= Radiant flux
{title2=$\Phi=dQ/dt$}
{wiki}
= Radiant power
{synonym}
<Radiant flux> is the <power> carried by <electromagnetic radiation>: radiation <energy> transferred per unit <time>, measured in <watts>, $\mathrm W=\mathrm{J\,s^{-1}}$. Specify what is counted: all radiation emitted by a source, radiation within one beam, or radiation intercepted by a <photodetector>. Writing $Q(t)$ for the cumulative <energy> crossing the specified boundary gives
$$
\Phi_e(t)=\frac{dQ}{dt},\qquad
\overline\Phi_e=\frac{Q(t_2)-Q(t_1)}{t_2-t_1},\qquad
Q(t_2)-Q(t_1)=\int_{t_1}^{t_2}\Phi_e(t)\,dt.
$$
The first expression is an instantaneous <derivative>; the second is an average over the stated <time> interval. If $0.020\,\mathrm J$ arrives during $0.010\,\mathrm s$, the mean <radiant flux> is $2\,\mathrm W$. The <photodetector>'s absorbed <power> equals this incident <radiant flux> only if it absorbs all of the incident radiation.
Keeping <radiant flux> fixed while widening a beam reduces its <irradiance>, the incident <power> per receiving <area>. <Radiance> additionally resolves the propagation direction and has units $\mathrm{W\,m^{-2}\,sr^{-1}}$; an <optical camera> can collect different <radiant fluxes> from sources with the same <radiance> but different apparent <solid angles>. <Luminous flux>, measured in lumens, weights the <optical spectrum> by the human eye's standardized response instead of counting <energy> equally at every <wavelength>. Equal <radiant fluxes> need not give equal <luminous fluxes>.<OSA Handbook of Optics, Volume III Visual Optics and Vision/Radiometry and Photometry: Review for Vision Optics>{ref}
<Radiant power> also differs from the <optical power> of an <optical lens>, which is reciprocal <focal length> in <dioptres>. Likewise, astronomical <radiative flux> is <power> per <area>. Stating the units prevents these shared words from hiding different physical quantities.
Back to article page
