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 @[email protected] from the given point, of the expression $$L_{\text{p}}\, \text{cos}\:\theta\, \text{d}\varOmega$$ the @[email protected] at the given point in the various directions of the incident beam of solid @[email protected] $$\varOmega$$ and $$\theta$$ the @[email protected] 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: $$E_{\text{p}} = \int_{2\pi} L_{\text{p}}\, \text{cos}\:\theta\, \text{d}\varOmega$$.
2. This term refers to a beam not scattered or reflected by the target or its surroundings. For a beam incident from all directions @[email protected] ($$E_{\text{p,o}}$$) is an equivalent term.
3. This quantity can be used on a @[email protected] basis by dividing $$E_{\text{p}}$$ by the @[email protected], 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]