-24-40524-R23","doi-asserted-by":"publisher","first-page":"4170","DOI":"10.1364\/OL.36.004170","volume":"36","author":"Smilie","year":"2011","journal-title":"Opt. Lett."},{"key":"oe-29-24-40524-R24","doi-asserted-by":"publisher","first-page":"91940K","DOI":"10.1117\/12.2062986","volume":"9194","author":"Suleski","year":"2014","journal-title":"Proc. SPIE"},{"key":"oe-29-24-40524-R25","doi-asserted-by":"publisher","first-page":"15627","DOI":"10.1364\/OE.27.015627","volume":"27","author":"Wilson","year":"2019","journal-title":"Opt. Express"},{"key":"oe-29-24-40524-R26","doi-asserted-by":"publisher","first-page":"596215","DOI":"10.1117\/12.622699","volume":"5962","author":"Hellmuth","year":"2005","journal-title":"Proc. SPIE"},{"key":"oe-29-24-40524-R27","doi-asserted-by":"publisher","first-page":"1669","DOI":"10.1364\/AO.9.001669","volume":"9","author":"Lohmann","year":"1970","journal-title":"Appl. Opt."},{"key":"oe-29-24-40524-R29","doi-asserted-by":"publisher","first-page":"25551","DOI":"10.1364\/OE.27.025551","volume":"27","author":"Aryan","year":"2019","journal-title":"Opt. Express"},{"key":"oe-29-24-40524-R30","doi-asserted-by":"publisher","first-page":"114830G","DOI":"10.1117\/12.2568723","volume":"11483","author":"Moein","year":"2020","journal-title":"Proc. SPIE"}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-29-24-40524","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-29-24-40524&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T15:28:16Z","timestamp":1722958096000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-29-24-40524"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,19]]},"references-count":26,"journal-issue":{"issue":"24","published-online":{"date-parts":[[2021]]},"published-print":{"date-parts":[[2021]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.439980","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,19]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.439980","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":"25 August 2021","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"9 November 2021","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"19 November 2021","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement","name":"copyright","label":"Copyright"}]}}