Intrinsic and Extrinsic Scattering and Absorption Coefficients New Equations in Four-flux and Two-flux Models Used for Determining Light Intensity Gradients

<!DOCTYPE html> <html lang="en" xml:lang="en"> <head> <meta charset="utf-8"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <title> Intrinsic and Extrinsic Scattering and Absorption Coefficients New Equations in Four-flux and Two-flux Models Used for Determining Light Intensity Gradients | Journal of Optics and Photonics Research </title> <link rel="icon" href="https://ojs.bonviewpress.com/public/journals/13/favicon_en_US.png"> <meta name="generator" content="Open Journal Systems 3.4.0.7"> <meta name="gs_meta_revision" content="1.1"/> <meta name="citation_journal_title" content="Journal of Optics and Photonics Research"/> <meta name="citation_journal_abbrev" content="JOPR"/> <meta name="citation_author" content="David Barrios Puerto"/> <meta name="citation_author_institution" content="Universidad Carlos III de Madrid, Spain"/> <meta name="citation_title" content="Intrinsic and Extrinsic Scattering and Absorption Coefficients New Equations in Four-flux and Two-flux Models Used for Determining Light Intensity Gradients"/> <meta name="citation_language" content="en"/> <meta name="citation_date" content="2024/04/30"/> <meta name="citation_volume" content="1"/> <meta name="citation_issue" content="3"/> <meta name="citation_firstpage" content="131"/> <meta name="citation_lastpage" content="144"/> <meta name="citation_doi" content="10.47852/bonviewJOPR42022261"/> <meta name="citation_abstract_html_url" content="https://ojs.bonviewpress.com/index.php/JOPR/article/view/2261"/> <meta name="citation_abstract" xml:lang="en" content="Collimated, diffuse, and total light intensity gradients, for forward and backward light senses, were determined in a three substrate layers – glass/electrolyte/glass – almost transparent sample, using optical constants and new equations for intrinsic and extrinsic scattering and absorption coefficients. These new equations were obtained for the inner electrolyte layer from the systems of differential equations of the four-flux and two-flux radiative transfer models, used for determining intrinsic and extrinsic coefficients, respectively, once knowing the optical constants of outer glass layers, from a single glass substrate sample measured in advance. Extinction coefficients were determined from optical constants and considering the wavelength compression of light when it enters into a material, decreasing its speed with respect to the vacuum. The same extinction coefficients for glass and electrolyte layers were computed in three different ways. First, from optical constants, they were determined using collimated transmittance and reflectance solutions of four-flux model. From them, collimated interface reflectance and attenuation due to extinction were computed. These intermediate parameters for glass and electrolyte layers were required for determining inner collimated light intensities at the interfaces, which were used at the collimated forward and backward differential equations, solving for the forward and backward extinction coefficients. The three-extinction matching requirement was successfully satisfied for the glass and electrolyte layers. Two average crossing parameters equations, for each sense, and four forward scattering ratios equations, for collimated and for diffuse light intensities for each sense, were used in the system of diffuse differential equations (DDE) for intrinsic coefficients. For them, intuitive equations were proposed based on collimated and diffuse light intensities at each interface. New equations for extrinsic parameters were determined by equalizing the system of total differential equations of the two-flux model to the sum of the systems of collimated and DDE of the four-flux model. Received: 9 December 2023 | Revised: 4 March 2024 | Accepted: 25 April 2024 Conflicts of Interest The author declares that he has no conflicts of interest to this work. Data Availability Statement Data are available from the corresponding author upon reasonable request."/> <meta name="citation_keywords" xml:lang="en" content="scattering and absorption coefficients"/> <meta name="citation_keywords" xml:lang="en" content="average crossing parameter"/> <meta name="citation_keywords" xml:lang="en" content="forward scattering ratio"/> <meta name="citation_keywords" xml:lang="en" content="four-flux model"/> <meta name="citation_keywords" xml:lang="en" content="two-flux model"/> <meta name="citation_pdf_url" content="https://ojs.bonviewpress.com/index.php/JOPR/article/download/2261/915"/> <link rel="schema.DC" href="http://purl.org/dc/elements/1.1/" /> <meta name="DC.Creator.PersonalName" content="David Barrios Puerto"/> <meta name="DC.Date.created" scheme="ISO8601" content="2024-04-30"/> <meta name="DC.Date.dateSubmitted" scheme="ISO8601" content="2023-12-09"/> <meta name="DC.Date.issued" scheme="ISO8601" content="2024-08-20"/> <meta name="DC.Date.modified" scheme="ISO8601" content="2024-08-20"/> <meta