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 (W/m²). The CGS unit erg per square centimetre per second (erg·cm⁻²·s⁻¹) 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 (W·m⁻²·nm⁻¹).

Irradiance of a surface, denoted E_e ("e" for "energetic", to avoid confusion with photometric quantities), is defined as

E e = ∂ Φ e ∂ A ,

where

∂ is the partial derivative symbol;

Φ_e is the radiant flux received;

A is the area.

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 E_e,ν, is defined as

E e , ν = ∂ E e ∂ ν ,

where ν is the frequency.

Spectral irradiance in wavelength of a surface, denoted E_e,λ, is defined as

E e , λ = ∂ E e ∂ λ ,

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 e = ⟨ | S | ⟩ cos ⁡ α ,

where

< • > is the time-average;

S is the Poynting vector;

α is the angle between a unit vector normal to the surface and S.

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

E e = n 2 μ 0 c E m 2 cos ⁡ α = n ε 0 c 2 E m 2 cos ⁡ α ,

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.

This formula assumes that the magnetic susceptibility is negligible, i.e. that 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 e = E e , d i r + E e , d i f f + E e , r e f l .

The integral of solar irradiance over a time period is called "solar exposure" or "insolation".

References

Irradiance Wikipedia

(Text) CC BY-SA

Contents

Irradiance

Spectral irradiance

Property

Solar energy

References