{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T20:03:03Z","timestamp":1790280183324,"version":"4.1.0"},"reference-count":40,"publisher":"Optica Publishing Group","issue":"20","license":[{"start":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T00:00:00Z","timestamp":1790208000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T00:00:00Z","timestamp":1790208000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62475122"],"award-info":[{"award-number":["62475122"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Young Scientists Fund of the National Natural Science Foundation of China","award":["62005271"],"award-info":[{"award-number":["62005271"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2026,10,5]]},"abstract":"<jats:p>To address the limited convergence accuracy in the computer-aided alignment of projection objectives caused by interferometric measurement noise, this study proposes a hierarchical denoising algorithm that integrates non-centered truncated singular value decomposition (SVD) with robust principal component analysis (RPCA). Dense noise is first reduced by applying truncated SVD directly to the repeated-measurement matrix acquired at each field, without row-wise centering or subsequent mean restoration. The field-wise estimates reconstructed from the retained singular components are then concatenated into a multi-field Zernike coefficient matrix, after which RPCA is used to separate the dominant low-rank aberration structure from sparse outliers. The refined matrix is finally embedded into the CAA workflow. The proposed method was numerically validated through Monte Carlo simulations on a DUV lithographic projection-objective design with NA\u2009=\u20091.2, which was used as a numerical proof-of-concept test case. At the nominal noise level, the mean field-averaged RMS wavefront error decreased from 0.020259\u2009\u00b1\u20090.001285\u03bb without denoising to 0.020013\u2009\u00b1\u20090.001283\u03bb after denoising, an absolute reduction of 0.000246\u03bb. Relative to the noise-free mean of 0.019997\u03bb, this reduction corresponds to suppression of approximately93.89% of the noise-induced degradation. Across noise levels from 1\u00d7 to 3\u00d7 the nominal level, the degradation-suppression ratio remained approximately 66.93%\u201393.89% for the investigated projection-objective model.<\/jats:p>","DOI":"10.1364\/oe.606273","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T04:00:08Z","timestamp":1789358408000},"page":"37432","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Joint robust principal component analysis and truncated-SVD denoising algorithm for computer-aided alignment of projection lens"],"prefix":"10.1364","volume":"34","author":[{"given":"Zheng","family":"Qingqing","sequence":"first","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Applied Optics"},{"name":"Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shangnan","family":"Zhao","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Applied Optics"},{"name":"Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-1880-9051","authenticated-orcid":true,"given":"Haokun","family":"Ye","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Applied Optics"},{"name":"Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaxuan","family":"Hui","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Applied Optics"},{"name":"Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guangwei","family":"Shi","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Applied Optics"},{"name":"Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Applied Optics"},{"name":"Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,9,24]]},"reference":[{"key":"oe-34-20-37432-R1","author":"Born","year":"1980"},{"key":"oe-34-20-37432-R2","author":"Levinson","year":"2010"},{"key":"oe-34-20-37432-R3","doi-asserted-by":"publisher","first-page":"942604","DOI":"10.1117\/12.2086357","type":"journal-article","volume":"9426","author":"Flagello","year":"2015","journal-title":"Proc. SPIE."