{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T11:06:00Z","timestamp":1785409560579,"version":"3.56.0"},"reference-count":19,"publisher":"Optica Publishing Group","issue":"23","license":[{"start":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T00:00:00Z","timestamp":1669075200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T00:00:00Z","timestamp":1669075200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"DoD Ordnance Technology Consortium (DOTC) Other Transaction Agreement","award":["W15QKN-18-9-1008"],"award-info":[{"award-number":["W15QKN-18-9-1008"]}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Lett."],"published-print":{"date-parts":[[2022,12,1]]},"abstract":"<jats:p>\n                    Analytic closed form expressions for orthonormal polynomials exhibiting both rotational and Gaussian symmetries are derived for both circular and elliptical geometries. They exhibit a close correspondence to the Zernike polynomials but are of Gaussian shape and orthogonal over the (\n                    <jats:italic toggle=\"yes\">x<\/jats:italic>\n                    ,\n                    <jats:italic toggle=\"yes\">y<\/jats:italic>\n                    ) plane. Consequently, they may be expressed in terms of Laguerre polynomials. Formulas for calculating the centroid of a real function are also presented and, along with the analytic expressions for the polynomials, may prove to be of especial use in reconstruction of the intensity distribution incident on a Shack\u2013Hartmann wavefront sensor.\n                  <\/jats:p>","DOI":"10.1364\/ol.475979","type":"journal-article","created":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T16:00:30Z","timestamp":1667318430000},"page":"6137","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Zernike-like Laguerre\u2013Gaussian orthonormal polynomials for optical field reconstruction"],"prefix":"10.1364","volume":"47","author":[{"given":"Benjamin D.","family":"Strycker","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04q745m62","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2022,11,22]]},"reference":[{"key":"ol-47-23-6137-R1","author":"Malacara","year":"2007"},{"key":"ol-47-23-6137-R2","author":"Salverda","year":"2016"},{"key":"ol-47-23-6137-R3","doi-asserted-by":"publisher","first-page":"972","DOI":"10.1364\/JOSA.69.000972","volume":"69","author":"Cubalchini","year":"1979","journal-title":"J. Opt. Soc. Am."},{"key":"ol-47-23-6137-R4","doi-asserted-by":"publisher","first-page":"1604","DOI":"10.1364\/JOSAA.31.001604","volume":"31","author":"Janssen","year":"2014","journal-title":"J. Opt. Soc. Am. A"},{"key":"ol-47-23-6137-R5","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1364\/OSAC.1.000581","volume":"1","author":"Biesheuvel","year":"2018","journal-title":"OSA Continuum"},{"key":"ol-47-23-6137-R6","doi-asserted-by":"publisher","first-page":"1012","DOI":"10.1364\/AO.41.001012","volume":"41","author":"Barchers","year":"2002","journal-title":"Appl. Opt."},{"key":"ol-47-23-6137-R7","doi-asserted-by":"publisher","first-page":"4167","DOI":"10.1364\/OL.44.004167","volume":"44","author":"Akondi","year":"2019","journal-title":"Opt. Lett."},{"key":"ol-47-23-6137-R8","doi-asserted-by":"publisher","first-page":"1699","DOI":"10.1364\/OL.389895","volume":"45","author":"DuBose","year":"2020","journal-title":"Opt. Lett."},{"key":"ol-47-23-6137-R9","first-page":"221","author":"NavarroAwrejcewicz","year":"2011"},{"key":"ol-47-23-6137-R10","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/0021-9991(92)90211-G","volume":"99","author":"Chin","year":"1992","journal-title":"J. Comput. Phys."},{"key":"ol-47-23-6137-R11","doi-asserted-by":"publisher","first-page":"8057","DOI":"10.1364\/AO.34.008057","volume":"34","author":"Mahajan","year":"1995","journal-title":"Appl. Opt."},{"key":"ol-47-23-6137-R12","author":"Mahajan","year":"2001"},{"key":"ol-47-23-6137-R13","doi-asserted-by":"publisher","first-page":"2336","DOI":"10.1364\/AO.56.002336","volume":"56","author":"Mafusire","year":"2017","journal-title":"Appl. Opt."},{"key":"ol-47-23-6137-R14","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1080\/09500340.2020.1759712","volume":"67","author":"Mafusire","year":"2020","journal-title":"J. Mod. Opt."},{"key":"ol-47-23-6137-R15","doi-asserted-by":"publisher","first-page":"1312","DOI":"10.1109\/PROC.1966.5119","volume":"54","author":"Kogelnik","year":"1966","journal-title":"Proc. IEEE"},{"key":"ol-47-23-6137-R16","author":"Siegman","year":"1986"},{"key":"ol-47-23-6137-R17","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1017\/S0305004100029066","volume":"50","author":"Bhatia","year":"1954","journal-title":"Math. Proc. Camb. Phil. Soc."},{"key":"ol-47-23-6137-R18","author":"Born","year":"1980"},{"key":"ol-47-23-6137-R21","doi-asserted-by":"publisher","first-page":"SuC1","DOI":"10.1364\/vsia.2000.suc1","volume":"18","author":"Thibos","year":"2002","journal-title":"J. Refract. Surg."}],"container-title":["Optics Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=ol-47-23-6137&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T15:33:18Z","timestamp":1722958398000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=ol-47-23-6137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,22]]},"references-count":19,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2022]]},"published-print":{"date-parts":[[2022]]}},"URL":"https:\/\/doi.org\/10.1364\/ol.475979","relation":{},"ISSN":["0146-9592","1539-4794"],"issn-type":[{"value":"0146-9592","type":"print"},{"value":"1539-4794","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,22]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OL.475979","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"letter","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":"21 September 2022","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"31 October 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"22 November 2022","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2022 Optica Publishing Group","name":"copyright","label":"Copyright"}]}}