Ab initio simulation of diffractometer instrumental function for high-resolution X-ray diffraction

Modeling of the X-ray diffractometer instrumental function for a given optics configuration is important both for planning experiments and for the analysis of measured data. A fast and universal method for instrumental function simulation, suitable for fully automated computer realization and describing both coplanar and noncoplanar measurement geometries for any combination of X-ray optical elements, is proposed. The method can be identified as semi-analytical backward ray tracing and is based on the calculation of a detected signal as an integral of X-ray intensities for all the rays reaching the detector. The high speed of calculation is provided by the expressions for analytical integration over the spatial coordinates that describe the detection point. Consideration of the three-dimensional propagation of rays without restriction to the diffraction plane provides the applicability of the method for noncoplanar geometry and the accuracy for characterization of the signal from a two-dimensional detector. The correctness of the simulation algorithm is checked in the following two ways: by verifying the consistency of the calculated data with the patterns expected for certain simple limiting cases and by comparing measured reciprocal-space maps with the corresponding maps simulated by the proposed method for the same diffractometer configurations. Both kinds of tests demonstrate the agreement of the simulated instrumental function shape with the measured data.