Hemispherical transmittance

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

${\displaystyle T={\frac {\Phi _{\mathrm {e} }^{\mathrm {t} }}{\Phi _{\mathrm {e} }^{\mathrm {i} }}},}$

where

• Φ_e^t is the radiant flux transmitted by that surface;
• Φ_eⁱ 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 T_ν and T_λ respectively, are defined as^[3]

${\displaystyle T_{\nu }={\frac {\Phi _{\mathrm {e} ,\nu }^{\mathrm {t} }}{\Phi _{\mathrm {e} ,\nu }^{\mathrm {i} }}},}$

${\displaystyle T_{\lambda }={\frac {\Phi _{\mathrm {e} ,\lambda }^{\mathrm {t} }}{\Phi _{\mathrm {e} ,\lambda }^{\mathrm {i} }}},}$

where

• Φ_e,ν^t is the spectral radiant flux in frequency transmitted by that surface;
• Φ_e,νⁱ is the spectral radiant flux in frequency received by that surface;
• Φ_e,λ^t is the spectral radiant flux in wavelength transmitted by that surface;
• Φ_e,λⁱ is the spectral radiant flux in wavelength received by that surface.

Directional transmittance

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

${\displaystyle T_{\Omega }={\frac {L_{\mathrm {e} ,\Omega }^{\mathrm {t} }}{L_{\mathrm {e} ,\Omega }^{\mathrm {i} }}},}$

where

• L_e,Ω^t is the radiance transmitted by that surface;
• L_e,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 T_ν,Ω and T_λ,Ω respectively, are defined as^[3]

${\displaystyle T_{\nu ,\Omega }={\frac {L_{\mathrm {e} ,\Omega ,\nu }^{\mathrm {t} }}{L_{\mathrm {e} ,\Omega ,\nu }^{\mathrm {i} }}},}$

${\displaystyle T_{\lambda ,\Omega }={\frac {L_{\mathrm {e} ,\Omega ,\lambda }^{\mathrm {t} }}{L_{\mathrm {e} ,\Omega ,\lambda }^{\mathrm {i} }}},}$

where

• L_e,Ω,ν^t is the spectral radiance in frequency transmitted by that surface;
• L_e,Ω,νⁱ is the spectral radiance received by that surface;
• L_e,Ω,λ^t is the spectral radiance in wavelength transmitted by that surface;
• L_e,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:

${\displaystyle T_{lum}={\frac {\int _{0}^{\infty }I(\lambda )T(\lambda )V(\lambda )d\lambda }{\int _{0}^{\infty }I(\lambda )V(\lambda )d\lambda }}}$

where:

• ${\displaystyle I(\lambda )}$ is the spectral radiant flux or intensity of the standard illuminant (unspecified magnitude).
• ${\displaystyle T(\lambda )}$ is the spectral transmittance of the filter
• ${\displaystyle V(\lambda )}$ 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.