{"id":"https://openalex.org/W2007753807","doi":"https://doi.org/10.1364/oe.22.022031","title":"Robust solution to the inverse problem in optical scatterometry","display_name":"Robust solution to the inverse problem in optical scatterometry","publication_year":2014,"publication_date":"2014-09-03","ids":{"openalex":"https://openalex.org/W2007753807","doi":"https://doi.org/10.1364/oe.22.022031","mag":"2007753807","pmid":"https://pubmed.ncbi.nlm.nih.gov/25321577"},"language":"en","primary_location":{"id":"doi:10.1364/oe.22.022031","doi":"https://doi.org/10.1364/oe.22.022031","is_oa":true,"landing_page_url":"https://doi.org/10.1364/oe.22.022031","pdf_url":null,"source":{"id":"https://openalex.org/S178776955","display_name":"Optics Express","issn_l":"1094-4087","issn":["1094-4087"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","ki-jl-1","medline","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315679","host_organization_name":"Optica Publishing Group","host_organization_lineage":["https://openalex.org/P4310315679"],"host_organization_lineage_names":["Optica Publishing Group"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optics Express","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1364/oe.22.022031","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061733763","display_name":"Jinlong Zhu","orcid":"https://orcid.org/0000-0002-5723-2879","observed_orcids":["https://orcid.org/0000-0002-5723-2879"]},"institutions":[{"id":"https://openalex.org/I4210138186","display_name":"Wuhan National Laboratory for Optoelectronics","ror":"https://ror.org/03c9ncn37","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210138186"]},{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinlong Zhu","raw_affiliation_strings":["Wuhan National Laboratory for Optoelectronics,  Huazhong University of Science & Technology,  Wuhan 430074,  China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wuhan National Laboratory for Optoelectronics,  Huazhong University of Science & Technology,  Wuhan 430074,  China","institution_ids":["https://openalex.org/I4210138186","https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100327227","display_name":"Shiyuan Liu","orcid":"https://orcid.org/0000-0002-0756-1439","observed_orcids":["https://orcid.org/0000-0002-0756-1439","https://orcid.org/0009-0006-0425-6531"]},"institutions":[{"id":"https://openalex.org/I4210138186","display_name":"Wuhan National Laboratory for Optoelectronics","ror":"https://ror.org/03c9ncn37","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210138186"]},{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shiyuan Liu","raw_affiliation_strings":["Wuhan National Laboratory for Optoelectronics,  Huazhong University of Science & Technology,  Wuhan 430074,  China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wuhan National Laboratory for Optoelectronics,  Huazhong University of Science & Technology,  Wuhan 430074,  China","institution_ids":["https://openalex.org/I4210138186","https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072683076","display_name":"Xiuguo Chen","orcid":"https://orcid.org/0000-0002-7067-5084","observed_orcids":["https://orcid.org/0000-0002-7067-5084"]},"institutions":[{"id":"https://openalex.org/I4210138186","display_name":"Wuhan National Laboratory for Optoelectronics","ror":"https://ror.org/03c9ncn37","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210138186"]},{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiuguo Chen","raw_affiliation_strings":["Wuhan National Laboratory for Optoelectronics,  Huazhong University of Science & Technology,  Wuhan 430074,  China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wuhan National Laboratory for Optoelectronics,  Huazhong University of Science & Technology,  Wuhan 430074,  China","institution_ids":["https://openalex.org/I4210138186","https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100737589","display_name":"Chuanwei Zhang","orcid":"https://orcid.org/0000-0002-0344-6847","observed_orcids":["https://orcid.org/0000-0002-0344-6847"]},"institutions":[{"id":"https://openalex.org/I4391767905","display_name":"State Key Laboratory of Digital Manufacturing Equipment and Technology","ror":"https://ror.org/004z1wz18","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4391767905","https://openalex.org/I47720641"]},{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuanwei Zhang","raw_affiliation_strings":["State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science & Technology, Wuhan 430074, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science & Technology, Wuhan 430074, China#TAB#","institution_ids":["https://openalex.org/I4391767905","https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053570676","display_name":"Hao