Radiant flux#units

File:Flow chart inspired by Lillesand, Kiefer, Chipman.. Remote Sensing and Image Interpretation, 7th Edition Appendix A.. Radiometric Concepts, Terminology, and Units.png

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 ({{nobreak|J/s}}), while that of spectral flux in frequency is the watt per hertz ({{nobreak|W/Hz}}) and that of spectral flux in wavelength is the watt per metre ({{nobreak|W/m}})—commonly the watt per nanometre ({{nobreak|W/nm}}).

Mathematical definitions

=Radiant flux=

Radiant flux, denoted Phi ('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

{{mvar|t}} is the time;
{{math|Q_e}} is the radiant energy passing out of a closed surface {{math|Σ}};
{{math|S}} is the Poynting vector, representing the current density of radiant energy;
{{math|n}} is the normal vector of a point on {{math|Σ}};
{{math|A}} represents the area of {{math|Σ}};
{{mvar|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

$\Phi_\mathrm{e} \approx \int_\Sigma \langle|\mathbf{S}|\rangle \cos \alpha\ dA ,$

where {{math|{{angle brackets|-}}}} is the time average, and {{mvar|α}} is the angle between {{math|n}} and $\langle|\mathbf{S}|\rangle.$

=Spectral flux=

Spectral flux in frequency, denoted Φ_e,ν, is defined as

$\Phi_{\mathrm{e},\nu} = \frac{\partial \Phi_\mathrm{e}}{\partial \nu} ,$

where {{mvar|ν}} is the frequency.

Spectral flux in wavelength, denoted {{math|Φ_e,λ}}, is defined as

$\Phi_{\mathrm{e},\lambda} = \frac{\partial \Phi_\mathrm{e}}{\partial \lambda} ,$

where {{mvar|λ}} is the wavelength.

{{anchor|units}}SI radiometry units

File:photometry_radiometry_units.svg

References

{{Reflist|refs=

{{cite web|url=http://www.iso.org/iso/home/store/catalogue_tc/catalogue_detail.htm?csnumber=16943 |title=Thermal insulation — Heat transfer by radiation — Physical quantities and definitions|work=ISO 9288:1989|publisher=ISO catalogue|year=1989|access-date=2015-03-15}}

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