## radiance, $$L$$

https://doi.org/10.1351/goldbook.R05037
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:
1. 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.
2. 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.
3. Equivalent to L = ∫(λ).Lλ.dλ, where Lλ is the @S05824@ at @W06659@ λ.
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)