name="DC.Description" xml:lang="en" content="Collimated, diffuse, and total light intensity gradients, for forward and backward light senses, were determined in a three substrate layers – glass/electrolyte/glass – almost transparent sample, using optical constants and new equations for intrinsic and extrinsic scattering and absorption coefficients. These new equations were obtained for the inner electrolyte layer from the systems of differential equations of the four-flux and two-flux radiative transfer models, used for determining intrinsic and extrinsic coefficients, respectively, once knowing the optical constants of outer glass layers, from a single glass substrate sample measured in advance. Extinction coefficients were determined from optical constants and considering the wavelength compression of light when it enters into a material, decreasing its speed with respect to the vacuum. The same extinction coefficients for glass and electrolyte layers were computed in three different ways. First, from optical constants, they were determined using collimated transmittance and reflectance solutions of four-flux model. From them, collimated interface reflectance and attenuation due to extinction were computed. These intermediate parameters for glass and electrolyte layers were required for determining inner collimated light intensities at the interfaces, which were used at the collimated forward and backward differential equations, solving for the forward and backward extinction coefficients. The three-extinction matching requirement was successfully satisfied for the glass and electrolyte layers. Two average crossing parameters equations, for each sense, and four forward scattering ratios equations, for collimated and for diffuse light intensities for each sense, were used in the system of diffuse differential equations (DDE) for intrinsic coefficients. For them, intuitive equations were proposed based on collimated and diffuse light intensities at each interface. New equations for extrinsic parameters were determined by equalizing the system of total differential equations of the two-flux model to the sum of the systems of collimated and DDE of the four-flux model. Received: 9 December 2023 | Revised: 4 March 2024 | Accepted: 25 April 2024 Conflicts of Interest The author declares that he has no conflicts of interest to this work. Data Availability Statement Data are available from the corresponding author upon reasonable request."/> <meta name="DC.Format" scheme="IMT" content="application/pdf"/> <meta name="DC.Identifier" content="2261"/> <meta name="DC.Identifier.pageNumber" content="131-144"/> <meta name="DC.Identifier.DOI" content="10.47852/bonviewJOPR42022261"/> <meta name="DC.Identifier.URI" content="https://ojs.bonviewpress.com/index.php/JOPR/article/view/2261"/> <meta name="DC.Language" scheme="ISO639-1" content="en"/> <meta name="DC.Rights" content="Copyright (c) 2024 Author"/> <meta name="DC.Rights" content="https://creativecommons.org/licenses/by/4.0/"/> <meta name="DC.Source" content="Journal of Optics and Photonics Research"/> <meta name="DC.Source.Issue" content="3"/> <meta name="DC.Source.Volume" content="1"/> <meta name="DC.Source.URI" content="https://ojs.bonviewpress.com/index.php/JOPR"/> <meta name="DC.Subject" xml:lang="en" content="scattering and absorption coefficients"/> <meta 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href="https://ojs.bonviewpress.com/index.php/JOPR/issue/view/91"> Vol. 1 No. 3 (2024) </a> <span class="separator">/</span> </li> <li class="current" aria-current="page"> <span aria-current="page"> Research Articles </span> </li> </ol> </nav> <article class="obj_article_details"> <h1 class="page_title"> Intrinsic and Extrinsic Scattering and Absorption Coefficients New Equations in Four-flux and Two-flux Models Used for Determining Light Intensity Gradients </h1> <div class="row"> <div class="main_entry"> <section class="item authors"> <h2 class="pkp_screen_reader">Authors</h2> <ul class="authors"> <li> <span class="name"> David Barrios Puerto </span> <span class="affiliation"> Universidad Carlos III de Madrid, Spain </span> <span class="orcid"> <svg class="orcid_icon" viewBox="0 0 256 256" aria-hidden="true"> <style type="text/css"> .st0{fill:#A6CE39;} .st1{fill:#FFFFFF;} </style> <path class="st0" 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crossing parameter, forward scattering ratio, four-flux model, two-flux model </span> </section> <section class="item abstract"> <h2 class="label">Abstract</h2> <p>Collimated, diffuse, and total light intensity gradients, for forward and backward light senses, were determined in a three substrate layers – glass/electrolyte/glass – almost transparent sample, using optical constants and new equations for intrinsic and extrinsic scattering and absorption coefficients. These new equations were obtained for the inner electrolyte layer from the systems of differential equations of the four-flux and two-flux radiative transfer models, used for determining intrinsic and extrinsic coefficients, respectively, once knowing the optical constants of