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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.
Mathematical definitions
Hemispherical transmittance
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 transmittance
Spectral hemispherical transmittance in frequency and spectral hemispherical transmittance in wavelength of a surface, denoted Tν and Tλ respectively, are defined as[3]
where
- Φe,νt is the spectral radiant flux in frequency transmitted by that surface;
- Φe,νi is the spectral radiant flux in frequency received by that surface;
- Φe,λt is the spectral radiant flux in wavelength transmitted by that surface;
- Φe,λi is the spectral radiant flux in wavelength received by that surface.
Directional transmittance
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 transmittance
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
- Le,Ω,νt is the spectral radiance in frequency transmitted by that surface;
- Le,Ω,νi is the spectral radiance received by that surface;
- Le,Ω,λt is the spectral radiance in wavelength transmitted by that surface;
- Le,Ω,λi is the spectral radiance in wavelength received by that surface.
Luminous transmittance
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:
- is the spectral radiant flux or intensity of the standard illuminant (unspecified magnitude).
- is the spectral transmittance of the filter
- is the luminous efficiency function
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.
Beer–Lambert law
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
- σi is the attenuation cross section of the attenuating species i in the material sample;
- ni is the number density of the attenuating species i in the material sample;
- εi is the molar attenuation coefficient of the attenuating species i in the material sample;
- ci is the amount concentration of the attenuating species i in the material sample;
- ℓ is the path length of the beam of light through the material sample.
Attenuation cross section and molar attenuation coefficient are related by
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