Hi Scott, Not exactly related to my last posint, here is an argument against any tampering with integration time, whether k^n or k^2n weighting... The Fourier transform of white noise is easy to calculate: it's magnitude does not depend on r, and this property is used as a measure of statistical errors in experimental data, by using the FT magnitude at higher r, as described in this document (page 5, eq. (6)): http://ixs.iit.edu/subcommittee_reports/sc/err-rep.pdf Since k-weighted integration time alters the noise, it is no longer white. That means, its FT at high r is not indicative of the noise at low r, because it varies with r. Moreover, according to literature, this behavior is strongly dependent on the Fourier window function used. Thus, Eq. (6) that is implemented in IFEFFIT, is no longer valid for statistical error analysis if variable integration time used. Eqs. (7) and (8) in this summary, that also can be used to estimate statistical errors do not allow to account for a measurement with variable integration times either. In summary, to my opinion, one may improve the data quality by varying integration time, but it is not straightforward how to quantify such an improvement in terms of the effect on statistical errors in the data made by such trick. Anatoly ****************** Anatoly Frenkel, Ph.D. Associate Professor Physics Department Yeshiva University 245 Lexington Avenue New York, NY 10016 (YU) 212-340-7827 (BNL) 631-344-3013 (Fax) 212-340-7788 anatoly.frenkel@yu.edu http://www.yu.edu/faculty/afrenkel -----Original Message----- From: ifeffit-bounces@millenia.cars.aps.anl.gov [mailto:ifeffit-bounces@millenia.cars.aps.anl.gov]On Behalf Of scalvin@slc.edu Sent: Thursday, August 25, 2005 10:58 PM To: XAFS Analysis using Ifeffit Subject: RE: [Ifeffit] A basic question about data collection Hi Anatoly, I agree--they are not equivalent, and the constant k-space increment with k-dependent integration time is formally "more proper." But if the spacing is small compared to the size of an EXAFS oscillation, then there isn't a lot of difference between the two. It could even be argued that sampling over a range of k (or E) and binning is less susceptible to artifacts than choosing fewer points and spending longer on them, although as was pointed out earlier, the former takes longer because of mono settling time. Unfortunately, the beam lines I work on don't have software implemented to use a k^n weighted integration time, so I'd have to define a scan with a lot of segments that gradually increase integration time. Constant energy increment is a lazier way to move things in that direction. The real solution is to think about getting the k-weighted integration time implemented in the software... Question: you say k^n weighted integration time. Shouldn't it ideally be k^(2n), since noise might be expected to decrease as the square root of the number of counts? --Scott Calvin Sarah Lawrence College
I am probably missing the point, but it is not immediately obvious to me
why the following is equivalent in terms of improving the signal to noise: a) constant E-space increment and b) constant k-space increment combined with k-dependent integration time. In a), the data cluster at high E, but each data point in E corresponds to a different final state and thus is unique. Averaging over E-space data in the small interval Delta E, (1/Delta E)*Int [xmu(E) dE] is not equivalent to the time average of xmu(E) collected at a fixed E: (1/T)*Int [xmu(E) dt]. Thus, k^n-weighted integration time, to my mind, is the only proper way of reducing statistical noise.
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