photon irradiance, \(E_{\text{p}}\)

https://doi.org/10.1351/goldbook.P04637
Number of photons (quanta of radiation, \(N_{\text{p}}\)) per time interval (photon flux), \(q_{\text{p}}\), incident from all upward directions on a small element of surface containing the point under consideration divided by the area of the element. SI unit is \(\text{m}^{-2}\ \text{s}^{-1}\). Equivalent definition: Integral, taken over the hemisphere @VT07496@ from the given point, of the expression \(L_{\text{p}}\, cos\:\theta\, \text{d}\varOmega\) the @P04639@ at the given point in the various directions of the incident beam of solid @A00346@ \(\varOmega\) and \(\theta\) the @A00346@ between any of these beams and the normal to the surface at the given point.
Notes:
  1. Mathematical definition: \(E_{\text{p}} = \text{d}q_{\text{p}}/\text{d}S\). If the photon flux is constant over the surface considered, \(E_{\text{p}} = q_{\text{p}}/S\). Equivalent definition: \(E_{\text{p}} = \int_{2\pi} L_{\text{p}}\, cos\:\theta\, \text{d}\varOmega\).
  2. This term refers to a beam not scattered or reflected by the target or its surroundings. For a beam incident from all directions@P04635@ (\(E_{\text{p,o}}\)) is an equivalent term.
  3. This quantity can be used on a @C01019@ basis by dividing \(E_{\text{p}}\) by the @A00543@, the symbol then being \(E_{n\text{,p}}\), the name 'photon irradiance, amount basis', SI unit is \(\text{mol m}^{-2}\ \text{s}^{-1}\); common unit is \(\text{einstein m}^{-2}\ \text{s}^{-1}\).
Source:
PAC, 2007, 79, 293. (Glossary of terms used in photochemistry, 3rd edition (IUPAC Recommendations 2006)) on page 396 [Terms] [Paper]