[Ifeffit] Distortion of transmission spectra due to particlesize

[Matt Newville]

Hi Jeremy, Anatoly,

Thanks, you're absolutely right -- I got the parentheses wrong.

Anatoly,
> However, thickness is present in mu*t only because of the total number of absorbers. There are 1/2 absorbers in
> the foil with 50% holes, and thus (t*mu)_measured is equal to (1/2) * t*mu_measured.

I agree, but I think that you'd have to know your sample was 50% holes
to make that work. I was considering 't*mu' to be a single thing
quantity (and really meant that to stand for -ln(I_t/I_0) in the sense
of the log of intensities sampled by ion chambers, not absolute
fluxes).

I think it should be  (starting with  I_t = I_0 * exp(-tmu)  ) that a
half full / half empty sample will have:
   I_t = (I_0  + I_0 * exp(-tmu) ) / 2  = I_0 * (1 + exp(-tmu) ) / 2

so that
   tmu_measured = -ln (I_t / I_0)  = -ln(  (1 + exp(-tmu))/2) =  ln(2)
- ln(1+ exp(-tmu))

As for whether there is a reduction in chi(k) of a factor of 2 or not,
I think this would depend on the sample thickness (or, the reltive
size of tmu to 1)  in the portion of the sample that was non-empty.
Using this corrected formula on cu foil data (that actually has an
edge jump ~= 2.3, so is probably on the thick side, but is still
decent data),  I do see a reduction in chi(k) that is a little more
than a factor of 2, with some k-dependence.  Attached is an Athena
project of original and "half empty" data.  Am I a pessimist for not
calling it "half full"?

--Matt

PS: I did this to make the half empty data, then read in the data file
into athena.
   read_data(cu.xmu, group =good)
   set pinhole.energy = good.energy
   set pinhole.xmu    = -ln( (1 + exp(-good.xmu) )/2)
   write_data(file=half_empty.xmu, pinhole.energy, pinhole.xmu)
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