# [Ifeffit] Ifeffit Digest, Vol 170, Issue 21

Matthew Marcus mamarcus at lbl.gov
Fri Apr 21 18:09:31 CDT 2017

```Suppose the data were tabulated locally on a 0.01A^-1 grid, then sampled on the default 0.05A grid with cubic-spline interpolation.  In that case, the spline interpolated value
depends mostly on the couple of samples nearest the new grid points, which means that you're not really using all the data equally.  I suppose it could be argued, then, that
smoothing distributes some of the weight of the 'in-between' points so that they're accounted for, the way boxcar averaging does.

What my code does (original idea frpm Brian Kincaid) is a linear weighting, essentially a triangular convolution kernel rather than a rectangle, as in boxcar averaging.
Think of it as A-frame averaging rather than boxcar.  That's sharper, so would result in less loss of amplitude in the high shells.

If you have a distance of 5A, then the phase shift between .05A^-1 gridpoints is 0.5rad.  At the top of a wiggle, you're essentially averaging cos(phi) over the range [-0.25,0.25],
which gives you an amplitude of sin(0.25)/0.25 = 0.98.  Thus, I don't understand how boxcar averaging makes a noticeable difference here except for really long paths.

For a triangular average over a phase range +-delta, the relevant amplitude reduction is

f = Integrate[Cos[phi]*(1 - phi/delta), {phi, 0, delta}]/Integrate[(1 - phi/delta), {phi, 0, delta}] (Mathematica notation, using symmetry of the functions)

which comes to f = 2(1-Cos(delta))/delta^2, whose leading term is 1-delta^2/12.  Thus, to lose 10%
of the amplitude, delta would have to be about 1.12rad, which means a phase shift between grid points of 2.24rad, thus a distance of 22A.

A caveat:  This derivation only covers the phase.  Presumably, an amplitude varying with k would cause a phase shift of the averaged wave.  I haven't worked out

The triangular kernel assigns the full weight of each input point to some combination of the new grid points on each side, so nobody's left out.
mam

On 4/21/2017 3:36 PM, Christopher Thomas Chantler wrote:
> �� I'm just agreeing with Matt's comment.
>
>
> Too fine a spacing does not help you due to typical broadening from imfp or thermal sources [or structural disorder].
>
>
> And the difference between operation of ifeffit and larch in this context is pretty interesting.
>
>
> --------------------------------------------------------------------------------------
> Christopher Chantler, Professor, FAIP, Fellow American Physical Society
> Editor-in-Chief, Radiation Physics and Chemistry
> Chair, International IUCr Commission on XAFS
> President, International Radiation Physics Society
> School of Physics, University of Melbourne
> Parkville Victoria 3010 Australia
> +61-3-83445437 FAX +61-3-93474783
> chantler at unimelb.edu.au <https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=mailto%3achantler%40unimelb.edu.au> chantler at me.com <https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=mailto%3achantler%40me.com>
> http://optics.ph.unimelb.edu.au/~chantler/xrayopt/xrayopt.html <https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=http%3a%2f%2foptics.ph.unimelb.edu.au%2f%7echantler%2fxrayopt%2fxrayopt.html>
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>
> ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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> Today's Topics:
>
>    1. Re: Ifeffit Digest, Vol 170, Issue 19 (Matt Newville)
>    2. Fwd:  Ifeffit Digest, Vol 170, Issue 19 (Matt Newville)
>    3. Looking for EXAFS data of Ni2+ ion in aqueous solution (Van Vu)
>
>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Thu, 20 Apr 2017 21:18:39 -0500
> From: Matt Newville <newville at cars.uchicago.edu>
> To: XAFS Analysis using Ifeffit <ifeffit at millenia.cars.aps.anl.gov>
> Subject: Re: [Ifeffit] Ifeffit Digest, Vol 170, Issue 19
> Message-ID:
>         <CA+7ESbpEWenMLpspnYAXT4j2T1LkjAaYua59XcGebLpteKTyWg at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Hi Chris,
>
> On Thu, Apr 20, 2017 at 5:02 PM, Christopher Thomas Chantler <
> chantler at unimelb.edu.au> wrote:
>
>> Note that in general any and every smoothing operation reduces the
>> information content of the data and its ability to reveal structure.
