Re: [Ifeffit] pi/2deltak

[Farquhar, Erik]

Any references to this quantity in more recent papers seem to point back to the 
1981 Lee/Citrin/Eisenberger/Kincaid Rev. Mod. Phys. Review - 
http://dx.doi.org/10.1103/RevModPhys.53.769 (see p. 794 in particular).

Erik

From: Ifeffit [mailto:ifeffit-boun...@millenia.cars.aps.anl.gov] On Behalf Of 
Ritimukta Sarangi
Sent: Saturday, January 30, 2016 8:35 PM
To: XAFS Analysis using Ifeffit
Subject: [Ifeffit] pi/2deltak

Hello,

I was recently asked about the accuracy of this formulation for obtaining EXAFS 
resolution and I did not have a good answer. Can someone point to a reference 
or explain here?
Thank you for your time,
Best,
-Riti

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Re: [Ifeffit] pi/2deltak

[Avakyan L.A.]

Hello Riti,

the criterion of R-resolution of pi/2deltak can be drawn from the 
Nyquist theorem.
The amount of information in the spectra is limited by Nidp = 2 deltak 
deltaR / pi.
Then, in assumption of equal distribution of information over the 
R-interval, the minimal interval can be estimated as deltaR / Nidp = 
pi/2deltak.
The problem is that exact formula for Nidp is not known. Sometimes it 
has addition of +1 or +2 to represent the fact that single point 
(deltak=0) still contains information.
Moreover, information is not equally distributed: some k-regions are 
more rich, other are less...


And when energy interval is very short (glass, liquid) this question 
becomes vital. Sometimes, this resolution limit can even be overcome as 
it is shown in [http://dx.doi.org/10.1103/PhysRevB.82.064204].


Best regards,
Leon

Leon Avakyan
PhDr, Physics Faculty,
Southern Federal University
laavak...@sfedu.ru


On 31.01.2016 21:00, ifeffit-requ...@millenia.cars.aps.anl.gov wrote:

Message: 2
Date: Sat, 30 Jan 2016 17:35:04 -0800
From: Ritimukta Sarangi
To: XAFS Analysis using Ifeffit
Subject: [Ifeffit] pi/2deltak
Message-ID:

Content-Type: text/plain; charset="utf-8"

Hello,

I was recently asked about the accuracy of this formulation for obtaining
EXAFS resolution and I did not have a good answer. Can someone point to a
reference or explain here?
Thank you for your time,
Best,
-Riti


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Re: [Ifeffit] pi/2deltak

[Matt Newville]

Hi Riti,

On Sat, Jan 30, 2016 at 7:35 PM, Ritimukta Sarangi 
wrote:

> Hello,
>
> I was recently asked about the accuracy of this formulation for obtaining
> EXAFS resolution and I did not have a good answer. Can someone point to a
> reference or explain here?
>
Thank you for your time,
> Best,
> -Riti
>
>
The deltaR = pi / 2DeltaK  follows from general Fourier analysis and
formulas like it can be found in many signal processing textbooks.For
on-line resources, googling "Frequency resolution Fourier transform" gives
several good references.

The idea is that (using sound-waves as an example) in order to distinguish
two close frequencies (say 440 Hz from 441 Hz, so a different of 1 Hz), you
have to sample many periods (pi seconds) to be able to do this.

For EXAFS, if there are contributions from two neighbors that are very
closely spaced, you would have to sample enough oscillations (go high
enough in k) to see the effect of these two different distances beating
against each other.   If you don't go out far enough in k,  you can't tell
that these two contributions are actually from different distances.

Hope that helps,

--Matt
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