Radiant flux

Radiant flux, denoted Φ_e ('e' for "energetic", to avoid confusion with photometric quantities), is defined as^[1]$${\displaystyle {\begin{aligned}\Phi _{\mathrm {e} }&={\frac {dQ_{\mathrm {e} }}{dt}}\\[2pt]Q_{\mathrm {e} }&=\int _{T}\int _{\Sigma }\mathbf {S} \cdot {\hat {\mathbf {n} }}\,dAdt\end{aligned}}}$$ where

• t is the time;
• Q_e is the radiant energy passing out of a closed surface Σ;
• S is the Poynting vector, representing the current density of radiant energy;
• n is the normal vector of a point on Σ;
• A represents the area of Σ;
• T represents the time period.

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$${\displaystyle \Phi _{\mathrm {e} }\approx \int _{\Sigma }\langle |\mathbf {S} |\rangle \cos \alpha \ dA,}$$ where ⟨-⟩ is the time average, and α is the angle between n and ${\displaystyle \langle |\mathbf {S} |\rangle .}$

Spectral flux in frequency, denoted Φ_e,ν, is defined as^[1]$${\displaystyle \Phi _{\mathrm {e} ,\nu }={\frac {\partial \Phi _{\mathrm {e} }}{\partial \nu }},}$$ where ν is the frequency.

Spectral flux in wavelength, denoted Φ_e,λ, is defined as^[1]$${\displaystyle \Phi _{\mathrm {e} ,\lambda }={\frac {\partial \Phi _{\mathrm {e} }}{\partial \lambda }},}$$ where λ is the wavelength.

• Luminous flux
• Heat flux
• Power (physics)
• Radiosity (heat transfer)

• Boyd, Robert (1983). Radiometry and the Detection of Optical Radiation (Pure & Applied Optics Series). Wiley-Interscience. ISBN 978-0-471-86188-1.