The quantum flux (also called photon flux) is defined as the number of photons (in µmol) per second and unit area on a surface and given in µE (µEinstein; 1 Einstein = energy of 1 mole of photons/m²·s). To convert irradiance in quantum flux (or photon flux) the following points have to be considered:
A photon has a distinct energy Ep which is defined by:
(with Planck constant h = 6.63 x 10-34 [J•s]; speed of light c = 2.998 x 108 [m/s]; frequency f [s-1]; wavelength λ [m])
Thus, the energy of a mole of photons of a given wavelength is Ep·NA (NA=6.022 x 1023 mol-1).
The number of photons per second and surface unit, Np, can be calculated from the irradiance (I) by (note: the nm value for λ is used, hence the 10-9 factor in the formula):
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The photon flux can be determined by converting the number of photons to µmoles of photons:
In summary, the following applies to the conversion of irradiance [W/m²] into quantum flux [µE] when wavelength is expressed in nm: