[Ifeffit] Fit in R and k space

[Kelly, Shelly D.]

Hi Michel,

Michel wrote:  
Finally, another issue - for which I would not lay out my neck, though -
is 
the noise. In EXAFS, the signal to noise increases with k, and of course

fitting in the raw k space is another way of dealing conveniently with
the 
noise -or relative uncertainty, as we may name it. However, the FT is a
way 
of filtering out some of this noise, and so maximise the signal from a 
shell. Likewise, fitting in filtered q-space may yield more accurate 
results, because some of the noise is filtered out. However, I concur
that 
somehow the fact that the uncertainty on the high-q part of the filtered

contribution os greater than in the low q-part should be implemented
somehow.

It is true that the signal to noise ratio becomes smaller at high k
values.  It does seem magical that the Fourier transform can pull a
signal out of the high k-range where the noise is large and that this
signal seems to be well defined.   I find it helpful to remember that
each signal in the EXAFS chi(k) spectra is given by ONE frequency.  That
frequency is well defined at low k were the signal to noise ratio is
large.  Extending this frequency into the high k-region is trivial as
long as that frequency co-exists with all the noise at high k.  In fact
I don't need data at all to extend a well defined frequency to infinity.
The part of the signal that is not so well defined at high k is the
amplitude.  A lot of noise often masks itself by a large variation in
amplitude for a given signal at high k, this effect will result in poor
values for CN and  2.  But the amplitude of the signal has a well known
k-dependence so with enough low k information about the amplitude even
the amplitude does not become affected by the noise at high k.  The
point to remember is that the signals are defined from k=0 to
k=something bigger than zero. As long as the signal to noise ratio is
reasonable from k=0 to some k~10?  Then the signal including frequency
and amplitude is well described all the way to k=infinity.  It is often
helpful to look at the fit and the data in k-space all the way out to 16
1/angstroms even if you are only using the k-range to 12 1/angstroms.
If the model continues to follow the data to 16 then it is a good model.

   
Shelly

Shelly Kelly 		Bldg 203 RM E113
Skelly at anl.gov		Argonne National Laboratory
630-252-7376		9700 S Cass Ave
www.mesg.anl.gov		Argonne, IL 60440