{"id":"https://openalex.org/W2082071958","doi":"https://doi.org/10.1364/josa.38.000448","title":"New Contributions to the Optics of Intensely Light-Scattering Materials Part I","display_name":"New Contributions to the Optics of Intensely Light-Scattering Materials Part I","publication_year":1948,"publication_date":"1948-05-01","ids":{"openalex":"https://openalex.org/W2082071958","doi":"https://doi.org/10.1364/josa.38.000448","mag":"2082071958","pmid":"https://pubmed.ncbi.nlm.nih.gov/18916891"},"language":"en","primary_location":{"id":"doi:10.1364/josa.38.000448","doi":"https://doi.org/10.1364/josa.38.000448","is_oa":false,"landing_page_url":"https://doi.org/10.1364/josa.38.000448","pdf_url":null,"source":{"id":"https://openalex.org/S4210189509","display_name":"Journal of the Optical Society of America","issn_l":"0030-3941","issn":["0030-3941","2375-1037"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Journal of the Optical Society of America","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2082071958"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","pubmed"],"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/A5051693148","display_name":"Paul Kubelka","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Paul Kubelka","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5051693148"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6974,"has_fulltext":false,"cited_by_count":2727,"citation_normalized_percentile":{"value":0.78014184,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"38","issue":"5","first_page":"448","last_page":"448"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12304","display_name":"Radiative Heat Transfer Studies","score":0.3422999978065491,"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/T12304","display_name":"Radiative Heat Transfer Studies","score":0.3422999978065491,"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/T13049","display_name":"Surface Roughness and Optical Measurements","score":0.3237000107765198,"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/T11666","display_name":"Color Science and Applications","score":0.20229999721050262,"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/kubelka-munk-equation","display_name":"Kubelka-Munk equation","score":0.9210000038146973},{"id":"https://openalex.org/keywords/light-scattering","display_name":"light scattering","score":0.8289999961853027},{"id":"https://openalex.org/keywords/diffuse-reflectance","display_name":"diffuse reflectance","score":0.7519999742507935},{"id":"https://openalex.org/keywords/optical-transmittance","display_name":"optical transmittance","score":0.8510000109672546},{"id":"https://openalex.org/keywords/reflectivity","display_name":"reflectivity","score":0.5289999842643738},{"id":"https://openalex.org/keywords/exact-differential-equations","display_name":"exact equations","score":0.4449999928474426},{"id":"https://openalex.org/keywords/thickness-dependence","display_name":"thickness dependence","score":0.3310000002384186}],"concepts":[{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.6194029450416565},{"id":"https://openalex.org/C120456961","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Light scattering","level":3,"score":0.6089586019515991},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5708147883415222},{"id":"https://openalex.org/C191486275","wikidata":"https://www.wikidata.org/wiki/Q210028","display_name":"Scattering","level":2,"score":0.5684492588043213},{"id":"https://openalex.org/C108597893","wikidata":"https://www.wikidata.org/wiki/Q663650","display_name":"Reflectivity","level":2,"score":0.5371001958847046},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.5154155492782593},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.5147683620452881},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4505982995033264},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4504013955593109},{"id":"https://openalex.org/C151596937","wikidata":"https://www.wikidata.org/wiki/Q856980","display_name":"Bidirectional reflectance distribution function","level":3,"score":0.4215864837169647},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4130604565143585},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2627197206020355},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2586696445941925},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10554420948028564},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D008027","descriptor_name":"Light","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008029","descriptor_name":"Lighting","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D055095","descriptor_name":"Optics