The transmission coefficients are calculated for the two parallel and perpendicular polarizations as:
:<math>T_{\|} = \frac{(1-{\Gamma_{\|}}^2) \exp(-jk_2 d (\mathbf{ \hat{k}'' \cdot \hat{n}}))}{ 1-{\Gamma_{\|}}^2 \exp( -2jk_2 d (\mathbf{ \hat{k}'' \cdot \hat{n} }) ) }</math>
:<math>T_{\perp} = \frac{(1-{\Gamma_{\perp}}^2) \exp(-jk_2 d (\mathbf{ \hat{k}'' \cdot \hat{n}}))}{ 1-{\Gamma_{\perp}}^2 \exp( -2jk_2 d (\mathbf{ \hat{k}'' \cdot \hat{n} }) ) }</math>
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where
:<math>\Gamma_{\|} = \frac{ \eta_2(\mathbf{ \hat{k}'' \cdot \hat{n} }) - \eta_1(\mathbf{ \hat{k} \cdot \hat{n} }) } { \eta_2(\mathbf{ \hat{k}'' \cdot \hat{n} }) + \eta_1(\mathbf{ \hat{k} \cdot \hat{n} }) }= \frac{\eta_2 \cos\theta'' - \eta_1 \cos\theta} {\eta_2 \cos\theta'' + \eta_1 \cos\theta} = \frac{Z_{2\|} - Z_{1\|}} {Z_{2\|} + Z_{1\|}} </math>
= \frac{\eta_2 \cos\theta'' - \eta_1 \cos\theta} {\eta_2 \cos\theta'' + \eta_1 \cos\theta}
= \frac{Z_{2\|} - Z_{1\|}} {Z_{2\|} + Z_{1\|}}</math> :<math>\Gamma_{\perp} = \frac{ \eta_2(\mathbf{ \hat{k} \cdot \hat{n} }) - \eta_1(\mathbf{ \hat{k}'' \cdot \hat{n} }) } { \eta_2(\mathbf{ \hat{k} \cdot \hat{n} }) + \eta_1(\mathbf{ \hat{k}'' \cdot \hat{n} }) } = \frac{\eta_2 / \cos\theta'' - \eta_1 / \cos\theta} {\eta_2 / \cos\theta'' + \eta_1 / \cos\theta} = \frac{Z_{2\perp} - Z_{1\perp}} {Z_{2\perp} + Z_{1\perp}}</math>
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