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 ().

Mathematical definitions

Radiant flux

Radiant flux, denoted Φ_e ('e' for "energetic", to avoid confusion with photometric quantities), is defined as
$\Phi_\mathrm = \frac$
:$Q_\mathrm = \int_ \mathbf\cdot \hat\mathbf\, dA$
where
*''t'' is the time;
*''Q''_e is the radiant energy flux of the field out of a closed surface $\Sigma$;
*S is the Poynting vector, representing the current density of radiant energy;
*n is the normal vector of a point on $\Sigma$;
*A represent the area of $\Sigma$.
But the time-average of the norm of the Poynting vector is used instead, because in radiometry it is the only quantity that radiation detectors are able to measure:
$\Phi_\mathrm \approx \int_\Sigma \langle, \mathbf, \rangle \cos \alpha\ dA ,$
where is the time-average, and ''α'' is the angle between n and $\langle, \mathbf, \rangle$.

Spectral flux

Spectral flux in frequency, denoted Φ_e,''ν'', is defined as
$\Phi_ = \frac ,$
where ''ν'' is the frequency.

Spectral flux in wavelength, denoted Φ_e,''λ'', is defined as
$\Phi_ = \frac ,$
where ''λ'' is the wavelength.

SI radiometry units

See also

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

References

Further reading

*

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Power (physics)
Physical quantities
Radiometry
Temporal rates