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In radiometry, irradiance and spectral irradiance of a surface are the radiant flux per unit area received by that surface. The SI unit of irradiance is the watt per square metre (W/m), while that of spectral irradiance is the watt per square metre per hertz (W·m·Hz) or the watt per square metre per metre (W·m)—commonly the watt per square metre per nanometre (W·m·nm)—, depending on whether the spectrum is taken as a function of frequency or of wavelength. The CGS unit erg per square centimeter per second (erg·cm·s) 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.

Definitions

Irradiance

Irradiance of a surface, denoted E_e ("e" for "energetic", to avoid confusion with photometric quantities, is given by

${\displaystyle E_{\mathrm {e} }={\frac {\partial \Phi _{\mathrm {e} }}{\partial A}},}$

where

• ∂ is the partial derivative symbol;
• Φ_e is the radiant flux received by that surface;
• A is the area of that surface.

Spectral irradiance

Irradiance of a surface per unit frequency, denoted E_e,ν, is given by

${\displaystyle E_{\mathrm {e} ,\nu }={\frac {\partial E_{\mathrm {e} }}{\partial \nu }},}$

where ν is the frequency.

Irradiance of a surface per unit wavelength, denoted E_e,λ, is given by

${\displaystyle E_{\mathrm {e} ,\lambda }={\frac {\partial E_{\mathrm {e} }}{\partial \lambda }},}$

where λ is the wavelength.

Alternative definition

Irradiance of a surface is also defined as the time-average of the component of the Poynting vector perpendicular to that surface:

${\displaystyle E_{\mathrm {e} }=\langle \mathbf {S} \cdot \mathbf {\hat {n}} \rangle ,}$

where

• S is the Poynting vector;
• ${\displaystyle \mathbf {\hat {n}} }$ is the normal vector to that surface;

In a propagating sinusoidal linearly polarized electromagnetic plane wave, the Poynting vector always points in the direction of propagation while oscillating in magnitude. The irradiance of a surface perpendicular to the direction of propagation is then given by:

${\displaystyle E_{\mathrm {e} }={\frac {n}{2\mu _{0}\mathrm {c} }}E_{\mathrm {m} }^{2}={\frac {n\epsilon _{0}\mathrm {c} }{2}}E_{\mathrm {m} }^{2},}$

where

• E_m is the amplitude of the wave's electric field;
• n is the refractive index of the propagation medium;
• 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:

${\displaystyle E_{\mathrm {e} }=E_{\mathrm {e} ,\mathrm {dir} }+E_{\mathrm {e} ,\mathrm {diff} }+E_{\mathrm {e} ,\mathrm {refl} }.}$

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

1. Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
2. ^ Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
3. ^ Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek letter nu, not to be confused with a letter "v", indicating a photometric quantity.)
4. ^ Spectral quantities given per unit wavelength are denoted with suffix "λ".
5. ^ Directional quantities are denoted with suffix "Ω".

See also

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

References

1. Griffiths, David J. (1999). Introduction to electrodynamics (3. ed., reprint. with corr. ed.). Upper Saddle River, NJ : Prentice-Hall. ISBN 0-13-805326-X.
2. ^ Quaschning, Volker (2003). "Technology fundamentals—The sun as an energy resource". Renewable Energy World. 6 (5): 90–93.
3. Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1016/0038-092X(60)90062-1, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1016/0038-092X(60)90062-1 instead.

• Physical quantities
• Radiometry