Changes

:<math> \mathbf{ \hat{u}_b' = \hat{k}' \times \hat{u}_f' } </math>

The diffraction coefficients are calculated in the following way:

:<math> D_h = \frac{-e^{-j\pi/4}}{2n \sqrt{2\pi k} \sin\beta_0'} \left\lbrace \begin{align} & \cot \left(\frac{\pi + (\phi-\phi')}{2n}\right) F[kLa^+(\phi-\phi')] + \cot \left(\frac{\pi - (\phi-\phi')}{2n}\right) F[kLa^-(\phi-\phi')] + \\ & R_{0 \|} \cot \left(\frac{\pi - (\phi+\phi')}{2n}\right) F[kLa^-(\phi+\phi')] + R_{n \|} \cot \left(\frac{\pi + (\phi+\phi')}{2n}\right) F[kLa^+(\phi+\phi')] \end{align} \right\rbrace </math>

where ''F(x)'' is the Fresnel Transition function:

:<math> F(x) = 2j \sqrt{x} e^{jx} \int_{\sqrt{x}}^{\infty} e^{-j\tau^2} \, d\tau </math>

In the above equations, we have

where <math>N^{\pm}</math> are the integers which most closely satisfy the equations <math> 2n\pi N^{\pm} - \nu = \pm \pi </math>.

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