photon radiance, Lp

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 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, $d S ⊥ = d S cos ⁡ θ$ , 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 angle $Ω$ and $θ$ the angle between any of these beams and the normal to the surface at the given point.

Notes:

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 angle $Ω$ containing the direction $θ$ . SI unit is $m −2 s −1 sr −1$ .
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 $m −2 s −1$ .
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