{"id":"https://openalex.org/W2080574330","doi":"https://doi.org/10.1631/jzus.c12a0116","title":"Optimized design of LED freeform lens for uniform circular illumination","display_name":"Optimized design of LED freeform lens for uniform circular illumination","publication_year":2012,"publication_date":"2012-12-01","ids":{"openalex":"https://openalex.org/W2080574330","doi":"https://doi.org/10.1631/jzus.c12a0116","mag":"2080574330"},"language":"en","primary_location":{"id":"doi:10.1631/jzus.c12a0116","is_oa":false,"landing_page_url":"https://doi.org/10.1631/jzus.c12a0116","pdf_url":null,"source":{"id":"https://openalex.org/S199067057","display_name":"Journal of Zhejiang University SCIENCE C","issn_l":"1869-1951","issn":["1869-1951","1869-196X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311937","host_organization_name":"Zhejiang University Press","host_organization_lineage":["https://openalex.org/P4310311937"],"host_organization_lineage_names":["Zhejiang University Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Zhejiang University SCIENCE C","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100346916","display_name":"Peng Liu","orcid":"https://orcid.org/0000-0003-4929-0531"},"institutions":[{"id":"https://openalex.org/I4391767668","display_name":"State Key Laboratory of Modern Optical Instruments","ror":"https://ror.org/018fpas51","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767668","https://openalex.org/I76130692"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Peng Liu","raw_affiliation_strings":["State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","Zhejiang, University"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","institution_ids":["https://openalex.org/I76130692","https://openalex.org/I4391767668"]},{"raw_affiliation_string":"Zhejiang, University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082305084","display_name":"Rengmao Wu","orcid":"https://orcid.org/0000-0001-9904-1600"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]},{"id":"https://openalex.org/I4391767668","display_name":"State Key Laboratory of Modern Optical Instruments","ror":"https://ror.org/018fpas51","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767668","https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Reng-mao Wu","raw_affiliation_strings":["State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","Zhejiang, University"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","institution_ids":["https://openalex.org/I76130692","https://openalex.org/I4391767668"]},{"raw_affiliation_string":"Zhejiang, University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063521420","display_name":"Zhenrong Zheng","orcid":"https://orcid.org/0000-0002-4586-6268"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]},{"id":"https://openalex.org/I4391767668","display_name":"State Key Laboratory of Modern Optical Instruments","ror":"https://ror.org/018fpas51","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767668","https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhen-rong Zheng","raw_affiliation_strings":["State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","Zhejiang, University"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","institution_ids":["https://openalex.org/I76130692","https://openalex.org/I4391767668"]},{"raw_affiliation_string":"Zhejiang, University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113663686","display_name":"Haifeng Li","orcid":"https://orcid.org/0000-0003-3593-5482"},"institutions":[{"id":"https://openalex.org/I4391767668","display_name":"State Key Laboratory of Modern Optical Instruments","ror":"https://ror.org/018fpas51","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767668","https://openalex.org/I76130692"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hai-feng Li","raw_affiliation_strings":["State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","Zhejiang, University"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","institution_ids":["https://openalex.org/I76130692","https://openalex.org/I4391767668"]},{"raw_affiliation_string":"Zhejiang, University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100331746","display_name":"X\u00fc Liu","orcid":"https://orcid.org/0000-0003-3982-3197"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]},{"id":"https://openalex.org/I4391767668","display_name":"State Key Laboratory of Modern Optical Instruments","ror":"https://ror.org/018fpas51","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767668","https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu Liu","raw_affiliation_strings":["State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","Zhejiang, University"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Modern Optical Instrumentation, Zhejiang University, Hangzhou, 310027, China","institution_ids":["https://openalex.org/I76130692","https://openalex.org/I4391767668"]},{"raw_affiliation_string":"Zhejiang, University","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100346916"],"corresponding_institution_ids":["https://openalex.org/I4391767668","https://openalex.org/I76130692"],"apc_list":null,"apc_paid":null,"fwci":1.5058,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.81666263,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"12","first_page":"929","last_page":"936"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11517","display_name":"Advanced optical system design","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11517","display_name":"Advanced optical system design","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11723","display_name":"Optical Coatings and Gratings","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/2508","display_name":"Surfaces, Coatings and Films"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11484","display_name":"Adaptive optics and wavefront sensing","score":0.9785000085830688,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/irradiance","display_name":"Irradiance","score":0.7948014736175537},{"id":"https://openalex.org/keywords/nonimaging-optics","display_name":"Nonimaging