[Ifeffit] rbkg

[Bruce Ravel]

On Monday 11 July 2005 17:28, Silvio Levy wrote:
> Hi, I'm a new reader of the list.  Thanks for all this very useful
> software and impressive documentation.

Thanks for the kind words.

> I'm having trouble understanding the role of rbkg in spline (or
> autobk).  Ravel's Exafs Analysis with FEFF and FEFFIT describes it as
> "the cutoff between the portion of the Fourier transformed spectrum
> dominated by the background function and the portion containing
> information about the local structure".
>
> This would seem to imply that after removal of the background spline,
> the signal will have NO frequencies below rbkg -- that is, in the R
> domain, it would be 0 (or close to 0) for R < Rbkg. 

That would be true if an infinite Fourier transform were possible.  Alas, our
FT is finite (no negative values of k and positive values only go out to 12 or
so).  Since the FT is finite, the Fourier components leak to the left and to
the right.  In practice, this means that our signal has non-zero spectral
weight below Rbkg and our background has non-zero spectral weight above that
value.  Thus, in practice, the background spline and the parameters we
eventually use to fit the data are correlated.

Although there are many things in that document that I would state differently
today, the language I used to describe Rbkg is valid.  Rbkg *is* the frequency
we choose as that cutoff, but the cutoff is never as clear as you anticipated.

All the details of the Autobk algorithm are in Physical Review B47:21 (1993)
p. 14126.

See page 30 in this PDF file
  http://cars9.uchicago.edu/xafs/NSLS_2003/Kelly.pdf 
for a nice graphical demonstration of what Rbkg means.  (The rest of that
document is pretty useful, as well.)

HTH,
B

-- 
 Bruce Ravel  ----------------------------------- bravel at anl.gov  -or-
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