Resolution function for X-ray powder diffraction in a noncoplanar measurement geometry with the detector arm having two degree of freedom

A noncoplanar measurement geometry, achieved by using a diffractometer equipped with a detector arm possessing two degrees of freedom, is a promising technique for the analysis of residual stress gradients in polycrystalline objects and for anisotropic microstructure investigations. The instrumental function for a parallel beam and a set of two orthogonal receiving Soller slits is considered in detail, and the explicit analytical expressions in terms of a convolution of functions are derived. A comparison of the calculated results with the measured profiles from a NIST SRM 660b LaB₆ powder standard sample shows a good agreement.