Scattering effects in multi-layer neutron optics

Modern neutron optical elements allow for high flexibility in shaping beams with extended reflection angles due to optimized multi-layer coatings. For applications where the shaped beam is relevant to generate resolution or to image certain geometries, the effect of scattering from the coating imperfections may be relevant, as it can generate undesired backgrounds. In a set of off-specular and grazing incidence small-angle neutron scattering experiments, we have characterized such scattering effects for coatings of Ni/Ti and Fe/Si. By using modelling, we identify that the scattering effects are dominated by waviness on the length scale of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> <mml:mo> </mml:mo> <mml:mrow> <mml:mi>μ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:math> that is correlated between layers as well as uncorrelated contributions in the nanometre range. The scattered signal for certain incident angles is remarkably similar between different substrates and coatings. We derive a simplified description that can be used to model these effects quantitatively in neutron instrument ray-tracing simulations.