[Ifeffit] weights data processing

[Scott Calvin]

At 01:30 PM 7/23/2004 +0200, Stefano wrote:
>Hi folks,
>
>1) when removing background using athena, there is an option of using 
>a k-weight different than 1 (I am NOT talking about k-weight for FT). 
>I noticed that changing this parameter the resulting chi(k) does not 
>change significantly. Actually, going from 1 to 4 as a value for 
>k-weight for Bkgd removal, the only effect I see is a significant 
>reduction of the peak below the first coordination shell in chi(R) 
>while the other features of the spectrum are essentially the same in 
>terms of absolute and relative intensity. A drastic change in both 
>chi(k) and chi(R) is seen if I use k-weight = 5 and above. What is 
>the exact meaning of it? I know what the meaning is in the FT 
>process, but I do not see the reason why I should use a weight 
>different than 1 (let's say 3 for my noisy data) for background 
>removal. How should I behave? SHould I take the largest value of 
>k-weight so that the essential features of the chi(k) and chi(R) do 
>not change?
>

Ifeffit is choosing a spline for the post-edge background that fits the
low-R part of the spectrum as well as possible (or, if you're using a
background standard, makes the low-R part of the spectrum as close to the
standard as possible). Since that means it's using a Fourier transform, it
can also be assigned a k-weight, just like when doing EXAFS fits. A high
k-weight means your placing a higher priority on making the spline match
the background at high-k; i.e., at energies far above the edge.

The default of 1 is reasonable, because it slightly deemphasizes the XANES
region which you're not going to use for an EXAFS fit anyway. I've also
used 0, although I then generally raise the low end of the energy range for
the background spline so it doesn't get hung up trying to figure out the
edge itself. If you use very high weights, the spline becomes obsessed with
features very far above the edge, which is probably not useful.

In other words, this parameter should not be that important. I'd just leave
it at 1 unless you have reason to believe that weighting it more toward the
behavior far above the edge is important. I wouldn't go as high as you can,
since then you may distort the low-k peaks where your data quality should
be best! I also don't think "noisy" data argues for a higher k-weight here;
I think then you risk the spline fixating on the noise at energies far
above the edge, which is probably not helpful.

>2) In artemis, is it a bug or a wanted feature to have the 
>possibility to activate more than one button for k-weight for the fit 
>and FT? I suppose it is a wanted feature, but then I wonder what is 
>the meaning of using more than one weight for the fit and FT. I am 
>sure some of you can unveil this enigma.
>

A very useful feature! For example, the effect of S02 and sigma2 are a bit
difficult to distinguish in a typical moderate-quality EXAFS spectrum,
since both effect amplitude. But S02 is an overall amplitude factor, while
the effect of sigma2 is weighted by k^2. Therefore changing k-weight will
often change the values Ifeffit finds for these two parameters. By fitting
more than one k-weight at once, Ifeffit is forced to choose a compromise
that finds a reasonable S02 and sigma2 that works at all k-weights;
reducing uncertainties and correlations. Note that E0 and delr suffer from
a similar problem: they both shift phase, but the effect of delr is
weighted by k while E0 is not (and if you use a third cumulant in your fits
it is weighted by k^3).

I personally avoid using multiple k-weights until I have a good "feel" for
how my fits are behaving, but if the fits are clearly having trouble
distinguishing between the sets of parameters I have mentioned (as
evidenced, for example, by high uncertainties and correlations), then I'll
try it. 

--Scott Calvin
Sarah Lawrence College
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