A technique to improve the stress measurement from a Debye–Scherrer ring (D–S ring) is reported. In a previous work, the authors reported a technique to calculate stress from the Fourier series of the normal strain of a D–S ring. That technique, similar to the cosα method that came before it, is inaccurate when the grain size of the specimen is relatively large. To cope with this problem, the authors propose using the oscillation of the X-ray incident angle. The present study demonstrates this technique to improve the stress measurement.

Residual stress measurements on strongly textured materials using the standard sin2ψ evaluation show significant non-linearities. According to EN 15305 there is currently no existing solution for this problem. A method is presented that solves this problem. It is based on two tools. (i) The use of a one-dimensional detector having a large capture angle that yields the full diffraction profiles at each point of the pole figures. Therefore, some hundreds of d-values can be used for the stress calculation. (ii) Data evaluation with the recently developed generalized sin2ψ method. This has the advantage of being based on a flawless theory (Hooke's law in the special form of Dölle–Hauk's equation) and being able to handle any distribution of measurement directions and any number of measured data. The method was successfully tried out at a sheet of brass with significant texture.

The sin2ψ method can be formulated as a single system of simultaneous linear equations. Using this it is easy to show that the sin2ψ method is not a least-squares method. It further helps to compare the accuracies of the stress tensors obtained by the sin2ψ method and the method of least squares. Quantitative comparisons have been made for different fictitious measurements. It is shown that the unnecessary loss in accuracy by using the sin2ψ method is quite significant and by no means negligible. The same course of action has been applied to compare the so-called Dölle-Hauk method with a least-squares method; the result is similar. Some other methods for X-ray stress determination, most often similar to the sin2ψ method, and their shortcomings are also discussed briefly, together with the corresponding, more effective and more versatile least-squares method.