Influence of crystal surface roughness on the angular spread of x-ray diffracted beam

One of the factors influencing the focus size in diffractive-refractive optics is the quality of diffracting surface. If the surface is uneven, then the diffraction at each point of the surface is a combination of an asymmetric and inclined diffraction (general asymmetric diffraction). This somewhat deviates and spreads the diffracted beam. The integration over the surface hit by an incident beam gives the angular spread of the diffracted beam. It is shown that in some cases (highly asymmetric, highly inclined cut) the etched surface may create the spread of the diffracted beam, such that it causes a significant broadening of the focus. In this case a mechanical-chemical polishing is necessary.