photon radiance, L p

https://dx.doi.org/10.1351/goldbook.P04639
Number of photons (quanta of radiation, N p) per time interval (photon flux), q p, 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, d S ⊥ = d S 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 L p cos ⁡ θ d Ω, with L p 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:
    L p = d 2 q p d Ω d S ⊥ = d 2 q p d Ω d S cos ⁡ θ
    for a divergent beam propagating in an elementary cone of the solid angleΩ 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, N p) per time interval (photon flux), q p, 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: L p = d q p / ( d S cos ⁡ θ ) If q p is constant over the surface area considered, L p = q p / S cos ⁡ θ, SI unit is m −2 s −1.
  3. This quantity can be used on a chemical amount basis by dividing L p by the Avogadro constant, the symbol then being L n , 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.
Source:
PAC, 2007, 79, 293 (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 396