Geometry:WAXS 3D

In wide-angle scattering (WAXS), one cannot simply assume that the detector plane is orthogonal to the incident x-ray beam. Converting from detector pixel coordinates to 3D q-vector is not always trivial, and depends on the experimental geometry.

Area Detector on Goniometer Arm

Consider a 2D (area) detector connected to a goniometer arm. The goniometer has a center of rotation at the center of the sample (i.e. the incident beam passes through this center, and scattered rays originate from this point also). Let $\scriptstyle \phi _{g}$ be the in-plane angle of the goniometer arm (rotation about $\scriptstyle z$-axis), and $\scriptstyle \theta _{g}$ be the elevation angle (rotation away from $\scriptstyle xy$ plane and towards $\scriptstyle z$ axis).

The final scattering vector depends on:

• $\scriptstyle x$: Pixel position on detector (horizontal).
• $\scriptstyle z$: Pixel position on detector (vertical).
• $\scriptstyle d$: Sample-detector distance.
• $\scriptstyle \theta _{g}$: Elevation angle of detector.
• $\scriptstyle \phi _{g}$: In-plane angle of detector.

Note that $\scriptstyle x$ and $\scriptstyle z$ are defined relative to the direct-beam. That is, for $\scriptstyle \theta _{g}=0$ and $\scriptstyle \phi _{g}=0$, the direct beam is at position $\scriptstyle (x,z)=(0,0)$ on the area detector.

Central Point

The point $\scriptstyle (x,z)=(0,0)$ on the detector probes the total scattering angle:

${\begin{alignedat}{2}2\theta _{s}=\Theta &=1\\&=1\end{alignedat}}$

See Also

• Geometry:TSAXS 3D
• $\scriptstyle \theta _{g}$