photon radiance, Lp

https://doi.org/10.1351/goldbook.P04639
Number of photons (quanta of radiation, Np) per time interval (photon flux), qp, 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=dScosθ, 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 LpcosθdΩ, with Lp 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:
  1. Mathematical definition: Lp=d2qpdΩdS=d2qpdΩdScosθ for a divergent beam propagating in an elementary cone of the solid
    angle
    Ω containing the direction θ. SI unit is m2 s1 sr1.
  2. For a parallel beam it is the number of photons (quanta of radiation, Np) per time interval (photon flux), qp, 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: Lp=dqp/(dScosθ) If qp is constant over the surface area considered, Lp=qp/(Scosθ), SI unit is m2 s1.
  3. This quantity can be used on a
    chemical amount
    basis by dividing Lp by the
    Avogadro constant
    , the symbol then being Ln,p, the name 'photon
    radiance
    , amount basis'. For a divergent beam SI unit is molm2s1sr1; common unit is einstein m2 s1 sr1. For a parallel beam SI unit is molm2s1; common unit is einstein m2 s1.
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 396 [Terms] [Paper]