Refraction distortion

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Illustration of GISAXS refraction distortion. The reciprocal-space scattering is a hexagonal array of peaks. However, these peaks are both shifted, and compressed/stretched along qz, due to refraction. This effect is especially pronounced near the Yoneda (orange line).

In GISAXS, GIWAXS, and other grazing-incidence techniques, the refractive index difference between the film and the ambient causes the incident and scattered x-ray beams to be refracted. This extent of refraction depends on the incident and exit angles. Thus, the data that appears on an area detector in a grazing-incidence experiment is non-linearly distorted. This makes data interpretation more problematic.


The GISAXS refraction distortion shifts the data along , leaving unaffected. The amount of the shift is given by:

Where is the incident angle, and is the critical angle of the film.

Figure from Lu. et al. (doi: 10.1107/S0021889812047887 J. of Appl. Cryst. 2013, 46, 165) showing the amount of distortion along qz, for different conditions.

Refraction Correction

When computing theoretical scattering patterns, one must account for the refraction correction. The correction is essentially an application of Snell's law, where one using the x-ray refractive index for ambient (), the thin film (), and the substrate (). For an incident angle of , one computes a refraction of:

That is, the direct beam shifts by . For a given , one can convert into scattering angle:

The scattered ray refracts as it exits from the film:

If , then scattering is above the horizon (GISAXS); if , then it is sub-horizon scattering (GTSAXS). For GISAXS, the final scattering angle is:

See Also