Irradiance
Irradiance is the power of electromagnetic radiation per unit area (radiative flux) incident on a surface. Radiant emittance or radiant exitance is the power per unit area radiated by a surface. The SI units for all of these quantities are watts per square meter (W/m2), while the cgs units are ergs per square centimeter per second (erg·cm−2·s−1, often used in astronomy). These quantities are sometimes called intensity, but this usage leads to confusion with radiant intensity, which has different units.
All of these quantities characterize the total amount of radiation present, at all frequencies. It is also common to consider each frequency in the spectrum separately. When this is done for radiation incident on a surface, it is called spectral irradiance, and has SI units W/m3, or commonly W·m−2·nm−1.
If a point source radiates light uniformly in all directions through a non-absorptive medium, then the irradiance decreases in proportion to the square of the distance from the object.
Technical details
The irradiance of a monochromatic light wave in matter is given in terms of its electric field by [1]
- ,
where E is the complex amplitude of the wave's electric field, n is the refractive index of the medium, is the speed of light in vacuum, and ϵ0 is the vacuum permittivity. (This formula assumes that the magnetic susceptibility is negligible, i.e. where is the magnetic permeability of the light transmitting media. This assumption is typically valid in transparent media in the optical frequency range.)
Irradiance is also the time average of the component of the Poynting vector perpendicular to the surface.
Solar energy
The global irradiance on a horizontal surface on Earth consists of the direct irradiance Edir and diffuse irradiance Edif. On a tilted plane, there is another irradiance component: Eref, which is the component that is reflected from the ground. The average ground reflection is about 20% of the global irradiance. Hence, the irradiance Etilt on a tilted plane consists of three components: Etilt = Edir + Edif + Eref.[2]
The integral of solar irradiance over a time period is solar irradiation or insolation. Irradiation is generally measured in J/m2 and is represented by the symbol H.[2]
Quantity | Unit | Dimension | Notes | ||
---|---|---|---|---|---|
Name | Symbol[nb 1] | Name | Symbol | ||
Radiant energy | Qe[nb 2] | joule | J | M⋅L2⋅T−2 | Energy of electromagnetic radiation. |
Radiant energy density | we | joule per cubic metre | J/m3 | M⋅L−1⋅T−2 | Radiant energy per unit volume. |
Radiant flux | Φe[nb 2] | watt | W = J/s | M⋅L2⋅T−3 | Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and called luminosity in Astronomy. |
Spectral flux | Φe,ν[nb 3] | watt per hertz | W/Hz | M⋅L2⋅T −2 | Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm−1. |
Φe,λ[nb 4] | watt per metre | W/m | M⋅L⋅T−3 | ||
Radiant intensity | Ie,Ω[nb 5] | watt per steradian | W/sr | M⋅L2⋅T−3 | Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. |
Spectral intensity | Ie,Ω,ν[nb 3] | watt per steradian per hertz | W⋅sr−1⋅Hz−1 | M⋅L2⋅T−2 | Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅nm−1. This is a directional quantity. |
Ie,Ω,λ[nb 4] | watt per steradian per metre | W⋅sr−1⋅m−1 | M⋅L⋅T−3 | ||
Radiance | Le,Ω[nb 5] | watt per steradian per square metre | W⋅sr−1⋅m−2 | M⋅T−3 | Radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit projected area. This is a directional quantity. This is sometimes also confusingly called "intensity". |
Spectral radiance Specific intensity |
Le,Ω,ν[nb 3] | watt per steradian per square metre per hertz | W⋅sr−1⋅m−2⋅Hz−1 | M⋅T−2 | Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is a directional quantity. This is sometimes also confusingly called "spectral intensity". |
Le,Ω,λ[nb 4] | watt per steradian per square metre, per metre | W⋅sr−1⋅m−3 | M⋅L−1⋅T−3 | ||
Irradiance Flux density |
Ee[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". |
Spectral irradiance Spectral flux density |
Ee,ν[nb 3] | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Irradiance of a surface per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density include jansky (1 Jy = 10−26 W⋅m−2⋅Hz−1) and solar flux unit (1 sfu = 10−22 W⋅m−2⋅Hz−1 = 104 Jy). |
Ee,λ[nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
Radiosity | Je[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity". |
Spectral radiosity | Je,ν[nb 3] | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. This is sometimes also confusingly called "spectral intensity". |
Je,λ[nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
Radiant exitance | Me[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant flux emitted by a surface per unit area. This is the emitted component of radiosity. "Radiant emittance" is an old term for this quantity. This is sometimes also confusingly called "intensity". |
Spectral exitance | Me,ν[nb 3] | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Radiant exitance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity". |
Me,λ[nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
Radiant exposure | He | joule per square metre | J/m2 | M⋅T−2 | Radiant energy received by a surface per unit area, or equivalently irradiance of a surface integrated over time of irradiation. This is sometimes also called "radiant fluence". |
Spectral exposure | He,ν[nb 3] | joule per square metre per hertz | J⋅m−2⋅Hz−1 | M⋅T−1 | Radiant exposure of a surface per unit frequency or wavelength. The latter is commonly measured in J⋅m−2⋅nm−1. This is sometimes also called "spectral fluence". |
He,λ[nb 4] | joule per square metre, per metre | J/m3 | M⋅L−1⋅T−2 | ||
See also: |
- ^ Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
- ^ a b c d e Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
- ^ a b c d e f g 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.)
- ^ a b c d e f g Spectral quantities given per unit wavelength are denoted with suffix "λ".
- ^ a b Directional quantities are denoted with suffix "Ω".
See also
- Radiometry
- Spectral flux density
- Photometry (optics) Main Photometry/Radiometry article—explains technical terms
- Albedo
- Illuminance
- Fluence
- Insolation
- Light diffusion
- Solar azimuth angle
- Solar irradiation
- Solar constant
- Solar noon
- Stefan-Boltzmann law
References
- ^ Griffiths, David J. (1999). Introduction to electrodynamics (3. ed., reprint. with corr. ed.). Upper Saddle River, NJ [u.a.]: Prentice-Hall. ISBN 0-13-805326-X.
- ^ a b Quaschning, Volker (2003). "Technology fundamentals—The sun as an energy resource". Renewable Energy World. 6 (5): 90–93.