and Photonics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":2,"locations":[{"id":"doi:10.1364/josa.38.000448","doi":"https://doi.org/10.1364/josa.38.000448","is_oa":false,"landing_page_url":"https://doi.org/10.1364/josa.38.000448","pdf_url":null,"source":{"id":"https://openalex.org/S4210189509","display_name":"Journal of the Optical Society of America","issn_l":"0030-3941","issn":["0030-3941","2375-1037"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"Journal of the Optical Society of America","raw_type":"journal-article"},{"id":"pmid:18916891","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/18916891","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":"Journal of the Optical Society of America","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1985524261","https://openalex.org/W2003301481","https://openalex.org/W2313687357","https://openalex.org/W4253980303"],"related_works":["https://openalex.org/W4385355348","https://openalex.org/W3043913507","https://openalex.org/W1993885081","https://openalex.org/W3137850757","https://openalex.org/W2014384011","https://openalex.org/W1974993796","https://openalex.org/W1990667519","https://openalex.org/W2126190882","https://openalex.org/W1969887984"],"abstract_inverted_index":{"The":[0,126,156],"system":[1,57],"of":[2,5,11,43,45,65,103,115,190,194],"differential":[3,117,145],"equations":[4,118,146,158],"Kubelka-Munk,":[6],"-di=-(S+K)idx+Sjdx,":[7],"dj=-(S+K)jdx+Sidx(i,":[8],"j\u22ef":[9],"intensities":[10],"the":[12,30,48,54,66,79,86,98,108,143,153,170,185,191,195,201,209],"light":[13,46],"traveling":[14,44],"inside":[15],"a":[16,40],"plane-parallel":[17],"light-scattering":[18],"specimen":[19,99],"towards":[20],"its":[21,24],"unilluminated":[22,31],"and":[23,84,96,128,169,174,197],"illuminated":[25],"surface;":[26],"x\u22ef":[27],"distance":[28],"from":[29,39,63,105,142],"surface":[32],"S,":[33],"K\u22ef":[34],"constants),":[35],"has":[36],"been":[37],"derived":[38,132],"simplified":[41],"model":[42],"in":[47,133],"material.":[49],"Now,":[50],"without":[51],"simplifying":[52],"assumptions":[53],"following":[55],"exact":[56,120,151,210],"is":[58,81,88,94,181],"derived:":[59],"-di=-12(S+K)uidx+12Svjdx,dj=-12(S+K)vjdx+12Suidx,u\u2261\u222b0\u03c0/2(\u2202i/i\u2202\u03c6)(d\u03c6/cos\u03c6),":[60],"v\u2261\u222b0\u03c0/2(\u2202j/j\u2202\u03c6)(d\u03c6/cos\u03c6),":[61],"\u03c6\u2261angle":[62],"normal":[64],"light).":[67],"Both":[68],"systems":[69],"become":[70],"identical":[71],"when":[72,78,85,121],"u=v=2,":[73],"that":[74],"is,":[75],"for":[76,162,179],"instance,":[77,180],"material":[80],"perfectly":[82,89],"dull":[83],"light,":[87],"diffused":[90],"or":[91],"if":[92],"it":[93],"parallel":[95],"hits":[97],"under":[100,152],"an":[101],"angle":[102],"60\u00b0":[104],"normal.":[106],"Consequently,":[107,148],"different":[109],"formulas":[110,211],"Kubelka-Munk":[111,144],"got":[112,141],"by":[113,136,165,184,200,215],"integration":[114],"their":[116,137],"are":[119,124,150],"these":[122],"conditions":[123],"fulfilled.":[125],"Gurevic":[127],"Judd":[129],"formulas,":[130],"although":[131],"another":[134],"way":[135],"authors,":[138],"may":[139,159,212],"be":[140,160,213],"too.":[147],"they":[149],"same":[154],"conditions.":[155],"integrated":[157],"adapted":[161],"practical":[163,207],"use":[164],"introducing":[166],"hyperbolic":[167],"functions":[168],"secondary":[171],"constants":[172],"a=12(1/R\u221e+R\u221e)":[173],"b=12(1/R\u221e-R\u221e),":[175],"(R\u221e\u2261reflectivity).":[176],"Reflectance":[177],"R,":[178],"then":[182],"represented":[183],"formula":[186,202],"R=1-Rg(a-b":[187],"ctghbSX)a+b":[188],"ctghbSX-Rg(Rg\u2261reflectance":[189],"backing,":[192],"X=thickness":[193],"specimen)":[196],"transmittance":[198],"T":[199],"T=ba":[203],"sinhbSX+b":[204],"coshbSX.In":[205],"many":[206],"cases":[208],"replaced":[214],"appropriated":[216],"approximations.":[217]},"counts_by_year":[{"year":2026,"cited_by_count":100},{"year":2025,"cited_by_count":98},{"year":2024,"cited_by_count":106},{"year":2023,"cited_by_count":118},{"year":2022,"cited_by_count":114},{"year":2021,"cited_by_count":141},{"year":2020,"cited_by_count":136},{"year":2019,"cited_by_count":139},{"year":2018,"cited_by_count":117},{"year":2017,"cited_by_count":109},{"year":2016,"cited_by_count":101},{"year":2015,"cited_by_count":90},{"year":2014,"cited_by_count":84},{"year":2013,"cited_by_count":83},{"year":2012,"cited_by_count":72}],"updated_date":"2026-11-14T11:04:58.165337","created_date":"2016-06-24T00:00:00"}