Jiang","orcid":"https://orcid.org/0000-0003-0561-5058","observed_orcids":["https://orcid.org/0000-0003-0561-5058","https://orcid.org/0009-0000-5435-5198","https://orcid.org/0009-0002-7372-3245"]},"institutions":[{"id":"https://openalex.org/I4391767905","display_name":"State Key Laboratory of Digital Manufacturing Equipment and Technology","ror":"https://ror.org/004z1wz18","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4391767905","https://openalex.org/I47720641"]},{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao Jiang","raw_affiliation_strings":["State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science & Technology, Wuhan 430074, China#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science & Technology, Wuhan 430074, China#TAB#","institution_ids":["https://openalex.org/I4391767905","https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2270,"currency":"USD","value_usd":2270},"apc_paid":{"value":2270,"currency":"USD","value_usd":2270},"fwci":5.722,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.95392491,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":"22","issue":"18","first_page":"22031","last_page":"22031"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13049","display_name":"Surface Roughness and Optical Measurements","score":0.4343000054359436,"subfield":{"id":"https://openalex.org/subfields/3105","display_name":"Instrumentation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13049","display_name":"Surface Roughness and Optical Measurements","score":0.4343000054359436,"subfield":{"id":"https://openalex.org/subfields/3105","display_name":"Instrumentation"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12050","display_name":"Optical Polarization and Ellipsometry","score":0.38839998841285706,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference techniques","score":0.027799999341368675,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/optical-scatterometry","display_name":"optical scatterometry","score":0.9990000128746033},{"id":"https://openalex.org/keywords/inverse-problems","display_name":"inverse problems","score":0.9509999752044678},{"id":"https://openalex.org/keywords/robust-estimation","display_name":"robust estimation","score":0.9890000224113464},{"id":"https://openalex.org/keywords/robust-regression","display_name":"robust regression","score":0.8180000185966492},{"id":"https://openalex.org/keywords/gauss-newton-method","display_name":"Gauss-Newton method","score":0.8009999990463257},{"id":"https://openalex.org/keywords/measurement-error-distribution","display_name":"measurement error distribution","score":0.7699999809265137},{"id":"https://openalex.org/keywords/non-normal-errors","display_name":"non-normal errors","score":0.5680000185966492},{"id":"https://openalex.org/keywords/parameter-estimation","display_name":"parameter estimation","score":0.5460000038146973},{"id":"https://openalex.org/keywords/least-squares","display_name":"least squares","score":0.4440000057220459}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.5583747029304504},{"id":"https://openalex.org/C19619285","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Observational error","level":2,"score":0.5378889441490173},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5140138864517212},{"id":"https://openalex.org/C69179731","wikidata":"https://www.wikidata.org/wiki/Q510427","display_name":"Point spread function","level":2,"score":0.5090743899345398},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.495230108499527},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4881380498409271},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4626854658126831},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.45680636167526245},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4215671718120575},{"id":"https://openalex.org/C70259352","wikidata":"https://www.wikidata.org/wiki/Q1847839","display_name":"Robust regression","level":3,"score":0.4151343107223511},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3063529431819916},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2500442564487457},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.24731257557868958},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18878567218780518},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1610342562198639},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.1426641047000885},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1364/oe.22.022031","doi":"https://doi.org/10.1364/oe.22.022031","is_oa":true,"landing_page_url":"https://doi.org/10.1364/oe.22.022031","pdf_url":null,"source":{"id":"https://openalex.org/S178776955","display_name":"Optics Express","issn_l":"1094-4087","issn":["1094-4087"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","ki-jl-1","medline","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315679","host_organization_name":"Optica Publishing