Radiant flux

A flow chart describing the relationship of various physical quantities, including radiant flux and exitance

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 (Template:Nobreak), while that of spectral flux in frequency is the watt per hertz (Template:Nobreak) and that of spectral flux in wavelength is the watt per metre (Template:Nobreak)—commonly the watt per nanometre (Template:Nobreak). Radiant flux is sometimes called luminosity, especially in astronomy contexts.

Mathematical definitions

Radiant flux

Radiant flux, denoted [[Phi|Template:Math]] ('e' for "energetic", to avoid confusion with photometric quantities), is defined as $$\begin{array}{cc}{\mathrm{\Phi }}_{\mathrm{e}}& =\frac{d{Q}_{\mathrm{e}}}{dt}\\ Q_{\mathrm{e}}& ={\int }_T{\int }_{\mathrm{\Sigma }}𝐒\cdot \widehat{𝐧}dAdt\end{array}$$ where

• Template:Math is the radiant energy passing out of a closed surface Template:Math in time interval Template:Mvar;
• Template:Mvar is time;
• Template:Mvar is the area of the surface Template:Math;
• Template:Math is the Poynting vector, representing the directional flow of energy per unit time, per unit area;
• Template:Math is the unit normal vector to the differential area element Template:Math.

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 $${\mathrm{\Phi }}_{\mathrm{e}}\approx {\int }_{\mathrm{\Sigma }}⟨|𝐒|⟩\cos \alpha dA,$$ where Template:Math is the time average, and Template:Mvar is the angle between Template:Math and Template:Math.

Spectral flux

Spectral flux in frequency, denoted Φ_e,ν, is defined as $${\mathrm{\Phi }}_{\mathrm{e},\nu }=\frac{\partial {\mathrm{\Phi }}_{\mathrm{e}}}{\partial \nu },$$ where Template:Mvar is the frequency.

Spectral flux in wavelength, denoted Template:Math, is defined as $${\mathrm{\Phi }}_{\mathrm{e},\lambda }=\frac{\partial {\mathrm{\Phi }}_{\mathrm{e}}}{\partial \lambda },$$ where Template:Mvar is the wavelength.

SI radiometry units

Comparison of photometric and radiometric quantities

See also

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

Further reading

• Template:Cite book