{"id":"https://openalex.org/W3201081617","doi":"https://doi.org/10.3390/sym13091733","title":"Theoretical Modeling and Analysis of Directional Spectrum Emissivity and Its Pattern for Random Rough Surfaces with a Matrix Method","display_name":"Theoretical Modeling and Analysis of Directional Spectrum Emissivity and Its Pattern for Random Rough Surfaces with a Matrix Method","publication_year":2021,"publication_date":"2021-09-18","ids":{"openalex":"https://openalex.org/W3201081617","doi":"https://doi.org/10.3390/sym13091733","mag":"3201081617"},"language":"en","primary_location":{"id":"doi:10.3390/sym13091733","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091733","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1733/pdf?version=1631955407","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/9/1733/pdf?version=1631955407","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047242519","display_name":"Jianrui Hu","orcid":null},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianrui Hu","raw_affiliation_strings":["Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","School of Mechanical Engineering, Shandong University, Jinan 250061, China"],"affiliations":[{"raw_affiliation_string":"Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering, Shandong University, Jinan 250061, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100446655","display_name":"Zhanqiang Liu","orcid":"https://orcid.org/0000-0002-4790-0052"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhanqiang Liu","raw_affiliation_strings":["Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","School of Mechanical Engineering, Shandong University, Jinan 250061, China"],"affiliations":[{"raw_affiliation_string":"Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering, Shandong University, Jinan 250061, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101839034","display_name":"Jinfu Zhao","orcid":"https://orcid.org/0009-0000-6624-556X"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinfu Zhao","raw_affiliation_strings":["Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","School of Mechanical Engineering, Shandong University, Jinan 250061, China"],"affiliations":[{"raw_affiliation_string":"Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering, Shandong University, Jinan 250061, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100446673","display_name":"Bing Wang","orcid":"https://orcid.org/0000-0003-3662-7625"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bing Wang","raw_affiliation_strings":["Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","School of Mechanical Engineering, Shandong University, Jinan 250061, China"],"affiliations":[{"raw_affiliation_string":"Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering, Shandong University, Jinan 250061, China","institution_ids":["https://openalex.org/I154099455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050044011","display_name":"Qinghua Song","orcid":"https://orcid.org/0000-0002-9792-9988"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qinghua Song","raw_affiliation_strings":["Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","School of Mechanical Engineering, Shandong University, Jinan 250061, China"],"affiliations":[{"raw_affiliation_string":"Key National Demonstration Center for Experimental Mechanical Engineering Education/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China","institution_ids":[]},{"raw_affiliation_string":"School of Mechanical Engineering, Shandong University, Jinan 250061, China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5100446655"],"corresponding_institution_ids":["https://openalex.org/I154099455"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5315,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.61474107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"13","issue":"9","first_page":"1733","last_page":"1733"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13049","display_name":"Surface Roughness and Optical Measurements","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T13049","display_name":"Surface Roughness and Optical Measurements","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9980999827384949,"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/T12019","display_name":"Calibration and Measurement Techniques","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/emissivity","display_name":"Emissivity","score":0.9344829320907593},{"id":"https://openalex.org/keywords/root-mean-square","display_name":"Root mean square","score":0.6708788871765137},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.5682279467582703},{"id":"https://openalex.org/keywords/surface-finish","display_name":"Surface finish","score":0.5661613941192627},{"id":"https://openalex.org/keywords/infrared","display_name":"Infrared","score":0.5495612621307373},{"id":"https://openalex.org/keywords/surface-roughness","display_name":"Surface roughness","score":0.5084423422813416},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.507342517375946},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5022661685943604},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.44795480370521545},{"id":"https://openalex.org/keywords/mean-squared-error","display_name":"Mean squared error","score":0.43537867069244385},{"id":"https://openalex.org/keywords/computational-physics","display_name":"Computational physics","score":0.39281919598579407},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3306775987148285},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3299662470817566},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2721218466758728},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1436244249343872},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.09074181318283081}],"concepts":[{"id":"https://openalex.org/C163651212","wikidata":"https://www.wikidata.org/wiki/Q899670","display_name":"Emissivity","level":2,"score":0.9344829320907593},{"id":"https://openalex.org/C71907059","wikidata":"https://www.wikidata.org/wiki/Q223323","display_name":"Root