outer glass layers, from a single glass substrate sample measured in advance. Extinction coefficients were determined from optical constants and considering the wavelength compression of light when it enters into a material, decreasing its speed with respect to the vacuum. The same extinction coefficients for glass and electrolyte layers were computed in three different ways. First, from optical constants, they were determined using collimated transmittance and reflectance solutions of four-flux model. From them, collimated interface reflectance and attenuation due to extinction were computed. These intermediate parameters for glass and electrolyte layers were required for determining inner collimated light intensities at the interfaces, which were used at the collimated forward and backward differential equations, solving for the forward and backward extinction coefficients. The three-extinction matching requirement was successfully satisfied for the glass and electrolyte layers. Two average crossing parameters equations, for each sense, and four forward scattering ratios equations, for collimated and for diffuse light intensities for each sense, were used in the system of diffuse differential equations (DDE) for intrinsic coefficients. For them, intuitive equations were proposed based on collimated and diffuse light intensities at each interface. New equations for extrinsic parameters were determined by equalizing the system of total differential equations of the two-flux model to the sum of the systems of collimated and DDE of the four-flux model.</p> <p> </p> <p><strong>Received:</strong> 9 December 2023 <strong>| Revised:</strong> 4 March 2024 <strong>| Accepted:</strong> 25 April 2024</p> <p> </p> <p><strong>Conflict</strong><strong>s</strong><strong> of Interest </strong></p> <p>The author declares that he has no conflicts of interest to this work.</p> <p> </p> <p><strong>Data Availability Statement </strong></p> <p>Data are available from the corresponding author upon reasonable request.</p> </section> <br /><div class="separator"></div><div class="item abstract" id="trendmd-suggestions"></div><script defer src='//js.trendmd.com/trendmd.min.js' data-trendmdconfig='{"website_id":"89272", "element":"#trendmd-suggestions"}'></script> </div> <div class="entry_details"> <div class="item cover_image"> <div class="sub_item"> <a href="https://ojs.bonviewpress.com/index.php/JOPR/issue/view/91"> <img src="https://ojs.bonviewpress.com/public/journals/13/cover_issue_91_en_US.png" alt=""> </a> </div> </div> <div class="item galleys"> <h2 class="pkp_screen_reader"> Downloads </h2> <ul class="value galleys_links"> <li> <a class="obj_galley_link pdf" href="https://ojs.bonviewpress.com/index.php/JOPR/article/view/2261/915"> PDF </a> </li> </ul> </div> <div class="item published"> <section class="sub_item"> <h2 class="label"> Published </h2> <div class="value"> <span>2024-04-30</span> </div> </section> </div> <div class="item issue"> <section class="sub_item"> <h2 class="label"> Issue </h2> <div class="value"> <a class="title" href="https://ojs.bonviewpress.com/index.php/JOPR/issue/view/91"> Vol. 1 No. 3 (2024) </a> </div> </section> <section class="sub_item"> <h2 class="label"> Section </h2> <div class="value"> Research Articles </div> </section> </div> <div class="item copyright"> <h2 class="label"> License </h2> <p>Copyright (c) 2024 Author</p> <a rel="license" href="https://creativecommons.org/licenses/by/4.0/"><img alt="Creative Commons License" src="//i.creativecommons.org/l/by/4.0/88x31.png" /></a><p>This work is licensed under a <a rel="license" href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a>.</p> </div> <div class="item citation"> <section class="sub_item citation_display"> <h2 class="label"> How to Cite </h2> <div class="value"> <div id="citationOutput" role="region" aria-live="polite"> <div class="csl-bib-body"> <div class="csl-entry">Barrios Puerto, D. 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Intrinsic and Extrinsic Scattering and Absorption Coefficients New Equations in Four-flux and Two-flux Models Used for Determining Light Intensity Gradients. <i>Journal of Optics and Photonics Research</i>, <i>1</i>(3), 131-144. <a href="https://doi.org/10.47852/bonviewJOPR42022261">https://doi.org/10.47852/bonviewJOPR42022261</a></div> </div> </div> <div class="citation_formats"> <button class="citation_formats_button label" aria-controls="cslCitationFormats" aria-expanded="false" data-csl-dropdown="true"> More Citation Formats </button> <div id="cslCitationFormats" class="citation_formats_list" aria-hidden="true"> <ul class="citation_formats_styles"> <li> <a aria-controls="citationOutput" href="https://ojs.bonviewpress.com/index.php/JOPR/citationstylelanguage/get/acm-sig-proceedings?submissionId=2261&publicationId=3436&issueId=91" data-load-citation 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Intrinsic and Extrinsic Scattering and Absorption Coefficients New Equations in Four-flux and Two-flux Models Used for Determining Light Intensity Gradients | Journal of Optics and Photonics Research