>>
>
> Well, maybe.  If one has mu(E) measured every 0.01 eV over an 600 eV EXAFS
> scan to k=12A^-1, one does not really 60,000 independent measures of the
> structure.  Yuji's data wasn't that absurd, but it did have close to 4000
> measurements for the full EXAFS spectrum out to k=18^-1.  And to be clear,
> there is not anything wrong with that, it's just a matter of how you decide
> to treat it.
>
> As the plots attached in Yuji's original message and my replies show, the
> resulting chi(k) definitely has is amplitude suppressed when doing a simple
> boxcar average of data onto the 0.05 Ang^-1 grid (Athena with Ifeffit).
> But when using cubic spline interpolation (Larch), the amplitude of the
> EXAFS oscillations are not noticeably suppressed, though the high frequency
> noise is also much higher.  Applying a Savitzky-Golay filter prior to the
> cubic spline interpolation did not appreciably suppress the EXAFS
> oscillations though the high frequency noise was reduced.
>
> Very finely-spaced energy data might reveal is at much higher R than we can
> hope to model with EXAFS.  A k-grid of 0.05 Ang^-1 can give frequencies to
> 31Ang, and so is probably accurate to 16Ang without significant signal
> loss.   That is, out to k=18Ang^-1, you really only need 360 samples, but
> you'd like these as noise-free as possible.  Having 3600 measurements on a
> grid of 0.005 Ang^-1  might give you data out to 160Ang in principle, but
> the photo-electron tends to not cooperate.
>
> --Matt
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> ------------------------------
>
> Message: 2
> Date: Thu, 20 Apr 2017 22:33:14 -0500
> From: Matt Newville <newville at cars.uchicago.edu>
> To: XAFS Analysis using Ifeffit <ifeffit at millenia.cars.aps.anl.gov>
> Subject: [Ifeffit] Fwd:  Ifeffit Digest, Vol 170, Issue 19
> Message-ID:
> Content-Type: text/plain; charset="utf-8"
>
> Hi Matthew,
>
>
> On Thu, Apr 20, 2017 at 5:34 PM, Matthew Marcus <mamarcus at lbl.gov> wrote:
>
>> Does Athena use a histogramming method for Fourier filtering?
>
>
> The autobk() in Ifeffit does.  That is, the background mu0(E) and chi(E)
> are found at all input energy points.  This is converted to chi(k) at k for
> all energy points, and then a boxcar average is applied to give chi(k) on
> the standard 0.05 k-grid.  As shown earlier, this diminishes the noise and
> also the amplitude of chi(k), especially at higher frequencies.
>
> In Larch, the cubic spline for the background mu0(E)  is found at all input
> energy points, but then evaluated at the values on the uniform k-grid.
> .
>
>> That's what I use.  The idea is that to grid the data we don't interpolate
>> but take averages over the data appearing within the bin,
>
>
>  OK, but that boxcar average will blur the data.    I definitely see this
> with QXAFS (well "continuous") where I can scan continuously but bin the
> measurements into 0.05Ang-1 bins -- that *does* reduce the amplitude
> compared to binning into 0.02 Ang^-1 bins and compared to step scans, where
> one measures at fixed energies, not slewing over an energy range.
>
> The data from SPRing8 was much finer spaced than EXAFS needs -- and boxcar
> averaging to 0.05 Ang^-1 does blur the data.
>
>
>> with interpolation only when there aren't any points within a bin. For
>> those, you have to bridge across a gap.  This is the best idea I've come up
>> with for using data which may be tabulated more finely than the k-grid of
>> the Fourier filtering process (typically dk=0.05A^-1).
>>
>
> Putting the spline through all the energy points does use all the data to
> predict the value on the 0.05 Ang^-1 grid, and avoids blurring the data.
> Yes, the result can be noisier, but it does not suppress the oscillations.
>
>
>> Something I've used in a XANES context but never tried for EXAFS is a
>> convolution with a kernel whose width depends on energy, such that it
>> matches the sharpest credible feature.  See Manceau, A., Marcus, M. A.,
>> Lenoir, T. (2014) Estimating the number of pure chemical components in a
>> mixture by X-ray absorption spectroscopy. J. Synchrotron Radiat.