Group","host_organization_lineage":["https://openalex.org/P4310315679"],"host_organization_lineage_names":["Optica Publishing Group"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optics Express","raw_type":"journal-article"},{"id":"pmid:25321577","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/25321577","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optics express","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1364/oe.22.022031","doi":"https://doi.org/10.1364/oe.22.022031","is_oa":true,"landing_page_url":"https://doi.org/10.1364/oe.22.022031","pdf_url":null,"source":{"id":"https://openalex.org/S178776955","display_name":"Optics Express","issn_l":"1094-4087","issn":["1094-4087"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-b","jufo-1","ki-jl-1","medline","norway-2","oarl","poland-140","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310315679","host_organization_name":"Optica Publishing Group","host_organization_lineage":["https://openalex.org/P4310315679"],"host_organization_lineage_names":["Optica Publishing Group"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optics Express","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4768211178","display_name":"\u57fa\u4e8e\u7ea2\u5916\u692d\u504f\u5149\u8c31\u7684\u9ad8\u6df1\u5bbd\u6bd4\u6df1\u6c9f\u69fd\u7ed3\u6784\u4fa7\u58c1\u5f62\u8c8c\u53c2\u6570\u6d4b\u91cf\u65b9\u6cd5\u7814\u7a76","funder_award_id":"51005091","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6372879777","display_name":null,"funder_award_id":"91023032","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1969934303","https://openalex.org/W1972046412","https://openalex.org/W1976806571","https://openalex.org/W1978107582","https://openalex.org/W1981933992","https://openalex.org/W1982263471","https://openalex.org/W2000863540","https://openalex.org/W2002190158","https://openalex.org/W2005524104","https://openalex.org/W2011579277","https://openalex.org/W2020143495","https://openalex.org/W2033894760","https://openalex.org/W2041135952","https://openalex.org/W2049719810","https://openalex.org/W2054506893","https://openalex.org/W2058063661","https://openalex.org/W2060612859","https://openalex.org/W2068861059","https://openalex.org/W2091690626","https://openalex.org/W2093037713","https://openalex.org/W2094285478","https://openalex.org/W2095398919","https://openalex.org/W2098097464","https://openalex.org/W2098558728","https://openalex.org/W2102080816","https://openalex.org/W2102154648","https://openalex.org/W2105865079","https://openalex.org/W2119952300","https://openalex.org/W2128074892","https://openalex.org/W2132360712","https://openalex.org/W2315139372","https://openalex.org/W4241745315","https://openalex.org/W4294373530"],"related_works":["https://openalex.org/W2002719740","https://openalex.org/W2291754240","https://openalex.org/W2732254308","https://openalex.org/W2053674240","https://openalex.org/W160786866","https://openalex.org/W979240671","https://openalex.org/W1981933992","https://openalex.org/W1969934303","https://openalex.org/W1989841893","https://openalex.org/W7034210734"],"abstract_inverted_index":{"In":[0,87],"optical":[1,85],"scatterometry,":[2],"the":[3,12,17,20,29,32,45,59,74,97,105,117,123,128,139],"least":[4],"squares":[5],"(LSQ)":[6],"function":[7,14,77],"is":[8,26,52,82,114],"usually":[9],"used":[10,83,115],"as":[11],"objective":[13],"to":[15,102,126],"quantify":[16],"difference":[18],"between":[19],"calculated":[21],"and":[22,135],"measured":[23],"signatures,":[24],"which":[25],"based":[27,78,95],"on":[28,96],"belief":[30],"that":[31],"actual":[33],"measurement":[34,50],"errors":[35,51,56],"are":[36],"normally":[37],"distributed":[38,107],"with":[39,104],"zero":[40],"mean.":[41],"However,":[42],"in":[43,84],"practice":[44],"normal":[46],"distribution":[47],"assumption":[48],"of":[49,62,99,119,122,141],"oversimplified":[53],"since":[54],"these":[55],"come":[57],"from":[58],"superimposed":[60],"effect":[61],"different":[63],"error":[64],"sources.":[65],"Biased":[66],"or":[67],"inaccurate":[68],"results":[69],"may":[70],"be":[71],"induced":[72],"when":[73],"traditional":[75],"LSQ":[76],"Gauss-Newton":[79],"(GN)":[80],"method":[81,94,125],"scatterometry.":[86],"this":[88],"paper,":[89],"we":[90],"propose":[91],"a":[92],"robust":[93,100,111],"principle":[98],"estimation":[101],"deal":[103],"abnormal":[106],"errors.":[108],"An":[109],"additional":[110],"regression":[112],"procedure":[113],"at":[116],"end":[118],"each":[120],"iteration":[121],"GN":[124],"obtain":[127],"more":[129],"accurate":[130],"parameter":[131],"departure":[132],"vector.":[133],"Simulations":[134],"experiments":[136],"have":[137],"demonstrated":[138],"feasibility":[140],"our":[142],"proposed":[143],"method.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":6}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}