Transmittance

Surface transmittance

Hemispherical transmittance

Hemispherical transmittance of a surface, denoted T, is defined as

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

where

• Φ_e^t is the radiant flux transmitted by that surface into the hemisphere on the opposite side from the incident radiation;
• Φ_eⁱ is the radiant flux received by that surface.

Hemispheric transmittance may be calculated as an integral over the directional transmittance described below.

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

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

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

where

• Φ_e,ν^t is the spectral radiant flux in frequency transmitted by that surface into the hemisphere on the opposite side from the incident radiation;
• 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 into the hemisphere on the opposite side from the incident radiation;
• 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

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

where

• L_e,Ω^t is the radiance transmitted by that surface into the solid angle Ω;
• 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

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

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

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:

${\displaystyle T_{lum}=\frac{{\int }_0^{\mathrm{\infty }}I(\lambda )T(\lambda )V(\lambda )d\lambda }{{\int }_0^{\mathrm{\infty }}I(\lambda )V(\lambda )d\lambda }}$

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.