Radiant exposure
In radiometry, radiant exposure or fluence is the radiant energy received by a surface per unit area, or equivalently the irradiance of a surface, integrated over time of irradiation, and spectral exposure is the radiant exposure per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of radiant exposure is the joule per square metre (J/m2), while that of spectral exposure in frequency is the joule per square metre per hertz (J⋅m−2⋅Hz−1) and that of spectral exposure in wavelength is the joule per square metre per metre (J/m3)—commonly the joule per square metre per nanometre (J⋅m−2⋅nm−1).
Mathematical definitions
Radiant exposure
Radiant exposure of a surface, denoted He ("e" for "energetic", to avoid confusion with photometric quantities), is defined as[1]
where
- ∂ is the partial derivative symbol;
- Qe is the radiant energy;
- A is the area;
- T is the duration of irradiation;
- Ee is the irradiance.
SI radiometry units
| Quantity | Unit | Dimension | Notes | |||||
|---|---|---|---|---|---|---|---|---|
| Name | Symbol[nb 1] | Name | Symbol | 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". | |||
| 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 | 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 | |||||
| Hemispherical emissivity | ε | N/A | 1 | Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface. | ||||
| Spectral hemispherical emissivity | εν or ελ |
N/A | 1 | Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. | ||||
| Directional emissivity | εΩ | N/A | 1 | Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface. | ||||
| Spectral directional emissivity | εΩ,ν or εΩ,λ |
N/A | 1 | Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface. | ||||
| Hemispherical absorptance | A | N/A | 1 | Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance". | ||||
| Spectral hemispherical absorptance | Aν or Aλ |
N/A | 1 | Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance". | ||||
| Directional absorptance | AΩ | N/A | 1 | Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance". | ||||
| Spectral directional absorptance | AΩ,ν or AΩ,λ |
N/A | 1 | Spectral radiance absorbed by a surface, divided by the spectral radiance incident onto that surface. This should not be confused with "spectral absorbance". | ||||
| Hemispherical reflectance | R | N/A | 1 | Radiant flux reflected by a surface, divided by that received by that surface. | ||||
| Spectral hemispherical reflectance | Rν or Rλ |
N/A | 1 | Spectral flux reflected by a surface, divided by that received by that surface. | ||||
| Directional reflectance | RΩ | N/A | 1 | Radiance reflected by a surface, divided by that received by that surface. | ||||
| Spectral directional reflectance | RΩ,ν or RΩ,λ |
N/A | 1 | Spectral radiance reflected by a surface, divided by that received by that surface. | ||||
| Hemispherical transmittance | T | N/A | 1 | Radiant flux transmitted by a surface, divided by that received by that surface. | ||||
| Spectral hemispherical transmittance | Tν or Tλ |
N/A | 1 | Spectral flux transmitted by a surface, divided by that received by that surface. | ||||
| Directional transmittance | TΩ | N/A | 1 | Radiance transmitted by a surface, divided by that received by that surface. | ||||
| Spectral directional transmittance | TΩ,ν or TΩ,λ |
N/A | 1 | Spectral radiance transmitted by a surface, divided by that received by that surface. | ||||
| Hemispherical attenuation coefficient | μ | reciprocal metre | m−1 | L−1 | Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
| Spectral hemispherical attenuation coefficient | μν or μλ |
reciprocal metre | m−1 | L−1 | Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
| Directional attenuation coefficient | μΩ | reciprocal metre | m−1 | L−1 | Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
| Spectral directional attenuation coefficient | μΩ,ν or μΩ,λ |
reciprocal metre | m−1 | L−1 | Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
| See also: SI · Radiometry · Photometry | ||||||||
- Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
- Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
- Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with suffix "v" (for "visual") indicating a photometric quantity.
- Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek).
- Directional quantities are denoted with suffix "Ω" (Greek).
References
- IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Radiant exposure". doi:10.1351/goldbook.R05042
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