[Ifeffit] continuous scan data

Carlo U. Segre segre at iit.edu
Thu Jul 18 10:45:43 CDT 2002

I would be willing to test any new code out.  We have been working with
this for diffraction patterns over the summer and we have not been happy
with the spline fit or a Bezier alternative.  Jeff Terry and Steve
Wasserman's Mathematica code uses an algorithm which sets bins in energy
space using the desired k-space resolution, say delta-k=0.05 and then
averages both mu(E) and E.  Then an interpolation scheme eventually puts
the data on an exactly even k-space grid since there is no guarantee that
the average E is in the correct place.


On Thu, 18 Jul 2002, Matt Newville wrote:

> Hi Carlo,
> Sorry I didn't answer this more clearly.
>  CS> What is done with the high density data when converting to
>  CS> k-space?  Do you rebin (averaging both E and mu data) or do you
>  CS> use a smoothing fit to take advantage of the statistics present
>  CS> in the excess data points, or do you just interpolate and throw
>  CS> away the extra statistics?
> BR> ... However, mesuring for one second per point on, say, a
> BR> 0.25 eV grid is similar in a counting statistics sense to
> BR> two measurements of one second per point on a 0.5 eV grid.
> BR> That counting statistics improvement is not lost in the
> BR> interpolation of chi(E) to chi(k).
> CS> I think that this last sentence is the answer that I was
> CS> looking for.  I wanted to know if the counting statistics
> CS> improvement is propagated in the transformation to k-space.
> CS> This is good since it means that we do not have to write
> CS> our own rebinning or smoothing routines before handing the
> CS> data off to athena and ifeffit.
> MN>  -- spline() generates k and chi arrays using a 0.05Ang-1 grid
> MN>     using a three-point interpolation of the chi(e) data.
> MN>     That could possibly be improved, I suppose.
> CS> I take this to mean, as Bruce mentioned in the previous
> CS> message, that the counting statistics improvement in these
> CS> fine-gridded data is used with this three point
> CS> interpolation.  If this was not the case, I would write a
> CS> program to rebin by averaging multiple points to an equally
> CS> spaced > k-grid in order to use the increased statistics.
> The three-point interpolation done probably WILL lose some
> statistics for finely gridded data.  That is, if data is binned
> at fine energy intervals through the EXAFS region, the method
> currently used will not use all that data to construct chi(k).
> As an example :
>    k = 10.00  ->  E-E0 = 381.0
>    k = 10.05  ->  E-E0 = 384.8
>    k = 10.10  ->  E-E0 = 388.7
> Currently, ifeffit marches in k-space in steps of 0.05Ang-1,
> and uses three energy points (the energy just below, the energy
> just below, and the next closest point) to make a parabola
> through chi(E) [that is, xmu(E)-bkg(E) at the energy points of
> the data], and uses the value of that parabola as chi(k).  The
> result is that if data is binned on a 0.5eV grid, some of it
> will be ignored when making chi(k) at k=10.Ang^-1.
> This could be improved.  Ifeffit really wants chi(k) on an even
> k-grid, so the options would be either a finer k-grid or a
> better interpolation scheme.  A finer grid in ifeffit could be
> possible, but it's a non-trivial change.
> A better interpolation scheme is easier to do.  Changing from
> 3-point interpolation to a cubic spline that passes through all
> the data points of chi(E) would be easy, and would use all the
> data for each chi(k) point.  Whether it actually 'preserves
> statistics' is a harder question to answer.  I think that any
> griddign of data could be said to lose statistics.  Some sort
> of rolling averaging could be used, which might preserve
> statistics better at the (small) expense of resolution.
> Anyway, the reason that's not cubic spline interpolation is not
> currently done is execution speed, but that's probably less
> important than throwing away data!
> Changing to the better interpolation scheme is easy enough to
> try.  I could send altered code if you like.
> --Matt
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Carlo U. Segre -- Professor of Physics
Illinois Institute of Technology
Voice: 312.567.3498            Fax: 312.567.3494
Carlo.Segre at iit.edu    http://www.iit.edu/~segre

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