[Ifeffit] number of independent points

[Bruce Ravel]

On 03/30/2017 11:07 PM, dcnguyen wrote:
> I have an issue of a discrepancy between values of independent points
> calculated by Demeter 0.9.25, on Windows 7, shown on the path page
> and the one presented on the log file after a fit to data. For an
> example, I use the file named FeS2_final.fpj that you have in your
> computer, and choose an R-range 1.2-4.2 A, and a k-range 3.00-14.80.
> Then the N value is calculated by Artemis and shown as 22.54 after
> clicking "shown Nidp" from the "Data" tab on the path page. The value
> is consistent with the formula N=(2/pi)*delta_K*delta_R. However,
> after I click the "Fit" button and look at the Log file, the Nidp is
> shown as 22.0312500. My question is what causes this discrepancy.
> When publishing data, which number shoud be reported? Thank you.

When you select the item from the Data menu, Artemis computes Nidp from 
the values you provide for kmin, kmax, rmin, and rmax.

At the end of the fit, Artemis reports Nidp computed using the actual data.

In your case, you asked for the fit to be done between 1.2 and 4.2 -- a 
span of 3.0 Ang.  The actual data range used in the fit is from 
1.2271846 to 4.1724277, a span of about 2.945 Ang, which is about 2% 
smaller than what you asked for.  Hence the value for Nidp reported 
after the fit is about 2% smaller than what the Data menu entry computes.

When doing a discrete Fourier transform, the size of the data array in k 
and the grid spacing in k sets the grid spacing in R.  After background 
removal, the data are interpolated on a grid of 0.05 invAng and put into 
a zero-padded array of length 2048.  The grid in R is set by the Fourier 
transform to be PI / (array_size*k-grid).  Plug in the numbers and you 
get that the R grid is close 0.0307 Ang.  The FT is done using data that 
fall /within/ the values of Rmin and Rmax you provide.

So, 1.2 and 4.2 are not points on the R grid, therefore the value 
computed using the Data menu entry is even more approximate that the 
after-fit value, which itself is only a crude approximation of the 
information content of the data.

HTH,
B



-- 
  Bruce Ravel  ------------------------------------ bravel at bnl.gov

  National Institute of Standards and Technology
  Synchrotron Science Group at NSLS-II
  Building 743, Room 114
  Upton NY, 11973

  Homepage:    http://bruceravel.github.io/home/
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