{"term":{"id":"04639","doi":"10.1351\/goldbook.P04639","code":"P04639","status":"current","longtitle":"IUPAC Gold Book - photon radiance","title":"photon radiance","index":"quantity","termversion":"2.3.3","lastupdated":"2014-02-24","definitions":[{"id":"1","text":"Number of photons (quanta of radiation, Np) per time interval (photon flux), qp, leaving or passing through a small transparent element of surface in a given direction from the source about the solid angleΩ, divided by the solid angle and by the orthogonally projected area of the element in a plane normal to the given beam direction, dS⊥ = dS cos θ, with θ the angle between the normal to the surface and the direction of the beam. Equivalent definition: Integral taken over the hemisphere visible from the given point, of the expression Lp.cos θ.dΩ, with Lp the photon radiance at the given point in the various directions of the incident beam of solid angleΩ and θ the angle between any of these beams and the normal to the surface at the given point.","notes":{"1":"Mathematical definition: Lp = d^2.qp\/dΩ.dS⊥ = d^2qp\/dΩ.dS.cos θ for a divergent beam propagating in an elementary cone of the solid angle Ω containing the direction θ. SI unit is m-2 s-1 sr-1.","2":"For a parallel beam it is the number of photons (quanta of radiation, Np) per time interval (photon flux), qp, leaving or passing through a small element of surface in a given direction from the source divided by the orthogonally projected area of the element in a plane normal to the given direction of the beam, θ. Mathematical definition in this case: Lp = dqp\/(dS.cos θ) If qp is constant over the surface area considered, Lp = qp\/(S.cos θ), SI unit is m-2 s-1.","3":"This quantity can be used on a chemical amount basis by dividing Lp by the Avogadro constant, the symbol then being Ln,p, the name 'photon radiance, amount basis'. For a divergent beam SI unit is mol m-2 s-1 sr-1; common unit is einstein m-2 s-1 sr-1. For a parallel beam SI unit is mol m-2 s-1; common unit is einstein m-2 s-1."},"links":[{"title":"angle","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/A00346"},{"title":"chemical amount","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/C01019"},{"title":"Avogadro constant","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/A00543"},{"title":"radiance","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/R05037"},{"title":"visible","type":"goldify","url":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/VT07496"}],"math":[{"alttext":"Np","latex":"N_{\\text{p}}"},{"alttext":"qp","latex":"q_{\\text{p}}"},{"alttext":"Ω","latex":"\\varOmega"},{"alttext":"dS⊥ = dS cos θ","latex":"\\text{d}S_{\\perp } = \\text{d}S\\, cos\\,\\theta"},{"alttext":"θ","latex":"\\theta"},{"type":"math","alttext":"Lp.cos θ.dΩ","latex":"L_{\\text{p}}\\, cos\\,\\theta\\,\\text{d}\\varOmega"},{"alttext":"Lp","latex":"L_{\\text{p}}"},{"alttext":"Ω","latex":"\\varOmega"},{"alttext":"θ","latex":"\\theta"},{"meaning":"Photon radiance","type":"equation","alttext":"Lp = d^2.qp\/dΩ.dS⊥ = d^2qp\/dΩ.dS.cos θ","latex":"L_{\\text{p}} = \\frac{\\text{d}^{2}q_{p}}{\\text{d}\\varOmega \\, \\text{d}S_{\\perp }} = \\frac{\\text{d}^{2}q_{p}}{\\text{d}\\varOmega \\, \\text{d}S\\, cos\\,\\theta}"},{"alttext":"Ω","latex":"\\varOmega"},{"alttext":"θ","latex":"\\theta"},{"alttext":"m-2 s-1 sr-1","latex":"\\text{m}^{-2}\\ \\text{s}^{-1}\\ \\text{sr}^{-1}"},{"alttext":"Np","latex":"N_{\\text{p}}"},{"alttext":"qp","latex":"q_{\\text{p}}"},{"alttext":"θ","latex":"\\theta"},{"meaning":"Photon radiance (for parallel beam)","type":"equation","alttext":"Lp = dqp\/(dS.cos θ)","latex":"L_{\\text{p}} = \\text{d}q_{\\text{p}}\/\\left ( \\text{d}S\\, cos\\,\\theta \\right )"},{"alttext":"qp","latex":"q_{\\text{p}}"},{"meaning":"Photon radiance (for constant surface area qp)","type":"equation","alttext":"Lp = qp\/(S.cos θ)","latex":"L_{\\text{p}} = q_{\\text{p}}\/\\left ( S\\, cos\\,\\theta \\right )"},{"alttext":"m-2 s-1","latex":"\\text{m}^{-2}\\ \\text{s}^{-1}"},{"alttext":"Lp","latex":"L_{\\text{p}}"},{"meaning":"Photon radiance (based on moles)","type":"quantity","alttext":"Ln,p","latex":"L_{n\\text{,p}}"},{"alttext":"mol m-2 s-1 sr-1","latex":"\\text{mol m}^{-2}\\ \\text{s}^{-1}\\ \\text{sr}^{-1}"},{"alttext":"einstein m-2 s-1 sr-1","latex":"\\text{einstein m}^{-2}\\ \\text{s}^{-1}\\ \\text{sr}^{-1}"},{"alttext":"mol m-2 s-1","latex":"\\text{mol m}^{-2}\\ \\text{s}^{-1}"},{"alttext":"einstein m-2 s-1","latex":"\\text{einstein m}^{-2}\\ \\text{s}^{-1}"}],"sources":["PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 396 (https:\/\/doi.org\/10.1351\/pac200779030293)"]}],"links":{"html":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/P04639\/html","json":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/P04639\/json","xml":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/P04639\/xml","plain":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/P04639\/plain","pdf":"https:\/\/dev.goldbook.iupac.org\/terms\/view\/P04639\/pdf"},"citation":"Citation: 'photon radiance' in IUPAC Compendium of Chemical Terminology, 3rd ed. International Union of Pure and Applied Chemistry; 2006. Online version 3.0.1, 2019. 10.1351\/goldbook.P04639","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":"2024-06-12T21:10:12+00:00"}}