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, that is the joule per second in SI base units, 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 Φe, is defined as
where
Spectral flux in frequency, denoted Φe,ν, is defined as
where ν is the frequency.
Spectral flux in wavelength, denoted Φe,λ, is defined as
where λ is the wavelength.

Relationship with the Poynting vector

One can show that the radiant flux of a surface is the flux of the Poynting vector through this surface, hence the name "radiant flux":
where
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:
where < • > is the time-average.

SI radiometry units