},{"key":"oe-34-20-37432-R4","doi-asserted-by":"publisher","first-page":"14267","DOI":"10.1364\/OE.26.014267","type":"journal-article","volume":"26","author":"Zhang","year":"2018","journal-title":"Opt. Express"},{"key":"oe-34-20-37432-R5","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1016\/j.optcom.2016.06.002","type":"journal-article","volume":"380","author":"Zhu","year":"2016","journal-title":"Opt. Commun."},{"key":"oe-34-20-37432-R6","doi-asserted-by":"publisher","first-page":"773","DOI":"10.1364\/OL.25.000773","type":"journal-article","volume":"25","author":"Shirai","year":"2000","journal-title":"Opt. Lett."},{"key":"oe-34-20-37432-R7","doi-asserted-by":"publisher","first-page":"1954","DOI":"10.1364\/AO.39.001954","type":"journal-article","volume":"39","author":"Hernandez-Gomez","year":"2000","journal-title":"Appl. Opt."},{"key":"oe-34-20-37432-R8","doi-asserted-by":"publisher","first-page":"763","DOI":"10.5768\/JAO202344.0401009","type":"journal-article","volume":"44","author":"Liu","year":"2023","journal-title":"Journal of Applied Optics"},{"key":"oe-34-20-37432-R9","doi-asserted-by":"publisher","first-page":"109370","DOI":"10.1016\/j.optlaseng.2025.109370","type":"journal-article","volume":"196","author":"Lei","year":"2026","journal-title":"Opt. Lasers Eng."},{"key":"oe-34-20-37432-R10","doi-asserted-by":"publisher","first-page":"802","DOI":"10.37188\/OPE.20223007.0802","type":"journal-article","volume":"30","author":"Luo","year":"2022","journal-title":"Opt. Precis. Eng."},{"key":"oe-34-20-37432-R11","doi-asserted-by":"publisher","first-page":"4853","DOI":"10.1109\/JLT.2021.3075781","type":"journal-article","volume":"39","author":"Plotnikov","year":"2021","journal-title":"J. Lightwave Technol."},{"key":"oe-34-20-37432-R12","doi-asserted-by":"publisher","first-page":"1647","DOI":"10.1109\/JQE.1982.1071416","type":"journal-article","volume":"18","author":"Dandridge","year":"1982","journal-title":"IEEE J. Quantum Electron."},{"key":"oe-34-20-37432-R13","doi-asserted-by":"publisher","first-page":"4976","DOI":"10.1016\/j.ijleo.2013.03.033","type":"journal-article","volume":"124","author":"Lin","year":"2013","journal-title":"Optik"},{"key":"oe-34-20-37432-R14","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1016\/j.optlaseng.2019.01.010","type":"journal-article","volume":"118","author":"Ren","year":"2019","journal-title":"Opt. Lasers Eng."},{"key":"oe-34-20-37432-R15","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-34-20-37432-R16","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1016\/j.optcom.2018.08.076","type":"journal-article","volume":"431","author":"Zhu","year":"2019","journal-title":"Opt. Commun."},{"key":"oe-34-20-37432-R17","first-page":"349","article-title":"Phase-measurement interferometry techniques","volume":"26","author":"CreathWolf","year":"1988"},{"key":"oe-34-20-37432-R18","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1364\/AO.35.001015","type":"journal-article","volume":"35","author":"Evans","year":"1996","journal-title":"Appl. Opt."},{"key":"oe-34-20-37432-R19","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1038\/s41377-022-00714-x","type":"journal-article","volume":"11","author":"Zuo","year":"2022","journal-title":"Light:Sci. Appl."},{"key":"oe-34-20-37432-R20","doi-asserted-by":"publisher","first-page":"16436","DOI":"10.1364\/OE.20.016436","type":"journal-article","volume":"20","author":"Gray","year":"2012","journal-title":"Opt. Express"},{"key":"oe-34-20-37432-R21","doi-asserted-by":"publisher","first-page":"1389","DOI":"10.1364\/JOSAA.22.001389","type":"journal-article","volume":"22","author":"Thompson","year":"2005","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-34-20-37432-R22","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1364\/JOSAA.28.000096","type":"journal-article","volume":"28","author":"Matsuzawa","year":"2011","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-34-20-37432-R23","doi-asserted-by":"publisher","first-page":"1213","DOI":"10.1364\/JOSAA.30.001213","type":"journal-article","volume":"30","author":"Braat","year":"2013","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-34-20-37432-R24","doi-asserted-by":"publisher","first-page":"26585","DOI":"10.1364\/OE.22.026585","type":"journal-article","volume":"22","author":"Fuerschbach","year":"2014","journal-title":"Opt. Express"},{"key":"oe-34-20-37432-R25","doi-asserted-by":"publisher","first-page":"2115","DOI":"10.1364\/JOSAA.36.002115","type":"journal-article","volume":"36","author":"Schiesser","year":"2019","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-34-20-37432-R26","doi-asserted-by":"publisher","first-page":"130696","DOI":"10.1016\/j.optcom.2024.130696","type":"journal-article","volume":"565","author":"Wan","year":"2024","journal-title":"Opt. Commun."