# Irradiance

In radiometry,

**irradiance**is the radiant flux ( power)*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" in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.**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 (W·m−2·Hz−1), while spectral irradiance of a wavelength spectrum is measured in watts per square metre per metre (W·m−3), or more commonly watts per square metre per nanometre ().## Mathematical definitions

### Irradiance

Irradiance of a surface, denoted*E*e ("e" for "energetic", to avoid confusion with photometric quantities), is defined as E_\mathrm{e} = \frac{\partial \Phi_\mathrm{e}}{\partial A}, where- ∂ is the partial derivative symbol;
- Φe is the radiant flux received;
*A*is the area.

*emitted*by a surface, we speak of radiant exitance.### Spectral irradiance

Spectral irradiance in frequency of a surface, denoted*E*e,ν, is defined as E_{\mathrm{e},\nu} = \frac{\partial E_\mathrm{e}}{\partial \nu}, where*ν*is the frequency. Spectral irradiance in wavelength of a surface, denoted*E*e,λ, is defined as E_{\mathrm{e},\lambda} = \frac{\partial E_\mathrm{e}}{\partial \lambda}, 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: E_\mathrm{e} = \langle|\mathbf{S}|\rangle \cos \alpha, where- < • > is the time-average;
**S**is the Poynting vector;*α*is the angle between a unit vector normal to the surface and**S**.

*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 E_\mathrm{e} = \frac{n}{2 \mu_0 \mathrm{c}} E_\mathrm{m}^2 \cos \alpha = \frac{n \varepsilon_0 \mathrm{c}}{2} E_\mathrm{m}^2 \cos \alpha, where*E*m is the amplitude of the wave's electric field;*n*is the refractive index of the medium of propagation;- c is the speed of light in vacuum;
- μ0 is the vacuum permeability;
- ε0 is the vacuum permittivity.

*μ*r ≈ 1 where*μ*r 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*E*e,dir and diffuse irradiance*E*e,diff. On a tilted plane, there is another irradiance component,*E*e,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*E*e on a tilted plane consists of three components: E_\mathrm{e} = E_{\mathrm{e},\mathrm{dir}} + E_{\mathrm{e},\mathrm{diff}} + E_{\mathrm{e},\mathrm{refl}}. The integral of solar irradiance over a time period is called " solar exposure" or " insolation".## SI radiometry units

## See also

- Illuminance
- Spectral flux density
- Albedo
- Fluence
- Insolation
- Light diffusion
- PI curve (photosynthesis-irradiance curve)
- Solar azimuth angle
- Solar irradiance
- Solar noon
- Stefan–Boltzmann law