optics","score":0.680860161781311},{"id":"https://openalex.org/keywords/lens","display_name":"Lens (geology)","score":0.6397556066513062},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5718214511871338},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4788953363895416},{"id":"https://openalex.org/keywords/figure-of-merit","display_name":"Figure of merit","score":0.47013646364212036},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.4499378204345703},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.44016867876052856},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43045127391815186},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.42994609475135803},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34736305475234985},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2056843340396881},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13207116723060608}],"concepts":[{"id":"https://openalex.org/C46423501","wikidata":"https://www.wikidata.org/wiki/Q830654","display_name":"Irradiance","level":2,"score":0.7948014736175537},{"id":"https://openalex.org/C97546620","wikidata":"https://www.wikidata.org/wiki/Q1656807","display_name":"Nonimaging optics","level":2,"score":0.680860161781311},{"id":"https://openalex.org/C15336307","wikidata":"https://www.wikidata.org/wiki/Q1766051","display_name":"Lens (geology)","level":2,"score":0.6397556066513062},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5718214511871338},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4788953363895416},{"id":"https://openalex.org/C130277099","wikidata":"https://www.wikidata.org/wiki/Q3676605","display_name":"Figure of merit","level":2,"score":0.47013646364212036},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.4499378204345703},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.44016867876052856},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43045127391815186},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.42994609475135803},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34736305475234985},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2056843340396881},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13207116723060608},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1631/jzus.c12a0116","is_oa":false,"landing_page_url":"https://doi.org/10.1631/jzus.c12a0116","pdf_url":null,"source":{"id":"https://openalex.org/S199067057","display_name":"Journal of Zhejiang University SCIENCE C","issn_l":"1869-1951","issn":["1869-1951","1869-196X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311937","host_organization_name":"Zhejiang University Press","host_organization_lineage":["https://openalex.org/P4310311937"],"host_organization_lineage_names":["Zhejiang University Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Zhejiang University SCIENCE C","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8999999761581421,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1548879090","https://openalex.org/W1964054890","https://openalex.org/W1978801485","https://openalex.org/W1981312974","https://openalex.org/W1981867245","https://openalex.org/W1983157591","https://openalex.org/W1984322901","https://openalex.org/W1991438666","https://openalex.org/W1998195151","https://openalex.org/W1999350738","https://openalex.org/W2007405721","https://openalex.org/W2009031397","https://openalex.org/W2009350638","https://openalex.org/W2012076333","https://openalex.org/W2029016732","https://openalex.org/W2036094580","https://openalex.org/W2039242546","https://openalex.org/W2047138534","https://openalex.org/W2057039357","https://openalex.org/W2075252239","https://openalex.org/W2075842384","https://openalex.org/W2087928071","https://openalex.org/W2093205068","https://openalex.org/W2096860047","https://openalex.org/W2098947260","https://openalex.org/W2101499860","https://openalex.org/W2116948246","https://openalex.org/W2119963893","https://openalex.org/W2138308105","https://openalex.org/W2139692960","https://openalex.org/W2142601283","https://openalex.org/W2156170592","https://openalex.org/W2166378316","https://openalex.org/W2168463105","https://openalex.org/W2169993546","https://openalex.org/W4205649593"],"related_works":["https://openalex.org/W2147777774","https://openalex.org/W2055545425","https://openalex.org/W2072442315","https://openalex.org/W2175090515","https://openalex.org/W2494161373","https://openalex.org/W1986953717","https://openalex.org/W1963766749","https://openalex.org/W1802882460","https://openalex.org/W2056447465","https://openalex.org/W2970307332"],"abstract_inverted_index":{"An":[0,57],"optimization":[1,61,123],"method":[2,22,124],"is":[3,23,48,63,74,100],"proposed":[4],"for":[5,65],"designing":[6],"an":[7,52],"LED":[8],"freeform":[9,37,69,130],"lens":[10],"which":[11],"produces":[12],"a":[13,104,117],"uniform":[14],"circular":[15],"pattern":[16],"with":[17,103,132],"high":[18],"energy":[19],"efficiency.":[20],"This":[21,122],"composed":[24],"of":[25,30,35,41,59,67,78,85,111,114,120],"three":[26],"main":[27],"aspects:":[28],"design":[29,129],"the":[31,36,42,68,79,83,86,93,97],"initial":[32,46],"guess,":[33],"parameterization":[34,66],"surface,":[38],"and":[39,82,92,116],"construction":[40],"merit":[43,72],"function.":[44],"The":[45,71],"guess":[47],"created":[49],"by":[50,76],"solving":[51],"ordinary":[53],"differential":[54],"equation":[55],"numerically.":[56],"approach":[58],"selecting":[60],"points":[62],"introduced":[64],"surface.":[70],"function":[73],"constructed":[75],"use":[77],"irradiance":[80,98],"uniformity":[81,106],"efficiency":[84,119],"lens.":[87],"Design":[88],"examples":[89],"are":[90],"given,":[91],"results":[94],"show":[95],"that":[96],"distribution":[99],"well":[101],"controlled":[102],"maximum":[105,118],"(the":[107],"relative":[108],"standard":[109],"deviation":[110],"irradiance,":[112],"RSD)":[113],"0.0122":[115],"93.88%.":[121],"can":[125],"be":[126],"generalized":[127],"to":[128],"lenses":[131],"different":[133],"lighting":[134],"patterns":[135],"or":[136],"without":[137],"rotational":[138],"symmetry.":[139]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
