Absorptance

Not to be confused with absorbance or absorption coefficient.

In the study of heat transfer, 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.<ref name=GoldBook>IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Absorptance". doi:10.1351/goldbook.A00035</ref>

Mathematical definitions

Hemispherical absorptance

Hemispherical absorptance of a surface, denoted A is defined as<ref name="ISO_9288-1989">"Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.</ref>

<math>A = \mathrm{ \frac{\Phi_e^a}{\Phi_e^i} },</math>

where

• <math>\mathrm{\Phi_e^a} </math> is the radiant flux absorbed by that surface;
• <math>\mathrm{\Phi_e^i} </math> 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<ref name="ISO_9288-1989" />

<math>\begin{align}

A_\nu &= \mathrm{ \frac{\Phi_{e,\nu}^a}{\Phi_{e,\nu}^i} }, \\ A_\lambda &= \mathrm{ \frac{\Phi_{e,\lambda}^a}{\Phi_{e,\lambda}^i} }, \end{align}</math> where

• <math>\mathrm{\Phi_{e,\nu}^a} </math> is the spectral radiant flux in frequency absorbed by that surface;
• <math>\mathrm{\Phi_{e,\nu}^i} </math> is the spectral radiant flux in frequency received by that surface;
• <math>\mathrm{\Phi_{e,\lambda}^a} </math> is the spectral radiant flux in wavelength absorbed by that surface;
• <math>\mathrm{\Phi_{e,\lambda}^i} </math> is the spectral radiant flux in wavelength received by that surface.

Directional absorptance

Directional absorptance of a surface, denoted A_Ω, is defined as<ref name="ISO_9288-1989" />

<math>A_\Omega = \frac{L_\mathrm{\mathrm{e},\Omega}^\mathrm{a}}{L_{\mathrm{e},\Omega}^\mathrm{i}},</math>

where

• <math>L\mathrm{_{e,\Omega}^a} </math> is the radiance absorbed by that surface;
• <math>L\mathrm{_{e,\Omega}^i} </math> 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<ref name="ISO_9288-1989" />

<math>\begin{align}

A_{\nu,\Omega} &= \frac{L\mathrm{_{e,\Omega,\nu}^a}}{L\mathrm{_{e,\Omega,\nu}^i}}, \\[4pt] A_{\lambda,\Omega} &= \frac{L\mathrm{_{e,\Omega,\lambda}^a}}{L\mathrm{_{e,\Omega,\lambda}^i}}, \end{align}</math> where

• <math>L\mathrm{_{e,\Omega,\nu}^a} </math> is the spectral radiance in frequency absorbed by that surface;
• <math>L\mathrm{_{e,\Omega,\nu}^i} </math> is the spectral radiance received by that surface;
• <math>L\mathrm{_{e,\Omega,\lambda}^a} </math> is the spectral radiance in wavelength absorbed by that surface;
• <math>L\mathrm{_{e,\Omega,\lambda}^i} </math> is the spectral radiance in wavelength received by that surface.

Other radiometric coefficients

Radiometry coefficients

Quantity		SI units	Notes
Name	Sym.
Hemispherical emissivity	ε	—	Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface.
Spectral hemispherical emissivity	εν ελ	—	Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.
Directional emissivity	εΩ	—	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 εΩ,λ	—	Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface.
Hemispherical absorptance	A	—	Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance".
Spectral hemispherical absorptance	Aν Aλ	—	Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance".
Directional absorptance	AΩ	—	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 AΩ,λ	—	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	—	Radiant flux reflected by a surface, divided by that received by that surface.
Spectral hemispherical reflectance	Rν Rλ	—	Spectral flux reflected by a surface, divided by that received by that surface.
Directional reflectance	RΩ	—	Radiance reflected by a surface, divided by that received by that surface.
Spectral directional reflectance	RΩ,ν RΩ,λ	—	Spectral radiance reflected by a surface, divided by that received by that surface.
Hemispherical transmittance	T	—	Radiant flux transmitted by a surface, divided by that received by that surface.
Spectral hemispherical transmittance	Tν Tλ	—	Spectral flux transmitted by a surface, divided by that received by that surface.
Directional transmittance	TΩ	—	Radiance transmitted by a surface, divided by that received by that surface.
Spectral directional transmittance	TΩ,ν TΩ,λ	—	Spectral radiance transmitted by a surface, divided by that received by that surface.
Hemispherical attenuation coefficient	μ	m−1	Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral hemispherical attenuation coefficient	μν μλ	m−1	Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.
Directional attenuation coefficient	μΩ	m−1	Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.
Spectral directional attenuation coefficient	μΩ,ν μΩ,λ	m−1	Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.