Separation According to Warren-Averbach

A model-free method for the analysis of lattice distortions is readily established from Eq. (8.13). It is an extension of Stokes [27] method for deconvolution and has been devised by Warren and Averbach [28,29] (textbooks Warren [97], Sect. 13.4 Guinier [6], p. 241-249 Alexander [7], Chap. 7). Eor the application to common soft matter it is of moderate value only, because the required accuracy of beam profile measurement is rarely achievable. On the other hand, for application to advanced polymeric materials its applicability has been demonstrated [109], although the classical graphical method suffers from extensive approximations that reduce its value for the typical polymer with small crystal sizes and stronger distortions. 

Elimination of Instrumental Broadening and Crystal Size Effect. Fourier transform of Eq. (8.13) turns the convolutions into multiplications (Sect. 2.7.8) 

moreover, we consider a set of peaks with the index (ft) counting the orders of re-fiections, then the effects of size and instrumental broadening are readily eliminated by normalizing 

Visualizing a Set of Pure Distortion Profiles. After Fourier back-transformation, we retrieve a set of reduced profiles that are only determined by lattice-distortion 

Only one peak has been consumed for normalization purpose. The profiles (s) 

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