{"paper_id":"027eb2d9-da76-439a-b0b8-133cd73a2cda","body_text":"Dynamic mathematical model of a non-dispersive infrared (NDIR) absorption spectroscopy measurement system for transient gas analysis | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Dynamic mathematical model of a non-dispersive infrared (NDIR) absorption spectroscopy measurement system for transient gas analysis sangwoon Park, Masahiko Inoue This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8710840/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Non-dispersive infrared (NDIR) absorption spectroscopy is widely used for quantitative gas analysis; however, the steady-state use of the Beer–Lambert law alone does not describe transient signals and temperature dependent behavior frequently encountered under practical flow conditions. Here, the effects of flow rate and cell temperature on transient NDIR responses are experimentally characterized, and a unified dynamic formulation is presented. The detection cell is modeled as a linear time-invariant system with a characteristic time constant τ = V/v (V: cell volume, v: volumetric flow rate), and, under isothermal operation, absorbance is expressed as the convolution of the input concentration with the instrumental impulse response. This representation accounts for response delays and waveform asymmetry under time-varying composition and flow, and it provides implementation-ready procedures for response correction and calibration in dynamic measurements. The formulation offers specification-level guidance beyond instrument-specific fixed settings and is expected to improve quantitative reliability for challenging sample matrices (e.g., powders, concrete, and liquids), thereby broadening NDIR applicability beyond conventional steel analysis. Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Mathematics and computing Physical sciences/Optics and photonics Physical sciences/Physics Non-dispersive infrared (NDIR) spectroscopy Transient gas analysis Convolution model Impulse response / time constant Flowrate and temperature dependence Response correction and dynamic calibration Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {\"props\":{\"pageProps\":{\"initialData\":{\"identity\":\"rs-8710840\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":589970241,\"identity\":\"016150da-f8d2-4920-87e8-a58a2d6dbefe\",\"order_by\":0,\"name\":\"sangwoon Park\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYLADxoaKAwwMzDwkaTlDspbGNqAWBgJa5NvPHn7NU2GTxyDd/OzjzHl35MzbeQ9+YKixicalxeBMXpo1z5m0YgaZY8YzN257ZixzmC9ZguFYWm4DLi0MOWbGuW2HExskEowZH247nDiDmcdAgrHhME4t8v1vYFrSPzM+nAPWYvwDnxaGGznGjyFacowZNzaAtZjhtcXgxhsz5j9n0hLbZM4UM844dthYgpkvzSIBj1/k+3OMP86osEnsl27fzNhTc1hOgv/s4RsfamxwO4yBgU0CQcJAAm7lIMD8AUxJ4Fc1CkbBKBgFIxgAABGVWlYT2ZrsAAAAAElFTkSuQmCC\",\"orcid\":\"\",\"institution\":\"Horiba (Japan)\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"sangwoon\",\"middleName\":\"\",\"lastName\":\"Park\",\"suffix\":\"\"},{\"id\":589970242,\"identity\":\"45ee1f23-e990-4b76-aa74-3f76684a9276\",\"order_by\":1,\"name\":\"Masahiko Inoue\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"Setsunan University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Masahiko\",\"middleName\":\"\",\"lastName\":\"Inoue\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2026-01-27 13:10:20\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-8710840/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-8710840/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":102749087,\"identity\":\"35376f30-d8f5-474b-b5ad-d78b625a1ecc\",\"added_by\":\"auto\",\"created_at\":\"2026-02-16 09:11:57\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":1149127,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"Dynamicmathematicalmodel.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-8710840/v1_covered_3f90218d-c8c5-4344-a719-b1c19c101ae1.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Dynamic mathematical model of a non-dispersive infrared (NDIR) absorption spectroscopy measurement system for transient gas analysis\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":true,\"hideJournal\":true,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"researchsquare\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":true,\"externalIdentity\":\"\",\"sideBox\":\"\",\"snPcode\":\"\",\"submissionUrl\":\"/submission\",\"title\":\"Research Square\",\"twitterHandle\":\"researchsquare\",\"acdcEnabled\":true,\"dfaEnabled\":false,\"editorialSystem\":\"\",\"reportingPortfolio\":\"\",\"inReviewEnabled\":false,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Non-dispersive infrared (NDIR) spectroscopy, Transient gas analysis, Convolution model, Impulse response / time constant, Flowrate and temperature dependence, Response correction and dynamic calibration\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-8710840/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-8710840/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eNon-dispersive infrared (NDIR) absorption spectroscopy is widely used for quantitative gas analysis; however, the steady-state use of the Beer\\u0026ndash;Lambert law alone does not describe transient signals and temperature dependent behavior frequently encountered under practical flow conditions. 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