{"id":"https://openalex.org/W3048279772","doi":"https://doi.org/10.1155/2020/8833305","title":"A Multifrequency Heterodyne Phase Error Compensation Method for 3D Reconstruction","display_name":"A Multifrequency Heterodyne Phase Error Compensation Method for 3D Reconstruction","publication_year":2020,"publication_date":"2020-08-08","ids":{"openalex":"https://openalex.org/W3048279772","doi":"https://doi.org/10.1155/2020/8833305","mag":"3048279772"},"language":"en","primary_location":{"id":"doi:10.1155/2020/8833305","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/8833305","pdf_url":"https://downloads.hindawi.com/journals/js/2020/8833305.pdf","source":{"id":"https://openalex.org/S96783963","display_name":"Journal of Sensors","issn_l":"1687-725X","issn":["1687-725X","1687-7268"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Sensors","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/js/2020/8833305.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100324772","display_name":"Zihao Yu","orcid":"https://orcid.org/0000-0001-7847-3359"},"institutions":[{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zihao Yu","raw_affiliation_strings":["School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China","institution_ids":["https://openalex.org/I141962983"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100768073","display_name":"Jin Liu","orcid":"https://orcid.org/0000-0001-5607-9940"},"institutions":[{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jin Liu","raw_affiliation_strings":["School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China","institution_ids":["https://openalex.org/I141962983"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042290525","display_name":"Haima Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I148128674","display_name":"University of Shanghai for Science and Technology","ror":"https://ror.org/00ay9v204","country_code":"CN","type":"education","lineage":["https://openalex.org/I148128674"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haima Yang","raw_affiliation_strings":["School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China"],"affiliations":[{"raw_affiliation_string":"School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai, 200093, China","institution_ids":["https://openalex.org/I148128674"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101566619","display_name":"Bo Huang","orcid":"https://orcid.org/0000-0002-5476-620X"},"institutions":[{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bo Huang","raw_affiliation_strings":["School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China","institution_ids":["https://openalex.org/I141962983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063678712","display_name":"Yumei Jian","orcid":"https://orcid.org/0000-0002-2386-777X"},"institutions":[{"id":"https://openalex.org/I141962983","display_name":"Shanghai University of Engineering Science","ror":"https://ror.org/0557b9y08","country_code":"CN","type":"education","lineage":["https://openalex.org/I141962983"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yumei Jian","raw_affiliation_strings":["School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China"],"affiliations":[{"raw_affiliation_string":"School of Electronic and Electrical Engineering, Shanghai University of Engineering Science, Shanghai, 201600, China","institution_ids":["https://openalex.org/I141962983"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5042290525","https://openalex.org/A5100768073"],"corresponding_institution_ids":["https://openalex.org/I141962983","https://openalex.org/I148128674"],"apc_list":{"value":2100,"currency":"USD","value_usd":2100},"apc_paid":{"value":2100,"currency":"USD","value_usd":2100},"fwci":0.4907,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66140048,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"10"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference techniques","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10638","display_name":"Optical measurement and interference techniques","score":1.0,"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"}},{"id":"https://openalex.org/T11583","display_name":"Advanced Measurement and Metrology Techniques","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T11211","display_name":"3D Surveying and Cultural Heritage","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1907","display_name":"Geology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/absolute-phase","display_name":"Absolute phase","score":0.6985375285148621},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.6434227228164673},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.5878726243972778},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5058812499046326},{"id":"https://openalex.org/keywords/compensation","display_name":"Compensation (psychology)","score":0.4854465126991272},{"id":"https://openalex.org/keywords/flatness","display_name":"Flatness (cosmology)","score":0.48525524139404297},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4630124568939209},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.46200627088546753},{"id":"https://openalex.org/keywords/inflection-point","display_name":"Inflection point","score":0.4209698736667633},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.41819214820861816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3553975224494934},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18632817268371582},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1577530801296234},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13413399457931519}],"concepts":[{"id":"https://openalex.org/C2776521118","wikidata":"https://www.wikidata.org/wiki/Q4669823","display_name":"Absolute phase","level":3,"score":0.6985375285148621},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.6434227228164673},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5878726243972778},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5058812499046326},{"id":"https://openalex.org/C2780023022","wikidata":"https://www.wikidata.org/wiki/Q1338171","display_name":"Compensation (psychology)","level":2,"score":0.4854465126991272},{"id":"https://openalex.org/C2778530986","wikidata":"https://www.wikidata.org/wiki/Q5457948","display_name":"Flatness (cosmology)","level":3,"score":0.48525524139404297},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4630124568939209},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46200627088546753},{"id":"https://openalex.org/C74545648","wikidata":"https://www.wikidata.org/wiki/Q212794","display_name":"Inflection point","level":2,"score":0.4209698736667633},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41819214820861816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3553975224494934},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18632817268371582},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1577530801296234},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13413399457931519},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.0},{"id":"https://openalex.org/C11171543","wikidata":"https://www.wikidata.org/wiki/Q41630","display_name":"Psychoanalysis","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/8833305","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/8833305","pdf_url":"https://downloads.hindawi.com/journals/js/2020/8833305.pdf","source":{"id":"https://openalex.org/S96783963","display_name":"Journal of Sensors","issn_l":"1687-725X","issn":["1687-725X","1687-7268"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Sensors","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b6619606446245d5b1367918d0641da6","is_oa":true,"landing_page_url":"https://doaj.org/article/b6619606446245d5b1367918d0641da6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Sensors, Vol 2020 (2020)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2020/8833305","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/8833305","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2020/8833305","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2020/8833305","pdf_url":"https://downloads.hindawi.com/journals/js/2020/8833305.pdf","source":{"id":"https://openalex.org/S96783963","display_name":"Journal of Sensors","issn_l":"1687-725X","issn":["1687-725X","1687-7268"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Sensors","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G189434237","display_name":null,"funder_award_id":"61701296","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2145724792","display_name":null,"funder_award_id":"SAST2017-062","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G2597807520","display_name":null,"funder_award_id":"17ZR1443500","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3853251732","display_name":null,"funder_award_id":"U1831133","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4464522008","display_name":null,"funder_award_id":"17ZR1443500","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7709891450","display_name":null,"funder_award_id":"2017-06","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8101012413","display_name":null,"funder_award_id":"SAST2017-062","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G85131847","display_name":null,"funder_award_id":"61701296","funder_id":"https://openalex.org/F4320309612","funder_display_name":"Natural Science Foundation of Shanghai"}],"funders":[{"id":"https://openalex.org/F4320309612","display_name":"Natural Science Foundation of Shanghai","ror":null},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3048279772.pdf","grobid_xml":"https://content.openalex.org/works/W3048279772.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1999111172","https://openalex.org/W2008239695","https://openalex.org/W2013587578","https://openalex.org/W2031151076","https://openalex.org/W2058259863","https://openalex.org/W2067464987","https://openalex.org/W2090741960","https://openalex.org/W2092336945","https://openalex.org/W2345939069","https://openalex.org/W2441234261","https://openalex.org/W2512159635","https://openalex.org/W2782946773","https://openalex.org/W2789248836","https://openalex.org/W2808086381","https://openalex.org/W2999117695","https://openalex.org/W3022412239"],"related_works":["https://openalex.org/W2361205043","https://openalex.org/W2023911433","https://openalex.org/W2798126247","https://openalex.org/W2370760154","https://openalex.org/W2789295429","https://openalex.org/W2355513343","https://openalex.org/W2488531810","https://openalex.org/W2066314436","https://openalex.org/W2733767282","https://openalex.org/W2950363176"],"abstract_inverted_index":{"In":[0],"view":[1],"of":[2,5,12,33,52,63,71,89,102,112,127,150,157,179],"the":[3,9,13,25,30,34,40,43,46,50,64,69,74,85,90,98,103,108,113,131,137,144,155,158,162,187,197,205],"problem":[4],"\u201cjumping":[6],"points\u201d":[7],"in":[8,49],"phase":[10,48,54,59,72,82,87,110,128,168,173,190],"unwrapping":[11,83,111],"multifrequency":[14,26],"heterodyne":[15],"principle,":[16],"this":[17],"paper":[18],"proposes":[19],"a":[20,77,183],"novel":[21],"method":[22,134,206],"to":[23,96,141],"improve":[24],"heterodyne.":[27],"By":[28],"solving":[29],"root-mean-square":[31],"error":[32,44,138,163,199],"original":[35],"frequency":[36],"function,":[37],"it":[38,57],"includes":[39],"relationship":[41],"between":[42],"and":[45,56,84,107,196,209],"adjacent":[47],"condition":[51],"constrained":[53],"unwrapping,":[55,73],"compensates":[58],"<mml:math":[60],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[61],"id=\"M1\"><mml:mo>\u00b1</mml:mo><mml:mn>2</mml:mn><mml:mi>\u03c0</mml:mi></mml:math>":[62],"skip":[65],"point.":[66],"To":[67],"ensure":[68],"accuracy":[70],"function":[75,93,116],"with":[76,117,130,171,182],"\u201cjump":[78],"point\u201d":[79],"after":[80,167,189],"each":[81],"absolute":[86],"curve":[88],"principal":[91,114],"value":[92,115],"are":[94],"used":[95],"establish":[97],"threshold":[99],"judgment":[100],"model":[101],"least":[104],"square":[105],"method,":[106],"initial":[109],"different":[118],"frequencies":[119],"is":[120,139,192,200,207],"carried":[121],"out":[122],"continuously.":[123],"The":[124,147,175],"simulation":[125],"analysis":[126],"compensation":[129,169,191],"four-step":[132],"phase-shifting":[133],"shows":[135,160,185],"that":[136,161,186],"reduced":[140],"36%":[142],"under":[143],"set":[145],"environment.":[146],"experimental":[148],"result":[149],"3D":[151],"reconstruction":[152,177],"by":[153,165],"measuring":[154],"flatness":[156],"plate":[159],"decreases":[164],"41%":[166],"compared":[170],"before":[172],"compensation.":[174],"three-dimensional":[176],"experiment":[178],"pitch":[180,198],"measurement":[181],"nut":[184,188],"smooth":[193],"without":[194],"noise,":[195],"0.033":[201],"mm,":[202],"which":[203],"verified":[204],"workable":[208],"effective.":[210]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}
