radiance, $L$

Radiant power, $P$ , leaving or passing through a small transparent element of surface in a given direction from the source about the solid angle $Ω$ , divided by the solid angle and by the orthogonally projected area of the element in a plane normal to the given beam direction, $d S ⊥ = d S cos ⁡ θ$

Notes:

Mathematical definition:
$L = d 2 P d Ω d S ⊥ = d 2 P d Ω d S cos ⁡ θ$
for a divergent beam propagating in an elementary cone of the solid angle $Ω$ containing the direction $θ$ . SI unit is $W m −2 sr −1$ .
For a parallel beam it is the radiant power, $P$ , of all wavelengths 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: $d P / ( d S cos ⁡ θ )$ If the radiant power is constant over the surface area considered, $P / S cos ⁡ θ$ . SI unit is $W m −2$ .
Equivalent to $L = ∫ λ L λ ⁢ d λ$ , where $L λ$ is the spectral radiance at wavelength $λ$ .

Source:

PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 408

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IUPAC > Gold Book > math/physics > quantities

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Cite as:
IUPAC. Compendium of Chemical Terminology, 2nd ed. (the "Gold Book"). Compiled by A. D. McNaught and A. Wilkinson. Blackwell Scientific Publications, Oxford (1997). XML on-line corrected version: http://goldbook.iupac.org (2006-) created by M. Nic, J. Jirat, B. Kosata; updates compiled by A. Jenkins. ISBN 0-9678550-9-8. https://doi.org/10.1351/goldbook.

Last update: 2014-02-24; version: 2.3.3.

DOI of this term: https://doi.org/10.1351/goldbook.R05037.

Original PDF version: http://www.iupac.org/goldbook/R05037.pdf. The PDF version is out of date and is provided for reference purposes only. For some entries, the PDF version may be unavailable.

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