In optical physics, transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is the ratio of the transmitted to incident electric field.^{[2]}
Internal transmittance refers to energy loss by absorption, whereas (total) transmittance is that due to absorption, scattering, reflection, etc.
Hemispherical transmittance of a surface, denoted T, is defined as^{[3]}
where
Spectral hemispherical transmittance in frequency and spectral hemispherical transmittance in wavelength of a surface, denoted T_{ν} and T_{λ} respectively, are defined as^{[3]}
where
Directional transmittance of a surface, denoted T_{Ω}, is defined as^{[3]}
where
Spectral directional transmittance in frequency and spectral directional transmittance in wavelength of a surface, denoted T_{ν,Ω} and T_{λ,Ω} respectively, are defined as^{[3]}
where
In the field of photometry (optics), the luminous transmittance of a filter is a measure of the amount of luminous flux or intensity transmitted by an optical filter. It is generally defined in terms of a standard illuminant (e.g. Illuminant A, Iluminant C, or Illuminant E). The luminous transmittance with respect to the standard illuminant is defined as:
where:
The luminous transmittance is independent of the magnitude of the flux or intensity of the standard illuminant used to measure it, and is a dimensionless quantity.
Main article: Beer–Lambert law |
By definition, internal transmittance is related to optical depth and to absorbance as
where
The Beer–Lambert law states that, for N attenuating species in the material sample,
or equivalently that
where
Attenuation cross section and molar attenuation coefficient are related by
and number density and amount concentration by
where N_{A} is the Avogadro constant.
In case of uniform attenuation, these relations become^{[4]}
or equivalently
Cases of non-uniform attenuation occur in atmospheric science applications and radiation shielding theory for instance.
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 | 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. |