Hello Bruce,
Although I prefer to think about the EXAFS problem in R space, I don't think this is the reason to do the fit in R space. Regardless of which fitting space you use, you are relying on Feff to supply some fraction of all the Fourier components in the data.
We could also used reference-derived phase and amplitude function, as in the good ol'time ;)
The first-shell feff path only has Fourier components (or frequencies, if you prefer) corresponding to the first-shell portion of chi(R). Thus that feff path can only fit those frequencies. That's true in k-space as well as in R-space
True in R-space, and that's why Athena-Ifeffit are doing such a wonderful job at providing windows to fit only selected area of the fourier transform. Almost true also in q-space. In k-space... hmmm, well, I would love to see the mathematical demonstration of it for a limited k-range and a Feff(k) (eventhoug I agree that many people have performed tha fit in k- and R-spaces, and found about the same paramters, so it must be verified somehow).
What's more, I think the problem of non-modelled shells affecting the modelled portion of the data exists in R-space just as much as in k-space. Because of sigma^2 and the finite data range, peaks have width. In R-space, a given path is centered at a particular R-value (or, in other words, its contribution to the spectrum is dominated by a particular frequency). However, the peak has width (it contains frequencies below and above the dominant frequency). Thus longer paths always interfere with shorter paths to some extent.
I think the effect of interfering contributions in the Konigsberger and Prins. What I noticed, though, is that the fit of closer shells can affect that of the furthest shell because of the "spillof" from the first peak. The recciprocal I was not aware of. But I do agree with you on the whole. However, I think that in the FT case, these interences are limited to the nearest shells, whereas in k-space, nothing protects you from shells at, say, 2R and 3R (so to speak. Best regards, Michel -- Michel Schlegel Commissariat à l'énergie atomique CEN de Saclay, DEN/DANS/DPC/SCP/LRSI Bat 391 - Piece 205B F91 191 Gif-sur-Yvette Cedex, France Ph: +33 (0)1 69 08 93 84 Fax: +33 (0)1 69 08 54 11