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A linearized analysis of the Debye–Scherrer ring (D–S ring) is proposed in this paper. In our previous works, the authors reported on a technique to calculate stress from the Fourier series of the normal strain of a D–S ring and demonstrated a technique to calculate stress from an imperfect D–S ring. In fact, the same equation can be deduced by linearizing the equation for the D–S ring. We analyzed the data from our previous work to demonstrate this technique. In addition, we propose a data selection technique that uses the distance between the measured data and the hyperplane.

Linearized analysis of X-ray stress measurement using the Debye–Scherrer ring