X-ray stress analysis with a 2D detector. Part 2. Goniometer alignment

The use of 2D detectors for stress/strain analysis enables new strategies for data acquisition and treatment to be devised, thus enabling faster measurements to be performed, including stress mapping without goniometer rotations. These advantages were developed in Part 1 of this work [François (2023). J. Appl. Cryst. 
 56, https://doi.org/10.1107/S1600576722010913], but they imply the occurrence of additional alignment issues that need to be addressed carefully. The aim of this second part is to describe the misalignment errors geometrically using the general formalism introduced in Part 1. Under the assumption that the defects of the equipment are small, closed-form analytical expressions are provided for each type of error. It is found that the trigonometric functions describing each defect are independent. Thus, it becomes possible to identify and quantify the type of error from measurements performed on a stress-free sample such as a powder specimen. This is achieved by a linear least-squares regression analysis on the measured peak positions for various values of the goniometric angles. The proposed method is then applied to an example.