Scattering geometry

[Coordinate system, see[29]:] Euclidean (orthonormal) system $[\mathbf u_1,\mathbf u_2,\mathbf u_3]$. The scattering plane, defined by the direction of the incident and final wave vectors $\mathbf k$ and $\mathbf k'$, contains $\mathbf u_1$ lying perpendicular and in the sense of $\mathbf k$ and $\mathbf u_3$ parallel to the scattering vector $\mathbf Q=\mathbf k-\mathbf k'$. [Polarisation of the Photon beam:] $\sigma$ and $\pi$ refer to the polarisation of the beam parallel and perpendicular to $\mathbf u2$, respectively. [Angles for azimuth $\Psi=0$:] $\alpha_i=\angle(\mathbf a_i \cdot \mathbf u_3)_{\Psi=0}$, $\delta_i=\angle(\mathbf a_i^{\perp}\cdot \mathbf u_1)_{\Psi=0}$, where $\mathbf a_{1,2,3}=\mathbf a,\mathbf b,\mathbf c$ and $\mathbf a_i^{\perp}$ is the projection of $\mathbf a_i$ onto the plane perpendicular to $\mathbf Q$. In the chosen experimental geometry azimuth $\Psi=0$, when $\mathbf a_1 = \mathbf a$ points to the x-ray source.