>> 21,1140-1147,
>> specifically the SI.
>
>
> I've read that paper, but I don't think I looked at the SI.  Will do.
>
>
>> The notion is that no real feature can be narrower than the combination of
>> corresponding to the maximum reasonable path length.  This is done
>> by transforming the data from E-space to a space in which a constant step
>> in the abscissa corresponds to this energy-dependent minimum credible
>> feature width.  Of course, in EXAFS this is mostly a constant width in k,
>> so some kind of smoothing would work if it's a constant kernel in k.
>
>
>  That's sort of what a Fourier filter does, for example zero all the data
> above R>10 and transform back to k.
>
> S-G smoothing assumes uniform tabulation so unless your data were taken on
>> a uniform k-grid, it doesn't really do the right thing.
>>
>
> The S-G smoothing does appear to help even if the data are not strictly
> uniform (see example posted earlier where the data was very finely spaced
> in energy, but not uniformly).    I did forget about the uniformity
> requirement, but I think that for the purposes here (smooth very fine
> slightly noisy data before fitting the cubic spline) it's probably not a
> disaster.
>
> I would agree that this filter is designed to reduce high-frequency noise
> is largely cosmetic, and is not really going to help reduce the noise in
> the frequency range of the data we actually care about.  In fact, for me
> the main point would be that the S-G filter does *not* greatly alter the
> frequencies we care about, whereas boxcar averaging most certainly does.
>
>
>
>> A problem with this method is that it drops off the very information you
>> need to see what your noise floor is.
>
>
> Yes, that's a good point.  Removing the obvious high-frequency noise gives
> the impression that there is no low-frequency noise, which is not correct.
>
>
>
>> I put this out there only for those who insist on smoothing.  I use my
>> data un-smoothed for EXAFS analysis, knowing that the treatment of noise
>> and sampling finer than the k-bin is not really right.
>>
>
>
>
>> I don't really see the usefulness of smoothing for XANES or EXAFS
>> analysis, though it might be OK for display if not overdone.
>>
>
> Yes, I agree -- not smoothing chi(k) is the best approach.  But if you do
> smooth, use Savitzky-Golay on the uniform chi(k).
>
>
> --
> --Matt
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> ------------------------------
>
> Message: 3
> Date: Fri, 21 Apr 2017 20:01:05 +0700
> From: Van Vu <vuxxx047 at umn.edu>
> To: XAFS Analysis using Ifeffit <ifeffit at millenia.cars.aps.anl.gov>
> Subject: [Ifeffit] Looking for EXAFS data of Ni2+ ion in aqueous
>         solution
> Message-ID:
> Content-Type: text/plain; charset="utf-8"
>
> Dear everyone,
> I am looking for XAS data of Ni2+ ion in aqueous solution that contains
> EXAFS data in the k range of 0-12 (Angstrom-1) or so for an undergraduate
> student project. I was wondering if anyone would be willing to share the
> data with me?
> Best,
> Van
>
> On Fri, Apr 21, 2017 at 5:02 AM, Christopher Thomas Chantler <
> chantler at unimelb.edu.au> wrote:
>
>> Note that in general any and every smoothing operation reduces the
>> information content of the data and its ability to reveal structure. Also,
>> many of the smoothing algorithms change the data point values at vertices,
>> so change the data prior to analysis.
>>
>>
>> Hence in general avoid unless you know exactly the physical cause
>> requiring smoothing.
