Polarization correction

The x-rays used in scattering experiments are frequently polarized. For instance, undulators sources generate x-rays polarized along a well-defined axis associated with the oscillation direction. (Some specialized undulators generate elliptically polarized light with control of the ellipticity and/or polarization direction.) The intensity of scattering is modulated by the angle between the incident x-ray polarization and the scattering direction, with the scattering probability (and thus measured scattering intensity) dropping to zero when these are aligned.

In particular, scattering occurs with an amplitude proportional to the sine of the angle between the direction of the electric vector of the incident radiation, and the direction of scattering. Assuming horizontally-polarized incident x-rays (i.e. linear polarization with the E-field horizontal), for an angle $\psi$ between the polarization axis and the scattering direction, one can define a polarization correction of:

$P_{h}=|\sin \psi |^{2}=1-\cos ^{2}\delta \sin ^{2}\gamma$

where $\gamma$ is the inplane angle of scattering, and $\delta$ is the out-of-plane (elevation) angle of the scattering. More generally for a source polarized to extent $\zeta$ (fraction of radiation polarized in horizontal) one can compute:

$P_{p}=\zeta P_{h}+(1-\zeta )P_{v}$

Assuming perfect horizontal polarization, for a total scattering angle of $2\theta$, we can expect:

Scattering direction	$\chi$	$\psi$	$\delta$	$\gamma$	$P_{h}$
Purely vertical	$0^{\circ }$	$90^{\circ }$	$2\theta$	$0^{\circ }$	1
Arbitrary angle	$\chi$		$\sin ^{-1}\left[\sin 2\theta \cos \chi \right]$	$\tan ^{-1}\left[\tan 2\theta \sin \chi \right]$	$1-\cos ^{2}\delta \sin ^{2}\gamma$
Purely horizontal	$90^{\circ }$	$90^{\circ }-2\theta$	$0^{\circ }$	$2\theta$	$|\cos 2\theta |^{2}$

See Also

• Lorentz–polarization correction (IUCr Online Dictionary of Crystallography)
• Z. Jiang GIXSGUI: a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films J. Appl. Cryst. 2015, 48, 3, 917-926. doi: 10.1107/S1600576715004434