Absorptance of the surface of a material is its effectiveness in absorbing radiant energy. It is the fraction of incident electromagnetic power that is absorbed at an interface, in contrast to the absorption coefficient, which is the ratio of the absorbed to incident electric field.^{[1]} This should not be confused with absorbance.
Contents
Mathematical definitions
Hemispherical absorptance
Hemispherical absorptance of a surface, denoted A, is defined as^{[2]}
where
- Φ_{e}^{a} is the radiant flux absorbed by that surface;
- Φ_{e}^{i} is the radiant flux received by that surface.
Spectral hemispherical absorptance
Spectral hemispherical absorptance in frequency and spectral hemispherical absorptance in wavelength of a surface, denoted A_{ν} and A_{λ} respectively, are defined as^{[2]}
where
- Φ_{e,ν}^{a} is the spectral radiant flux in frequency absorbed by that surface;
- Φ_{e,ν}^{i} is the spectral radiant flux in frequency received by that surface;
- Φ_{e,λ}^{a} is the spectral radiant flux in wavelength absorbed by that surface;
- Φ_{e,λ}^{i} is the spectral radiant flux in wavelength received by that surface.
Directional absorptance
Directional absorptance of a surface, denoted A_{Ω}, is defined as^{[2]}
where
- L_{e,Ω}^{a} is the radiance absorbed by that surface;
- L_{e,Ω}^{i} is the radiance received by that surface.
Spectral directional absorptance
Spectral directional absorptance in frequency and spectral directional absorptance in wavelength of a surface, denoted A_{ν,Ω} and A_{λ,Ω} respectively, are defined as^{[2]}
where
- L_{e,Ω,ν}^{a} is the spectral radiance in frequency absorbed by that surface;
- L_{e,Ω,ν}^{i} is the spectral radiance received by that surface;
- L_{e,Ω,λ}^{a} is the spectral radiance in wavelength absorbed by that surface;
- L_{e,Ω,λ}^{i} is the spectral radiance in wavelength received by that surface.
SI radiometry units
Quantity | Unit | Dimension | Notes | |||||
---|---|---|---|---|---|---|---|---|
Name | Symbol^{[nb 1]} | Name | Symbol | Symbol | ||||
Radiant energy | Q_{e}^{[nb 2]} | joule | J | M⋅L^{2}⋅T^{−2} | Energy of electromagnetic radiation. | |||
Radiant energy density | w_{e} | joule per cubic metre | J/m^{3} | M⋅L^{−1}⋅T^{−2} | Radiant energy per unit volume. | |||
Radiant flux | Φ_{e}^{[nb 2]} | watt | W = J/s | M⋅L^{2}⋅T^{−3} | Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power". | |||
Spectral flux | Φ_{e,ν}^{[nb 3]} or Φ_{e,λ}^{[nb 4]} |
watt per hertz or watt per metre |
W/Hz or W/m |
M⋅L^{2}⋅T^{−2} or M⋅L⋅T^{−3} |
Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm^{−1}. | |||
Radiant intensity | I_{e,Ω}^{[nb 5]} | watt per steradian | W/sr | M⋅L^{2}⋅T^{−3} | Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. | |||
Spectral intensity | I_{e,Ω,ν}^{[nb 3]} or I_{e,Ω,λ}^{[nb 4]} |
watt per steradian per hertz or watt per steradian per metre |
W⋅sr^{−1}⋅Hz^{−1} or W⋅sr^{−1}⋅m^{−1} |
M⋅L^{2}⋅T^{−2} or M⋅L⋅T^{−3} |
Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr^{−1}⋅nm^{−1}. This is a directional quantity. | |||
Radiance | L_{e,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 | L_{e,Ω,ν}^{[nb 3]} or L_{e,Ω,λ}^{[nb 4]} |
watt per steradian per square metre per hertz or watt per steradian per square metre, per metre |
W⋅sr^{−1}⋅m^{−2}⋅Hz^{−1} or W⋅sr^{−1}⋅m^{−3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
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". | |||
Irradiance Flux density |
E_{e}^{[nb 2]} | watt per square metre | W/m^{2} | M⋅T^{−3} | Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". | |||
Spectral irradiance Spectral flux density |
E_{e,ν}^{[nb 3]} or E_{e,λ}^{[nb 4]} |
watt per square metre per hertz or watt per square metre, per metre |
W⋅m^{−2}⋅Hz^{−1} or W/m^{3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
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} = 10^{4} Jy). | |||
Radiosity | J_{e}^{[nb 2]} | watt per square metre | W/m^{2} | 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 | J_{e,ν}^{[nb 3]} or J_{e,λ}^{[nb 4]} |
watt per square metre per hertz or watt per square metre, per metre |
W⋅m^{−2}⋅Hz^{−1} or W/m^{3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
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". | |||
Radiant exitance | M_{e}^{[nb 2]} | watt per square metre | W/m^{2} | 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 | M_{e,ν}^{[nb 3]} or M_{e,λ}^{[nb 4]} |
watt per square metre per hertz or watt per square metre, per metre |
W⋅m^{−2}⋅Hz^{−1} or W/m^{3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
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". | |||
Radiant exposure | H_{e} | joule per square metre | J/m^{2} | 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 | H_{e,ν}^{[nb 3]} or H_{e,λ}^{[nb 4]} |
joule per square metre per hertz or joule per square metre, per metre |
J⋅m^{−2}⋅Hz^{−1} or J/m^{3} |
M⋅T^{−1} or M⋅L^{−1}⋅T^{−2} |
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". | |||
Hemispherical emissivity | ε | 1 | Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface. | |||||
Spectral hemispherical emissivity | ε_{ν} or ε_{λ} |
1 | Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. | |||||
Directional emissivity | ε_{Ω} | 1 | Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface. | |||||
Spectral directional emissivity | ε_{Ω,ν} or ε_{Ω,λ} |
1 | Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface. | |||||
Hemispherical absorptance | 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 | A_{ν} or A_{λ} |
1 | Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance". | |||||
Directional absorptance | A_{Ω} | 1 | Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance". | |||||
Spectral directional absorptance | A_{Ω,ν} or A_{Ω,λ} |
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 | 1 | Radiant flux reflected by a surface, divided by that received by that surface. | |||||
Spectral hemispherical reflectance | R_{ν} or R_{λ} |
1 | Spectral flux reflected by a surface, divided by that received by that surface. | |||||
Directional reflectance | R_{Ω} | 1 | Radiance reflected by a surface, divided by that received by that surface. | |||||
Spectral directional reflectance | R_{Ω,ν} or R_{Ω,λ} |
1 | Spectral radiance reflected by a surface, divided by that received by that surface. | |||||
Hemispherical transmittance | T | 1 | Radiant flux transmitted by a surface, divided by that received by that surface. | |||||
Spectral hemispherical transmittance | T_{ν} or T_{λ} |
1 | Spectral flux transmitted by a surface, divided by that received by that surface. | |||||
Directional transmittance | T_{Ω} | 1 | Radiance transmitted by a surface, divided by that received by that surface. | |||||
Spectral directional transmittance | T_{Ω,ν} or T_{Ω,λ} |
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 | μ_{ν} or μ_{λ} |
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 | μ_{Ω} | 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 | μ_{Ω,ν} or μ_{Ω,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.
- ^ ^{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)—not to be confused with suffix "v" (for "visual") indicating a photometric quantity.
- ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek).
- ^ ^{a} ^{b} Directional quantities are denoted with suffix "Ω" (Greek).
References
- ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Absorptance". doi:10.1351/goldbook.A00035
- ^ ^{a} ^{b} ^{c} ^{d} "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.