RE: how to find out POLARISATION Factor

[Zuev]

Dear Dr. A. Coelho, dear Rietvelders     there are four points to be considered. 1. Precision of the fit (using the convolution approach). 2. Theoretical basis of the convolution approach. 3. Calculation time with the method in my paper. 4. “… some inaccuracies of the above mentioned paper”     1. There is no doubt that convolution approach provides good agreement in profile fitting with ray traycing.   2. It is not obviously with the rigorous theoretical validation of the convolution method. I mean the following aspects: a) Strictly speaking, even the flat specimen aberration coupled with the receiving slit width can not be mathematically described as convolution. It is not critique, but just a statement of fact. Well, the convolution can be used, but this is only approximation (even if it is good for the certain conditions).   b) The same is valid for the axial aberration. Also the treatment of the axial aberration is an approximation (“More recently Cheary and Coelho [3,4] have developed a semi-analytical approach to the calculation and their results have been incorporated into a profile refinement procedure.” From R. W. Cheary, A. A. Coelho, J. P. Cline.  Fundamental Parameters Line Profile Fitting in Laboratory Diffractometers, J. Res. Natl. Inst. Stand. Technol. 109, 1-25 (2004))   3. Calculation time. There is only the approach in my article was represented. It makes possible to develop a number of the (exact) modifications and approximations (without lost of  accuracy). I had not yet made optimization. I mean not the code optimization “at an assembler code level” (From R. W. Cheary, A. A. Coelho, J. P. Cline.   Fundamental Parameters Line Profile Fitting in Laboratory Diffractometers, J. Res. Natl. Inst. Stand. Technol. 109, 1-25 (2004))), but only the mathematical algorithms. Partly I have made it.   4. About “some inaccuracies of the above mentioned paper”   1) The reference was made on page 310-311 and to quote the text of Zuev:   "Reefman has shown, by analyzing the effect of transparency, that the convolution model is not valid in the general case."   This of course is correct as the convolution approach is not valid for axial divergence greater than probably 10 degrees in both the primary and secondary beams and linear absorption coefficients less than 10 (1/cm).   Self-explanatory.   2) Back to the paper by Zuev; page 304-305: "To compensate for lack of knowledge about the influence of coupling specific instrumental functions in FPA, it is also necessary to tune the fundamental parameters to allow a best fit for the experimental data (Cheary et al., 2004)."   Coupling effects were always investigated during the development of FPA by Cheary and Coelho. This led to the need to partially number cruch the Full Axial Model which considers primary and secondary axial divergence together.   I would like to cite the other paper: “Fine tuning is sometimes necessary to accommodate a monochromator or to compensate for the fact that certain aberrations are not completely independent [8].” (From R. W. Cheary, A. A. Coelho, J. P. Cline.   Fundamental Parameters Line Profile Fitting in Laboratory Diffractometers, J. Res. Natl. Inst. Stand. Technol. 109, 1-25 (2004))     OK, it may be significant whether the fundamental parameter are fine tuned intentionally to compensate coupling effect, or to compensate for lack of knowledge.   I would like to emphasize that I had not criticized the convolution approach, but I was only guided by the opinion of the authors of the convolution approach.       With best regards, Alexander Zuev