Term: radiance, \(L\)
https://doi.org/10.1351/goldbook.R05037

Definition:
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, dS⊥ = dS cos θ

Notes:
0) Mathematical definition: \[L = \frac{\text{d}^{2}P}{\text{d}\Omega \, \text{d}S_{\perp }} = \frac{\text{d}^{2}P}{\text{d}\Omega \, \text{d}S\, \text{cos}\,\theta}\] for a divergent beam propagating in an elementary cone of the solid @A00346@ Ω containing the direction θ. SI unit is W m-2 sr-1.
1) For a parallel beam it is the @R05046-2@, 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: dP/(dS cos θ). If the @R05046-1@ is constant over the surface area considered, P/S cosθ. SI unit is W m-2.
2) Equivalent to L = ∫(λ).Lλ.dλ, where Lλ is the @S05824@ at @W06659@ λ.

Related Terms:
1) angle (http://doi.org/10.1351/goldbook.A00346).
2) radiant power (http://doi.org/10.1351/goldbook.R05046-2).
3) spectral radiance (http://doi.org/10.1351/goldbook.S05824).
4) wavelength (http://doi.org/10.1351/goldbook.W06659).
5) radiant power (http://doi.org/10.1351/goldbook.R05046-1).

Source: PAC, 2007, 79, 293. 'Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)' on page 408 (https://doi.org/10.1351/pac200779030293)

Citation: 'radiance, \(L\)' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. https://doi.org/10.1351/goldbook.R05037

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