# Absorptance

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.

## Mathematical definitions
### Hemispherical absorptance

Hemispherical absorptance of a surface, denoted A is defined as
    $A=\mathrm {\frac {\Phi _{e}^{a}}{\Phi _{e}^{i}}} ,$
where
* ⁠$\mathrm {\Phi _{e}^{a}}$⁠ is the radiant flux absorbed by that surface;
* ⁠$\mathrm {\Phi _{e}^{i}}$⁠ 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
    ${\begin{aligned}A_{\nu }&=\mathrm {\frac {\Phi _{e,\nu }^{a}}{\Phi _{e,\nu }^{i}}} ,\\A_{\lambda }&=\mathrm {\frac {\Phi _{e,\lambda }^{a}}{\Phi _{e,\lambda }^{i}}} ,\end{aligned}}$
where
* ⁠$\mathrm {\Phi _{e,\nu }^{a}}$⁠ is the spectral radiant flux in frequency absorbed by that surface;
* ⁠$\mathrm {\Phi _{e,\nu }^{i}}$⁠ is the spectral radiant flux in frequency received by that surface;
* ⁠$\mathrm {\Phi _{e,\lambda }^{a}}$⁠ is the spectral radiant flux in wavelength absorbed by that surface;
* ⁠$\mathrm {\Phi _{e,\lambda }^{i}}$⁠ is the spectral radiant flux in wavelength received by that surface.

### Directional absorptance

Directional absorptance of a surface, denoted A$_Ω$, is defined as
    $A_{\Omega }={\frac {L_{\mathrm {\mathrm {e} ,\Omega } }^{\mathrm {a} }}{L_{\mathrm {e} ,\Omega }^{\mathrm {i} }}},$
where
* ⁠$L\mathrm {_{e,\Omega }^{a}}$⁠ is the radiance absorbed by that surface;
* ⁠$L\mathrm {_{e,\Omega }^{i}}$⁠ 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
    ${\begin{aligned}A_{\nu ,\Omega }&={\frac {L\mathrm {_{e,\Omega ,\nu }^{a}} }{L\mathrm {_{e,\Omega ,\nu }^{i}} }},\\[4pt]A_{\lambda ,\Omega }&={\frac {L\mathrm {_{e,\Omega ,\lambda }^{a}} }{L\mathrm {_{e,\Omega ,\lambda }^{i}} }},\end{aligned}}$
where
* ⁠$L\mathrm {_{e,\Omega ,\nu }^{a}}$⁠ is the spectral radiance in frequency absorbed by that surface;
* ⁠$L\mathrm {_{e,\Omega ,\nu }^{i}}$⁠ is the spectral radiance received by that surface;
* ⁠$L\mathrm {_{e,\Omega ,\lambda }^{a}}$⁠ is the spectral radiance in wavelength absorbed by that surface;
* ⁠$L\mathrm {_{e,\Omega ,\lambda }^{i}}$⁠ is the spectral radiance in wavelength received by that surface.

## Other radiometric coefficients

Radiometry coefficientsvte :
| Quantity | Quantity | SI units | Notes |
| Name | Sym. | SI units | Notes |
| 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 | ε$_ν$ ε$_λ$ | — | Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. |
| Directional emissivity | ε$_Ω$ | — | Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface. |
| Spectral directional emissivity | ε$_{Ω,ν}$ ε$_{Ω,λ}$ | — | 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 | A$_ν$ A$_λ$ | — | Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance". |
| Directional absorptance | A$_Ω$ | — | Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance". |
| Spectral directional absorptance | A$_{Ω,ν}$ A$_{Ω,λ}$ | — | 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 | R$_ν$ R$_λ$ | — | Spectral flux reflected by a surface, divided by that received by that surface. |
| Directional reflectance | R$_Ω$ | — | Radiance reflected by a surface, divided by that received by that surface. |
| Spectral directional reflectance | R$_{Ω,ν}$ R$_{Ω,λ}$ | — | 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 | T$_ν$ T$_λ$ | — | Spectral flux transmitted by a surface, divided by that received by that surface. |
| Directional transmittance | T$_Ω$ | — | Radiance transmitted by a surface, divided by that received by that surface. |
| Spectral directional transmittance | T$_{Ω,ν}$ T$_{Ω,λ}$ | — | 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 | μ$_ν$ μ$_λ$ | m$^{−1}$ | Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. |
| Directional attenuation coefficient | μ$_Ω$ | m$^{−1}$ | Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. |
| Spectral directional attenuation coefficient | μ$_{Ω,ν}$ μ$_{Ω,λ}$ | m$^{−1}$ | Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. |