mean square","level":2,"score":0.6708788871765137},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.5682279467582703},{"id":"https://openalex.org/C71039073","wikidata":"https://www.wikidata.org/wiki/Q3439090","display_name":"Surface finish","level":2,"score":0.5661613941192627},{"id":"https://openalex.org/C158355884","wikidata":"https://www.wikidata.org/wiki/Q11388","display_name":"Infrared","level":2,"score":0.5495612621307373},{"id":"https://openalex.org/C107365816","wikidata":"https://www.wikidata.org/wiki/Q114817","display_name":"Surface roughness","level":2,"score":0.5084423422813416},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.507342517375946},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5022661685943604},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.44795480370521545},{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.43537867069244385},{"id":"https://openalex.org/C30475298","wikidata":"https://www.wikidata.org/wiki/Q909554","display_name":"Computational physics","level":1,"score":0.39281919598579407},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3306775987148285},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3299662470817566},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2721218466758728},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1436244249343872},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.09074181318283081},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13091733","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091733","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1733/pdf?version=1631955407","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:65f6ac33c71c4a98bb33b3062c8ca318","is_oa":true,"landing_page_url":"https://doaj.org/article/65f6ac33c71c4a98bb33b3062c8ca318","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 9, p 1733 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/9/1733/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13091733","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13091733","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13091733","pdf_url":"https://www.mdpi.com/2073-8994/13/9/1733/pdf?version=1631955407","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.41999998688697815,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G281741784","display_name":null,"funder_award_id":"No. 91860207","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6880727134","display_name":null,"funder_award_id":"2019YFB2005401","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3201081617.pdf","grobid_xml":"https://content.openalex.org/works/W3201081617.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W834164233","https://openalex.org/W1970141088","https://openalex.org/W1973325501","https://openalex.org/W1976100392","https://openalex.org/W1985921481","https://openalex.org/W1987029633","https://openalex.org/W1988312167","https://openalex.org/W1988786264","https://openalex.org/W2002306355","https://openalex.org/W2004459160","https://openalex.org/W2011360018","https://openalex.org/W2011853556","https://openalex.org/W2015133545","https://openalex.org/W2016677450","https://openalex.org/W2019012012","https://openalex.org/W2048155292","https://openalex.org/W2063299167","https://openalex.org/W2066896062","https://openalex.org/W2078339496","https://openalex.org/W2082268738","https://openalex.org/W2085222029","https://openalex.org/W2150027424","https://openalex.org/W2154028411","https://openalex.org/W2171006361","https://openalex.org/W2584307220","https://openalex.org/W2625887608","https://openalex.org/W2795167206","https://openalex.org/W2883452347","https://openalex.org/W2904540326","https://openalex.org/W3023605785","https://openalex.org/W3035679816","https://openalex.org/W3035734794","https://openalex.org/W3044993990"],"related_works":["https://openalex.org/W2386922414","https://openalex.org/W2048078370","https://openalex.org/W3011201302","https://openalex.org/W4313638943","https://openalex.org/W1966522691","https://openalex.org/W4304014137","https://openalex.org/W3034740403","https://openalex.org/W2032025132","https://openalex.org/W4297916609","https://openalex.org/W2349732462"],"abstract_inverted_index":{"The":[0,76],"emissivity":[1,25,70],"is":[2,27,44],"an":[3],"important":[4],"surface":[5,34],"property":[6],"parameter":[7],"in":[8,92,111,144],"many":[9],"fields,":[10],"including":[11,146],"infrared":[12,119],"temperature":[13,121],"measurement.":[14],"In":[15],"this":[16],"research,":[17],"a":[18,41,90,109],"symmetry":[19],"theoretical":[20],"model":[21,132],"of":[22,52,55,123],"directional":[23,68],"spectral":[24],"prediction":[26],"proposed":[28],"based":[29,39,46,117],"on":[30,40,47,66,118],"Gaussian":[31],"random":[32,137],"rough":[33,138],"theory.":[35],"A":[36],"numerical":[37],"solution":[38],"matrix":[42],"method":[43],"determined":[45],"its":[48],"symmetrical":[49],"characteristics.":[50],"Influences":[51],"the":[53,59,67,97],"index":[54],"refraction":[56],"n":[57,83,102],"and":[58,74,84,103,140],"root":[60],"mean":[61],"square":[62],"(RMS)":[63],"roughness":[64],"\u03c3rms":[65,86,105],"spectrum":[69],"\u03b5":[71],"are":[72],"analyzed":[73],"discussed.":[75],"results":[77],"indicate":[78],"that":[79],"surfaces":[80,99,127,139],"with":[81,100],"higher":[82,104],"lower":[85,101],"tend":[87,106],"to":[88,107,135],"have":[89,108],"peak":[91,110],"high":[93],"viewing":[94,113],"angles.":[95,114],"On":[96],"contrary,":[98],"low":[112],"Experimental":[115],"verifications":[116],"(IR)":[120],"measurement":[122],"Inconel":[124],"718":[125],"sandblasted":[126],"were":[128],"carried":[129],"out.":[130],"This":[131],"would":[133],"contribute":[134],"understand":[136],"their":[141],"emitting":[142],"properties":[143],"fields":[145],"machining,":[147],"process":[148],"controlling,":[149],"remote":[150],"sensing,":[151],"etc.":[152]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-29T08:15:47.926485","created_date":"2025-10-10T00:00:00"}