Absorptance

Absorptance of the surface of a material is its effectiveness in absorbing radiant energy. It is the ratio of the absorbed to the incident radiant power.[1] This should not be confused with absorbance and absorption coefficient.

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

Φ_e^a is the radiant flux absorbed by that surface;
Φ_eⁱ 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]

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

Φ_e,ν^a is the spectral radiant flux in frequency absorbed by that surface;
Φ_e,νⁱ 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,λⁱ 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]

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

where

L_e,Ω^a is the radiance absorbed by that surface;
L_e,Ωⁱ 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]

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

L_e,Ω,ν^a is the spectral radiance in frequency absorbed by that surface;
L_e,Ω,νⁱ 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,λⁱ is the spectral radiance in wavelength received by that surface.

SI radiometry units

SI radiometry units
Quantity		Unit		Dimension	Notes
Name	Symbol[nb 1]	Name	Symbol	Symbol	Notes
Radiant energy	Q_e[nb 2]	joule	J	M⋅L²⋅T⁻²	Energy of electromagnetic radiation.
Radiant energy density	w_e	joule per cubic metre	J/m³	M⋅L⁻¹⋅T⁻²	Radiant energy per unit volume.
Radiant flux	Φ_e[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	Φ_e,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.
Spectral flux	Φ_e,λ[nb 4]	watt per metre	W/m	M⋅L⋅T⁻³
Radiant intensity	I_e,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	I_e,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.
Spectral intensity	I_e,Ω,λ[nb 4]	watt per steradian per metre	W⋅sr⁻¹⋅m⁻¹	M⋅L⋅T⁻³
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]	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".
Spectral radiance	L_e,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	E_e[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	E_e,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).
Spectral irradiance Spectral flux density	E_e,λ[nb 4]	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiosity	J_e[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	J_e,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".
Spectral radiosity	J_e,λ[nb 4]	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiant exitance	M_e[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	M_e,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".
Spectral exitance	M_e,λ[nb 4]	watt per square metre, per metre	W/m³	M⋅L⁻¹⋅T⁻³
Radiant exposure	H_e	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	H_e,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".
Spectral exposure	H_e,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	ε_ν or ε_λ	N/A		1	Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.
Directional emissivity	ε_Ω	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	ε_Ω,ν or ε_Ω,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	A_ν or A_λ	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	A_Ω	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	A_Ω,ν or A_Ω,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	R_ν or R_λ	N/A		1	Spectral flux reflected by a surface, divided by that received by that surface.
Directional reflectance	R_Ω	N/A		1	Radiance reflected by a surface, divided by that received by that surface.
Spectral directional reflectance	R_Ω,ν or R_Ω,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	T_ν or T_λ	N/A		1	Spectral flux transmitted by a surface, divided by that received by that surface.
Directional transmittance	T_Ω	N/A		1	Radiance transmitted by a surface, divided by that received by that surface.
Spectral directional transmittance	T_Ω,ν or T_Ω,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	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.
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–) "Absorptance". doi:10.1351/goldbook.A00035
"Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.

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[note-suffix-e-3] Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.

[note-alternative-symbol-radiometric-4] Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.

[note-suffix-nu-5] 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.

[note-suffix-lambda-6] Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek).

[note-suffix-omega-7] Directional quantities are denoted with suffix "Ω" (Greek).

[GoldBook-1] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Absorptance". doi:10.1351/goldbook.A00035

[ISO_9288-1989-2] "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.