Radiant exitance
In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. This is the emitted component of radiosity. The SI unit of radiant exitance is the watt per square metre (W/m2), while that of spectral exitance in frequency is the watt per square metre per hertz (W·m−2·Hz−1) and that of spectral exitance in wavelength is the watt per square metre per metre (W·m−3)—commonly the watt per square metre per nanometre (W·m−2·nm−1). The CGS unit erg per square centimeter per second (erg·cm−2·s−1) is often used in astronomy. Radiant exitance is often called "intensity" in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.
Mathematical definitions
[edit]Radiant exitance
[edit]Radiant exitance of a surface, denoted Me ("e" for "energetic", to avoid confusion with photometric quantities), is defined as[1] where ∂ is the partial derivative symbol, Φe is the radiant flux emitted, and A is the surface area.
If we want to talk about the radiant flux received by a surface, we speak of irradiance.
The radiant exitance of a black surface, according to the Stefan–Boltzmann law, is equal to: where σ is the Stefan–Boltzmann constant, and T is the temperature of that surface. For a real surface, the radiant exitance is equal to: where ε is the emissivity of that surface.
Spectral exitance
[edit]Spectral exitance in frequency of a surface, denoted Me,ν, is defined as[1]
where ν is the frequency.
Spectral exitance in wavelength of a surface, denoted Me,λ, is defined as[1] where λ is the wavelength.
The spectral exitance of a black surface around a given frequency or wavelength, according to the Lambert's cosine law and the Planck's law, is equal to:
where h is the Planck constant, ν is the frequency, λ is the wavelength, k is the Boltzmann constant, c is the speed of light in the medium, T is the temperature of that surface. For a real surface, the spectral exitance is equal to:
SI radiometry units
[edit]
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".
![](http://upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Photometry_radiometry_units.svg/330px-Photometry_radiometry_units.svg.png)
See also
[edit]References
[edit]- ^ a b c "Thermal insulation — Heat transfer by radiation — Vocabulary". ISO_9288:2022. International Organization for Standardization. 2022. Retrieved 2023-06-17.