ISO/TC 211 Multi-Lingual Glossary of Terms (MLGT)

Note 1 to entry: The parameters are, collectively, known as the Stokes Real {ordered}, a ${\displaystyle 4\times 1}$ Real {ordered}.

Note 2 to entry: The Stokes parameters were introduced as a mathematically convenient alternative by Sir George Stokes.[14,17] These four parameters are related to the horizontally and vertically polarized components of electric field by: ${\displaystyle \left[\begin{array}{c}I\\ Q\\ U\\ V\end{array}\right]=\frac{1}{\eta }\left[\begin{array}{c}\langle {\left|E_{\text{v}}\right|}^2\rangle +{\langle \left|E_{\text{h}}\right|\rangle }^2\\ {\langle \left|E_{\text{v}}\right|\rangle }^2-{\langle \left|E_{\text{h}}\right|\rangle }^2\\ 2\text{Re}\langle E_{\text{v}}{E}_{\text{h}}^{\ast }\rangle \\ 2\text{Im}\langle E_{\text{v}}{E}_{\text{h}}^{\ast }\rangle \end{array}\right]}$ where ${\displaystyle E_{\text{v}}}$ is the vertically polarized component of electric field; ${\displaystyle E_{\text{h}}}$ is the horizontally polarized component of electric field. The units of the Stokes parameters are ${\displaystyle W/m^2}$ . The first Stokes parameter (${\displaystyle I}$ ) gives the total radiation power density, and the second Stokes parameter (${\displaystyle Q}$ ) represents the power density difference between the two linearly polarized components. The third and fourth Stokes parameters (${\displaystyle U}$ and ${\displaystyle V}$ ) describe the correlation between these two components.

Note 3 to entry: For microwave remote sensing, modified Stokes parameters are often used. Under the Rayleigh-Jeans approximation, the modified Stokes parameters in brightness temperature are given by the following formula:[19], [37] ${\displaystyle \left[\begin{array}{c}{T}_{\text{v}}\\ T_{\text{h}}\\ T_3\\ T_4\end{array}\right]=\frac{{\lambda }^2}{\text{k}\eta B}\left[\begin{array}{c}\langle {\left|E_{\text{v}}\right|}^2\rangle \\ \langle {\left|E_{\text{h}}\right|}^2\rangle \\ 2\text{Re}\langle E_{\text{v}}{E}_{\text{h}}^{\ast }\rangle \\ 2\text{Im}\langle E_{\text{v}}{E}_{\text{h}}^{\ast }\rangle \end{array}\right]}$ where ${\displaystyle T_{\text{v}}}$ , ${\displaystyle T_{\text{h}}}$ , ${\displaystyle T_3}$ and ${\displaystyle T_4}$ are, respectively, the vertically and horizontally polarized and the third and fourth Stokes parameters, and ${\displaystyle B}$ is the radiometer system bandwidth.