>>
>>
>> Best wishes
>>
>>
>> ------------------------------------------------------------
>> --------------------------
>> Christopher Chantler, Professor, FAIP, Fellow American Physical Society
>> Editor-in-Chief, Radiation Physics and Chemistry
>> Chair, International IUCr Commission on XAFS
>> President, International Radiation Physics Society
>> School of Physics, University of Melbourne
>> Parkville Victoria 3010 Australia
>> +61-3-83445437 FAX +61-3-93474783
>> chantler at unimelb.edu.au
>> <https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=mailto%3achantler%40unimelb.edu.au>
>> chantler at me.com
>> <https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=mailto%3achantler%40me.com>
>> http://optics.ph.unimelb.edu.au/~chantler/xrayopt/xrayopt.html
>> <https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=http%3a%2f%2foptics.ph.unimelb.edu.au%2f%7echantler%2fxrayopt%2fxrayopt.html>
>> http://optics.ph.unimelb.edu.au/~chantler/home.html
>> <https://owa.unimelb.edu.au/owa/redir.aspx?C=c7BoS0kVVkC1_S95-9x9l5cBu6YTjdAITgSrfUpfDAUV5oUH1LFYBcz08w8xvHMJoosZRdagfQM.&URL=http%3a%2f%2foptics.ph.unimelb.edu.au%2f%7echantler%2fhome.html>
>>
>> ------------------------------
>> *From:* Ifeffit <ifeffit-bounces at millenia.cars.aps.anl.gov> on behalf of
>> ifeffit-request at millenia.cars.aps.anl.gov <ifeffit-request at millenia.
>> https://protect-au.mimecast.com/s/GN1VBvt6aeV8I1?domain=cars.aps.anl.gov <http://cars.aps.anl.gov>>
>> *Sent:* Friday, 21 April 2017 3:00:01 AM
>> *To:* ifeffit at millenia.cars.aps.anl.gov
>> *Subject:* Ifeffit Digest, Vol 170, Issue 19
>>
>> Send Ifeffit mailing list submissions to
>>         ifeffit at millenia.cars.aps.anl.gov
>>
>> To subscribe or unsubscribe via the World Wide Web, visit
>>         https://protect-au.mimecast.com/s/krZOBlimO6EJCD?domain=millenia.cars.aps.anl.gov <http://millenia.cars.aps.anl.gov/mailman/listinfo/ifeffit>
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>> than "Re: Contents of Ifeffit digest..."
>>
>>
>> Today's Topics:
>>
>>    1. Re: The difference of EXAFS oscillation when using Athena and
>>       when using Larch (Yuji Mahara)
>>
>>
>> ----------------------------------------------------------------------
>>
>> Message: 1
>> Date: Thu, 20 Apr 2017 19:47:20 +0900
>> From: "Yuji Mahara" <mahara.yuji at e.mbox.nagoya-u.ac.jp>
>> To: "'XAFS Analysis using Ifeffit'"
>>         <ifeffit at millenia.cars.aps.anl.gov>
>> Subject: Re: [Ifeffit] The difference of EXAFS oscillation when using
>>         Athena  and when using Larch
>> Message-ID: <003501d2b9c3\$7c75c560\$75615020\$@e.mbox.nagoya-u.ac.jp>
>> Content-Type: text/plain; charset="utf-8"
>>
>> Dear Matt
>>
>>
>>
>>
>> I confirmed that chi (k) becomes smooth by the Savitzky-Goley method by
>> doing the attached lar file.
>>
>>
>>
>> I will try on various conditions from now.
>>
>> I may also ask if there is something I do not understand.
>>
>> Thank you for your help again!
>>
>>
>>
>> Bests,
>>
>> Yuji Mahara
>>
>>
>>
>>
>>
>> From: Ifeffit [mailto:ifeffit-bounces at millenia.cars.aps.anl.gov
>> <ifeffit-bounces at millenia.cars.aps.anl.gov>] On Behalf Of Matt Newville
>> Sent: Thursday, April 20, 2017 5:26 AM
>> To: XAFS Analysis using Ifeffit <ifeffit at millenia.cars.aps.anl.gov>
>> Subject: Re: [Ifeffit] The difference of EXAFS oscillation when using
>> Athena and when using Larch
>>
>>
>>
>> Hi Yuji,
>>
>> The attached larch script (a modification of your script but note: not
>> python, so you may have to add a bunch of '_larch=mylarch' arguments) to
>> show the effects of smoothing with Savitzky-Golay and of interpolating onto
>> a "classic XAFS energy grid".   You might want to play around with this
>> different options.  It definitely seems that none of these methods are
>> systematically over-smoothing the data and reducing the amplitudes of the
>> oscillations -- one more reason to use Larch instead of Ifeffit.  But it
>> also seems like smoothing this data with a Savitzky-Golay fitler is helpful.
>>
>> Also attached are plots showing k- and R-space generated from the attached
>> script.
>>
>>
>>
>> --Matt
>>
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