On the instrumental resolution in X-ray reflectivity experiments

A general method to describe the instrumental resolution function for grazi ng-angle X-ray scattering experiments is presented. A resolution function R is introduced as the Gaussian joint-distribution function of the (interdep endent) random deviation q' associated with the wavevector transfer q. Usef ul expressions for the mean square values of q' are derived for some common scattering geometries, such as rocking scans, and scans out of the plane o f incidence. The mean square values related to the incident beam dispersion and the detector acceptance angles are included in the treatment of R. As an example, R is incorporated in the calculation of the diffuse scattering from freestanding smectic films within the framework of the first Born appr oximation and the main resolution effects are discussed.