= Kiessig fringe
{c}
A <Kiessig fringe> is an oscillation in reflected intensity caused by <wave interference> between contributions from the two sides of a thin film. For specular <neutron scattering> at grazing angle $\theta$ and <wavelength> $\lambda$, the normal <wave vector> transfer is $q_z=4\pi\sin\theta/\lambda$. Well above the critical edge, a film of thickness $d$ contributes a relative <wave phase> approximately $q_zd$, giving fringe spacing
$$
\Delta q_z\simeq\frac{2\pi}{d}.
$$
Thus closely spaced fringes indicate a thicker film. As a calculated example, spacing $0.0628\,\mathrm{nm^{-1}}$ corresponds to about $100\,\mathrm{nm}$. Interface <surface roughness>, contrast, additional layers and instrumental resolution affect the fringe pattern; thickness is inferred with an appropriate reflectivity model, especially near the critical edge.<Understanding PNR Data Features by National Institute of Standards and Technology>[Thickness fringes, critical edge and their relation to layer thickness and scattering-length-density contrast]{ref}
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