# Absorptance

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.

## Mathematical definitions

### Hemispherical absorptance

Hemispherical absorptance of a surface, denoted A, is defined as[2]

$A = \frac{\Phi_\mathrm{e}^\mathrm{a}}{\Phi_\mathrm{e}^\mathrm{i}},$

where

• Φea is the radiant flux absorbed by that surface;

### Spectral hemispherical absorptance

Spectral hemispherical absorptance in frequency and spectral hemispherical absorptance in wavelength of a surface, denoted Aν and Aλ respectively, are defined as[2]

$A_\nu = \frac{\Phi_{\mathrm{e},\nu}^\mathrm{a}}{\Phi_{\mathrm{e},\nu}^\mathrm{i}},$
$A_\lambda = \frac{\Phi_{\mathrm{e},\lambda}^\mathrm{a}}{\Phi_{\mathrm{e},\lambda}^\mathrm{i}},$

where

### Directional absorptance

Directional absorptance of a surface, denoted AΩ, is defined as[2]

$A_\Omega = \frac{L_{\mathrm{e},\Omega}^\mathrm{a}}{L_{\mathrm{e},\Omega}^\mathrm{i}},$

where

• Le,Ωa is the radiance absorbed by that surface;

### Spectral directional absorptance

Spectral directional absorptance in frequency and spectral directional absorptance in wavelength of a surface, denoted Aν,Ω and Aλ,Ω respectively, are defined as[2]

$A_{\nu,\Omega} = \frac{L_{\mathrm{e},\Omega,\nu}^\mathrm{a}}{L_{\mathrm{e},\Omega,\nu}^\mathrm{i}},$
$A_{\lambda,\Omega} = \frac{L_{\mathrm{e},\Omega,\lambda}^\mathrm{a}}{L_{\mathrm{e},\Omega,\lambda}^\mathrm{i}},$

where

Quantity Unit Dimension Notes
Name Symbol[nb 1] Name Symbol Symbol
Radiant energy density we joule per cubic metre J/m3 ML−1T−2 Radiant energy per unit volume.
Radiant flux Φe[nb 2] watt W or J/s ML2T−3 Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power".
Spectral flux Φe,ν[nb 3]
or
Φe,λ[nb 4]
watt per hertz
or
watt per metre
W/Hz
or
W/m
ML2T−2
or
MLT−3
Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1.
Radiant intensity Ie,Ω[nb 5] watt per steradian W/sr ML2T−3 Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity.
Spectral intensity Ie,Ω,ν[nb 3]
or
Ie,Ω,λ[nb 4]
or
W⋅sr−1⋅Hz−1
or
W⋅sr−1⋅m−1
ML2T−2
or
MLT−3
Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is a directional quantity.
Radiance Le,Ω[nb 5] watt per steradian per square metre W⋅sr−1⋅m−2 MT−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".
or
Le,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
MT−2
or
ML−1T−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 Ee[nb 2] watt per square metre W/m2 MT−3 Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity".
or
Ee,λ[nb 4]
watt per square metre per hertz
or
watt per square metre, per metre
W⋅m−2⋅Hz−1
or
W/m3
MT−2
or
ML−1T−3
Irradiance of a surface per unit frequency or wavelength. The former is commonly measured in 10−22 W⋅m−2⋅Hz−1, known as solar flux unit, and the latter in W⋅m−2⋅nm−1.[nb 6] This is sometimes also confusingly called "spectral intensity".
Radiosity Je[nb 2] watt per square metre W/m2 MT−3 Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity".
or
Je,λ[nb 4]
watt per square metre per hertz
or
watt per square metre, per metre
W⋅m−2⋅Hz−1
or
W/m3
MT−2
or
ML−1T−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 Me[nb 2] watt per square metre W/m2 MT−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]
or
Me,λ[nb 4]
watt per square metre per hertz
or
watt per square metre, per metre
W⋅m−2⋅Hz−1
or
W/m3
MT−2
or
ML−1T−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 He joule per square metre J/m2 MT−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]
or
He,λ[nb 4]
joule per square metre per hertz
or
joule per square metre, per metre
J⋅m−2⋅Hz−1
or
J/m3
MT−1
or
ML−1T−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 εν
or
ελ
1 Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.
Directional emissivity εΩ 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
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 Aν
or
Aλ
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 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
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 Rν
or
Rλ
1 Spectral flux reflected by a surface, divided by that received by that surface.
Directional reflectance RΩ 1 Radiance reflected by a surface, divided by that received by that surface.
Spectral directional reflectance RΩ,ν
or
RΩ,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 Tν
or
Tλ
1 Spectral flux transmitted by a surface, divided by that received by that surface.
Directional transmittance TΩ 1 Radiance transmitted by a surface, divided by that received by that surface.
Spectral directional transmittance TΩ,ν
or
TΩ,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 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.