},{"key":"oe-34-20-37432-R27","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/j.optcom.2014.05.003","type":"journal-article","volume":"329","author":"Yan","year":"2014","journal-title":"Opt. Commun."},{"key":"oe-34-20-37432-R28","doi-asserted-by":"publisher","first-page":"109783","DOI":"10.1016\/j.sigpro.2024.109783","type":"journal-article","volume":"229","author":"Ma","year":"2025","journal-title":"Signal Processing"},{"key":"oe-34-20-37432-R29","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1007\/s11222-013-9444-y","type":"journal-article","volume":"25","author":"Verbanck","year":"2015","journal-title":"Stat. Comput."},{"key":"oe-34-20-37432-R30","doi-asserted-by":"publisher","first-page":"1405","DOI":"10.1007\/s11760-019-01489-2","type":"journal-article","volume":"13","author":"Routray","year":"2019","journal-title":"Signal Image Video Process."},{"key":"oe-34-20-37432-R31","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1186\/1475-925X-13-112","type":"journal-article","volume":"13","author":"Ai","year":"2014","journal-title":"BioMed. Eng. OnLine"},{"key":"oe-34-20-37432-R32","doi-asserted-by":"publisher","first-page":"119634","DOI":"10.1016\/j.neuroimage.2022.119634","type":"journal-article","volume":"263","author":"Mosso","year":"2022","journal-title":"NeuroImage"},{"key":"oe-34-20-37432-R33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1162\/imag_a_00049","type":"journal-article","volume":"1","author":"Henriques","year":"2023","journal-title":"Imaging Neurosci."},{"key":"oe-34-20-37432-R34","doi-asserted-by":"publisher","first-page":"5837","DOI":"10.1109\/TSP.2019.2946026","type":"journal-article","volume":"67","author":"Liu","year":"2019","journal-title":"IEEE Trans. Signal Process."},{"key":"oe-34-20-37432-R35","doi-asserted-by":"publisher","first-page":"130746","DOI":"10.1016\/j.optcom.2024.130746","type":"journal-article","volume":"569","author":"Liu","year":"2024","journal-title":"Opt. Commun."},{"key":"oe-34-20-37432-R36","doi-asserted-by":"publisher","first-page":"111779","DOI":"10.1016\/j.optlastec.2024.111779","type":"journal-article","volume":"181","author":"Kim","year":"2025","journal-title":"Opt. Laser Technol."},{"key":"oe-34-20-37432-R37","doi-asserted-by":"publisher","first-page":"5059","DOI":"10.1364\/OE.15.005059","type":"journal-article","volume":"15","author":"Kim","year":"2007","journal-title":"Opt. Express"},{"key":"oe-34-20-37432-R38","doi-asserted-by":"publisher","first-page":"2595","DOI":"10.3788\/OPE.20152309.2595","type":"journal-article","volume":"23","author":"Gu","year":"2015","journal-title":"Opt. Precis. Eng."},{"key":"oe-34-20-37432-R39","doi-asserted-by":"publisher","first-page":"649","DOI":"10.3969\/j.issn.1007-5461.2024.04.009","type":"journal-article","volume":"41","author":"Zuo","year":"2024","journal-title":"Chin. J. Quantum Electron."},{"key":"oe-34-20-37432-R40","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1970392.1970395","type":"journal-article","volume":"58","author":"Cand\u00e8s","year":"2011","journal-title":"J. ACM"}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-34-20-37432&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T19:40:22Z","timestamp":1790278822000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-34-20-37432"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,24]]},"references-count":40,"journal-issue":{"issue":"20","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.606273","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,24]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.606273","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":"28 May 2026","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"10 September 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"24 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"}]}}