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, 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 [Phi|], is defined as
where

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

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
where is the time average, and is the angle between and.

Spectral flux

Spectral flux in frequency, denoted Φ_e,ν, is defined as
where is the frequency.
Spectral flux in wavelength, denoted, is defined as
where is the wavelength.