Radiant flux



In radiometry, radiant flux or radiant power is the radiant energy emitted, reflected, transmitted, or received per unit time, and spectral flux or spectral power is the radiant flux per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant flux is the watt (W), one joule per second, while that of spectral flux in frequency is the watt per hertz and that of spectral flux in wavelength is the watt per metre —commonly the watt per nanometre.

Radiant flux
Radiant flux, denoted $Φ_{e}$ ('e' for "energetic", to avoid confusion with photometric quantities), is defined as $$\begin{align} \Phi_\mathrm{e} &= \frac{d Q_\mathrm{e}}{d t} \\[2pt] Q_\mathrm{e} &= \int_{T} \int_{\Sigma} \mathbf{S}\cdot \hat\mathbf{n}\, dA dt \end{align}$$ where The rate of energy flow through the surface fluctuates at the frequency of the radiation, but radiation detectors only respond to the average rate of flow. This is represented by replacing the Poynting vector with the time average of its norm, giving $$\Phi_\mathrm{e} \approx \int_\Sigma \langle|\mathbf{S}|\rangle \cos \alpha\ dA ,$$ where $Q_{e}$ is the time average, and $t$ is the angle between $&Sigma;$ and $$\langle|\mathbf{S}|\rangle.$$
 * $T$ is the time;
 * $S$ is the radiant energy passing out of a closed surface $n$;
 * $&Sigma;$ is the Poynting vector, representing the current density of radiant energy;
 * $A$ is the normal vector of a point on $&Sigma;$;
 * $$ represents the area of $n$;
 * $α$ represents the time period.

Spectral flux
Spectral flux in frequency, denoted Φe,ν, is defined as $$\Phi_{\mathrm{e},\nu} = \frac{\partial \Phi_\mathrm{e}}{\partial \nu} ,$$ where $ν$ is the frequency.

Spectral flux in wavelength, denoted $Φ_{e,λ}$, is defined as $$\Phi_{\mathrm{e},\lambda} = \frac{\partial \Phi_\mathrm{e}}{\partial \lambda} ,$$ where $λ$ is the wavelength.