Transmittance

Summary

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]

Earth's atmospheric transmittance over 1 nautical mile sea level path (infrared region[1]). Because of the natural radiation of the hot atmosphere, the intensity of radiation is different from the transmitted part.
Transmittance of ruby in optical and near-IR spectra. Note the two broad blue and green absorption bands and one narrow absorption band on the wavelength of 694 nm, which is the wavelength of the ruby laser.

Internal transmittance refers to energy loss by absorption, whereas (total) transmittance is that due to absorption, scattering, reflection, etc.

Mathematical definitionsEdit

Hemispherical transmittanceEdit

Hemispherical transmittance of a surface, denoted T, is defined as[3]

 

where

  • Φet is the radiant flux transmitted by that surface;
  • Φei is the radiant flux received by that surface.

Spectral hemispherical transmittanceEdit

Spectral hemispherical transmittance in frequency and spectral hemispherical transmittance in wavelength of a surface, denoted Tν and Tλ respectively, are defined as[3]

 
 

where

Directional transmittanceEdit

Directional transmittance of a surface, denoted TΩ, is defined as[3]

 

where

  • Le,Ωt is the radiance transmitted by that surface;
  • Le,Ωi is the radiance received by that surface.

Spectral directional transmittanceEdit

Spectral directional transmittance in frequency and spectral directional transmittance in wavelength of a surface, denoted Tν,Ω and Tλ,Ω respectively, are defined as[3]

 
 

where

Beer–Lambert lawEdit

By definition, internal transmittance is related to optical depth and to absorbance as

 

where

  • τ is the optical depth;
  • A is the absorbance.

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 NA 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.

Other radiometric coefficientsEdit

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
 or
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
 or
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
 or
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
 or
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
 or
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
 or
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
 or
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
 or
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
 or
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
 or
μΩ,λ
m−1 Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.

See alsoEdit

ReferencesEdit

  1. ^ "Electronic warfare and radar systems engineering handbook". Archived from the original on September 13, 2001.{{cite web}}: CS1 maint: unfit URL (link)
  2. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Transmittance". doi:10.1351/goldbook.T06484
  3. ^ a b c d "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.
  4. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Beer–Lambert law". doi:10.1351/goldbook.B00626