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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \psi} between the polarization axis and the scattering direction, one can define a polarization correction of:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_h = | \sin \psi |^2 = 1 - \cos^2 \delta \sin^2 \gamma }

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \delta} is the inplane angle of scattering, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma} is the out-of-plane (elevation) angle of the scattering.

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