{"term":{"id":"14077","title":"radiative transfer equation","longtitle":"IUPAC Gold Book - radiative transfer equation","doi":"10.1351\/goldbook.14077","code":"14077","status":"current","initialism":"<em>initialism<\/em>: RTE","definitions":[{"id":1,"text":"When a photon beam of radiance \\(L_{\\lambda}\\) and angular distribution \\(\\mathit{\\Omega}\\) passes along a single direction of propagation through a medium, which is totally absorbing and\/or scattering, i.e., the processes occurring are described by the following equation: \\[\\begin{array} \\\\ \\frac{{\\rm{d}}L_{\\Omega,\\lambda}(\\boldsymbol{x},t)}{{\\rm{d}}s} + \\underbrace{\\alpha_{\\lambda}(\\boldsymbol{x},t) L_{\\mathit{\\Omega},\\lambda}(\\boldsymbol{x},t)}_{\\rm{adsorption}} + \\underbrace{\\sigma_{\\lambda}(\\boldsymbol{x},t) L_{\\mathit{\\Omega},\\lambda}(\\boldsymbol{x},t)}_{\\rm{out\\mbox{-}scattering}} = \\\\ \\underbrace{j_{\\lambda}(\\boldsymbol{x},t)}_{\\rm{emission}} + \\underbrace{\\frac{\\sigma_{\\lambda}(\\boldsymbol{x},t)}{4\\pi}B_{\\lambda}(\\mathit{\\Omega}' \\to \\mathit{\\Omega}) L_{\\mathit{\\Omega},\\lambda}(\\boldsymbol{x},t){\\rm{d}}\\mathit{\\Omega}'}_{\\rm{in\\mbox{-}scattering}} \\end{array}\\] where \\(\\frac{{\\rm{d}}L_{\\Omega,\\lambda}(\\boldsymbol{x},t)}{{\\rm{d}}s}\\) is the directional derivative along the direction \\(s\\) at a point \\(\\boldsymbol{x}\\) in the reaction space of the incident radiance, \\(\\alpha_{\\lambda}(\\boldsymbol{x},t)\\) is the space- and time-dependent spectral linear napierian absorption coefficient, \\(\\sigma_{\\lambda}(\\boldsymbol{x},t)\\) is the space- and time-dependent spectral linear napierian scattering coefficient, \\(j_{\\lambda}(\\boldsymbol{x},t)\\) represents the spontaneous and\/or induced emission, and \\(B_{\\lambda}\\) is the phase function. All quantities are a function of time. The RTE is written for the direction \\(s\\).","notes":{"1":"Absorption and out-scattering reduce the radiance along the axis of propagation, whereas in-scattering and emission, increases it. Normally, emission can be safely neglected in photocatalysis.","2":"The RTE is a representation of the (radiation) energy conservation law and its solution in cases with complex geometry and in the presence of scattering remains a challenging issue.","3":"Back scattering and forward scattering are global effects derived from the integration of absorption, in-scattering, out-scattering, and emission."},"links":[{"term":"in-scattering","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/14023"},{"term":"local differential absorption","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/14028"},{"term":"out-scattering","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/14030"},{"term":"phase function","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/14031"}],"sources":["PAC, 2011, 83, 931. 'Glossary of terms used in photocatalysis and radiation catalysis (IUPAC Recommendations 2011)' on page 983 (https:\/\/doi.org\/10.1351\/PAC-REC-09-09-36)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/14077\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/14077\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/14077\/plain"},"citation":"Citation: 'radiative transfer equation' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351\/goldbook.14077","license":"The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/) for individual terms.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2026-06-28T19:24:17+00:00"}}