[Ifeffit] Rebinning

[Matt Newville]

Hi Carlo,

On Tue, 11 Mar 2003, Carlo U. Segre wrote:
 
> Matt:
> 
> Jeff Terry mentioned that perhaps I did not explain myself adequately with
> the last message.
> 
> The algorithm averages BOTH counts and Energy.  We do not just place the
> average number of counts at the center of the bin.  Because of this, there
> should be no distortion and no need to weight.
> 
> Carlo

I'm not sure I see that at first glance, but I'll take your word
for it.  That isn't what I'm concerned about.

Let me explain where I get stuck: let's say you have data
collected in energy steps of 0.25eV -- could be QEXAFS, could be
step scan.  For the sake of argument, lets' set the energy
resolution to 1eV.  You have to get the data on the 0.25eV grid
to an even k-grid for the analysis (at least in ifeffit).  For
the sake of argument, we'll say dk = 0.05Ang^-1, No matter what
the details are, you need to get values of mu(E) for the data
onto a gridded set E={E_i}.

At k=4, E~=61.0, and k=0.05 corresponds to 1.5eV.  A boxcar
average will average the original data between 60.25 and 61.75
and call that the new data for E=61.  Seems reasonable, though
giving equal weight to the data at 61.0 and 61.75 could be
questioned for 1eV resolution.

At k=16, E~=975.0 eV, k=0.05 corresponds to 6eV.  So here, you
average of data between E=972.0 and 978.0eV and call that the
data for E=975.0eV.  Giving equal weight to the data at 972.0 and
975.0 when the resolution is 1eV is what worries me.  The simple
average of mu(E) between 972.0 and 978.0 is definitely not the
same as mu(E) at E=975.0. It would probably be better to average
the original data between 974.0 and 976.0 for the new data at
975.0, and might be preferrable to just do a convolution with a
1eV point spread function for all the data.

Certainly, if you were to re-bin data collected in 0.25eV steps
to a grid of 10eV there would be real problems.  By 'using all
the data', one can use too much data and spoil the resolution.

I don't claim that the boxcar average is wrong, or that 
convolution is definitely the right thing to do, just that I'm 
confused by this.

--Matt