Irradiance


In radiometry, irradiance is the radiant flux received by a surface per unit area. The SI unit of irradiance is the watt per square metre. The CGS unit erg per square centimetre per second is often used in astronomy. Irradiance is often called intensity, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity. In astrophysics, irradiance is called radiant flux.
Spectral irradiance is the irradiance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The two forms have different dimensions: spectral irradiance of a frequency spectrum is measured in watts per square metre per hertz, while spectral irradiance of a wavelength spectrum is measured in watts per square metre per metre, or more commonly watts per square metre per nanometre.

Mathematical definitions

Irradiance

Irradiance of a surface, denoted Ee, is defined as
where
If we want to talk about the radiant flux emitted by a surface, we speak of radiant exitance.

Spectral irradiance

Spectral irradiance in frequency of a surface, denoted Ee,ν, is defined as
where ν is the frequency.
Spectral irradiance in wavelength of a surface, denoted Ee,λ, is defined as
where λ is the wavelength.

Property

Irradiance of a surface is also, according to the definition of radiant flux, equal to the time-average of the component of the Poynting vector perpendicular to the surface:
where
For a propagating sinusoidal linearly polarized electromagnetic plane wave, the Poynting vector always points to the direction of propagation while oscillating in magnitude. The irradiance of a surface is then given by
where
This formula assumes that the magnetic susceptibility is negligible, i.e. that μr ≈ 1 where μr is the magnetic permeability of the propagation medium. This assumption is typically valid in transparent media in the optical frequency range.

Solar energy

The global irradiance on a horizontal surface on Earth consists of the direct irradiance Ee,dir and diffuse irradiance Ee,diff. On a tilted plane, there is another irradiance component, Ee,refl, which is the component that is reflected from the ground. The average ground reflection is about 20% of the global irradiance. Hence, the irradiance Ee on a tilted plane consists of three components:
The integral of solar irradiance over a time period is called "solar exposure" or "insolation".

SI radiometry units