Editing Transmittance (section)

==Surface Transmittance==
===Hemispherical transmittance===
'''Hemispherical transmittance''' of a surface, denoted ''T'', is defined as<ref name="ISO_9288-1989">{{cite web |date=August 1, 2022 |year= |title=Thermal insulation — Heat transfer by radiation — Vocabulary |url=http://www.iso.org/iso/homehttps://www.iso.org/standard/82088.html/store/catalogue_tc/catalogue_detail.htm?csnumber=16943 |access-date=February 12, 2025 |work=ISO 9288:2022 |publisher=[[International Organization for Standardization|ISO]] catalogue}}</ref>
:<math>T = \frac{\Phi_\mathrm{e}^\mathrm{t}}{\Phi_\mathrm{e}^\mathrm{i}},</math>
where
*Φ<sub>e</sub><sup>t</sup> is the [[radiant flux]] ''transmitted'' by that surface into the hemisphere on the opposite side from the incident radiation;
*Φ<sub>e</sub><sup>i</sup> 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''<sub>ν</sub> and ''T''<sub>λ</sub> respectively, are defined as<ref name="ISO_9288-1989" />
:<math>T_\nu = \frac{\Phi_{\mathrm{e},\nu}^\mathrm{t}}{\Phi_{\mathrm{e},\nu}^\mathrm{i}},</math>
:<math>T_\lambda = \frac{\Phi_{\mathrm{e},\lambda}^\mathrm{t}}{\Phi_{\mathrm{e},\lambda}^\mathrm{i}},</math>
where
*Φ<sub>e,ν</sub><sup>t</sup> is the [[Radiant flux|spectral radiant flux in frequency]] ''transmitted'' by that surface into the hemisphere on the opposite side from the incident radiation;
*Φ<sub>e,ν</sub><sup>i</sup> is the spectral radiant flux in frequency received by that surface;
*Φ<sub>e,λ</sub><sup>t</sup> is the [[Radiant flux|spectral radiant flux in wavelength]] ''transmitted'' by that surface into the hemisphere on the opposite side from the incident radiation;
*Φ<sub>e,λ</sub><sup>i</sup> is the spectral radiant flux in wavelength received by that surface.

===Directional transmittance===
'''Directional transmittance''' of a surface, denoted ''T''<sub>Ω</sub>, is defined as<ref name="ISO_9288-1989" />
:<math>T_\Omega = \frac{L_{\mathrm{e},\Omega}^\mathrm{t}}{L_{\mathrm{e},\Omega}^\mathrm{i}},</math>
where
*''L''<sub>e,Ω</sub><sup>t</sup> is the [[radiance]] ''transmitted'' by that surface into the [[solid angle]] Ω;
*''L''<sub>e,Ω</sub><sup>i</sup> 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''<sub>ν,Ω</sub> and ''T''<sub>λ,Ω</sub> respectively, are defined as<ref name="ISO_9288-1989" />
:<math>T_{\nu,\Omega} = \frac{L_{\mathrm{e},\Omega,\nu}^\mathrm{t}}{L_{\mathrm{e},\Omega,\nu}^\mathrm{i}},</math>
:<math>T_{\lambda,\Omega} = \frac{L_{\mathrm{e},\Omega,\lambda}^\mathrm{t}}{L_{\mathrm{e},\Omega,\lambda}^\mathrm{i}},</math>
where
*''L''<sub>e,Ω,ν</sub><sup>t</sup> is the [[Radiance|spectral radiance in frequency]] ''transmitted'' by that surface;
*''L''<sub>e,Ω,ν</sub><sup>i</sup> is the spectral radiance received by that surface;
*''L''<sub>e,Ω,λ</sub><sup>t</sup> is the [[Radiance|spectral radiance in wavelength]] ''transmitted'' by that surface;
*''L''<sub>e,Ω,λ</sub><sup>i</sup> 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:

:<math>T_{lum} = \frac{\int_0^\infty I(\lambda)T(\lambda)V(\lambda)d\lambda}{\int_0^\infty I(\lambda)V(\lambda)d\lambda}</math>

where:
*<math>I(\lambda)</math> is the spectral radiant flux or intensity of the standard illuminant (unspecified magnitude).
*<math>T(\lambda)</math> is the spectral transmittance of the filter
*<math>V(\lambda)</math> 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]].