The X-ray diffraction patterns of materials which are used in the construction of industrial structures and machines generally have so widely diffused profiles that their K-alpha doublets can not be distinguished and these peaks are superposed.
The calculation of residual stresses with the use of X-ray are carried out by measuring the peak positions of back reflection lines, but these broad lines contain some errors in the measurement of the peak shift.
The shift of the peak positions are the movement of the whole profile and it would be calculated from Fourier's coefficients when the profiles are analysed by Fourier's method. This method of calculation is described in this paper.