scippneutron.conversion.beamline.two_theta#

scippneutron.conversion.beamline.two_theta(*, incident_beam, scattered_beam)[source]#

Compute the scattering angle between scattered and transmitted beams.

See beamline for the definition of the angle.

The result is equivalent to

\[\begin{split}b_1 &= \mathtt{incident\_beam} / |\mathtt{incident\_beam}| \\ b_2 &= \mathtt{scattered\_beam} / |\mathtt{scattered\_beam}| \\ 2\theta &= \mathsf{acos}(b_1 \cdot b_2)\end{split}\]

but uses a numerically more stable implementation by W. Kahan described in paragraph of [Kah00]. See also https://people.eecs.berkeley.edu/~wkahan/MathH110/Cross.pdf.

Parameters:

incident_beam (Variable | DataArray | Dataset | DataGroup[Any]) – Beam from source to sample. Expects dtype=vector3.
scattered_beam (Variable | DataArray | Dataset | DataGroup[Any]) – Beam from sample to detector. Expects dtype=vector3.

Returns:

Variable | DataArray | Dataset | DataGroup[Any] – \(2\theta\)