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), that is the joule per second (J/s) in SI base units, while that of spectral flux in frequency is the watt per hertz (W/Hz) and that of spectral flux in wavelength is the watt per metre (W/m)—commonly the watt per nanometre (W/nm).

Radiant flux, denoted Φ_e ("e" for "energetic", to avoid confusion with photometric quantities), is defined as

Φ e = ∂ Q e ∂ t ,

where

∂ is the partial derivative symbol;

Q_e is the radiant energy emitted, reflected, transmitted or received;

t is the time.

Spectral flux

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

Φ e , ν = ∂ Φ e ∂ ν ,

where ν is the frequency.

Spectral flux in wavelength, denoted Φ_e,λ, is defined as

Φ e , λ = ∂ Φ e ∂ λ ,

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":

Φ e = ∮ Σ S ⋅ n ^ d A = ∮ Σ | S | cos ⁡ α d A ,

where

Σ is the surface;

S is the Poynting vector;

n is a unit normal vector to that surface;

A is the area of that surface;

α is the angle between n and S.

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:

Φ e = ∮ Σ ⟨ | S | ⟩ cos ⁡ α d A ,

where < • > is the time-average.

References

Radiant flux Wikipedia

(Text) CC BY-SA

Contents

Radiant flux

Spectral flux

Relationship with the Poynting vector

References