{"term":{"id":"13987","title":"absorbed local spectral radiance","longtitle":"IUPAC Gold Book - absorbed local spectral radiance","doi":"10.1351\/goldbook.13987","code":"13987","status":"current","synonym":"<em>synonym<\/em>: local volumetric rate of energy absorption","definitions":[{"id":1,"text":"Local value of the spectral radiance, or energy density absorption rate, defined for a three-dimensional space, often in terms of napierian properties.","notes":{"1":"Mathematical expression for one spatial dimension is \\[L_{\\lambda}^{\\rm{a}} (x,t) = \\alpha_{\\lambda} (\\boldsymbol{x},t) L_{\\lambda} (x,t)\\] where \\(L_{\\lambda}(x,t)\\) is the time-dependent spectral radiance incident from one direction at a point \\(x\\) defined in the space coordinates, \\(\\alpha_{\\lambda}(\\boldsymbol{x},t)\\) is the space- and time-dependent linear napierian absorption coefficient. SI unit is \\(\\pu{W m-4}\\). Common unit is \\(\\pu{W cm-3 nm-1}\\).The equation above is valid for a collimated beam of radiation, for which \\(E_{\\lambda,{\\rm{o}}}(\\boldsymbol{x},t) = L_{\\lambda}(\\boldsymbol{x},t)\\).","2":"For a divergent beam, the mathematical definition is: \\[L_{\\lambda}^{\\rm{a}} (\\boldsymbol{x},t) = \\alpha_{\\lambda} (\\boldsymbol{x},t) E_{\\lambda,o} (\\boldsymbol{x},t)\\]. In this case, \\(\\boldsymbol{x}\\) is a position vector in a three-dimensional space. Units are the same as above.","3":"Rigorously speaking, the general definition should be written in terms of \\(E_{\\lambda,o}\\). However, for a collimated beam of radiation, it is clearer to write it directly in terms of \\(L_{\\lambda}\\).","4":"Also called local volumetric rate of energy absorption, LVREA, [either \\(e_{\\lambda}^{\\rm{a}}(x,t)\\) for one spatial dimension or \\(e_{\\lambda}^{\\rm{a}}(\\boldsymbol{x},t)\\) for three dimensions].","5":"In practice, for polychromatic irradiation, the quantity is integrated in the wavelength range used."},"sources":["PAC, 2011, 83, 931. 'Glossary of terms used in photocatalysis and radiation catalysis (IUPAC Recommendations 2011)' on page 936 (https:\/\/doi.org\/10.1351\/PAC-REC-09-09-36)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/13987\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/13987\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/13987\/plain"},"citation":"Citation: 'absorbed local spectral radiance' 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.13987","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":"2026-05-07T00:07:39+00:00"}}