Dear EXAFS folk,
I'm a graduate student in Jerry Seidler's group at the University of Washington, Seattle. I've been doing a numerical and experimental study on how to optimize k-weighting for EXAFS when the total experimental measurement time for a study is constrained, i.e., when you have 1 hour at some given I0 flux and your job is to get the best results, in terms of best fits or cleanest g(R).
Can anyone aim me at 'famous' papers (or at least 'standard' papers) on the best use of k-weighting? Also, it would be great if people could informally email me how they, personally, do k-weighting and what their personal experience has been. My email is
jbferre@uw.edu.
Are you asking about weighting the integration time for data collection, or weighting the chi(k) data for analysis? I'm not sure the answer is really different, but I'm also not sure that this is really an answer or even that there is a single answer.
I am not aware of any papers that analyze the selection of k-weighting to optimize data collection efficiency or to optimize actual results of refinements. I believe that the idea of always and only k-weighting by a simple power of k is probably historical, and while easy to do and explain and clearly helpful for many cases, is not really all that well-justified. For sure, when extracting structural parameters from a refinement, it is definitely advantageous to k-weight the data. But I don't think your going to find that some kweight is always best.
There is a 1/k in the EXAFS equation, and F(k) generally decays with k. The challenge is that this decay changes with Z. So, "normally" one might say that using k-weight of 2 or 3 is necessary to see lighter elements at high k. In fact, F(k) for oxygen sort of looks like k^{-2} at high k, so if the goal is to refine g(R) for light elements, using k-weight of 3 seems like a reasonable choice. If there are heavier scatterers that will usually dominate the high-k portion of chi(k). Disorder terms in g(R) also strongly reduce chi(k) as a function of k and k-weighting can sort of help compensate for that, and give a relatively strong and uniform signal over the full k range. But these decays are actually power laws, so any attempt to normalize so that the g(R) for any scatterer is uniformly sampled over k is probably not realistic.
For many analyses, especially from dilute samples measured in fluorescence, the noise in the data is appreciable and has an important contribution from counting statistics. Some (perhaps most?) data acquisition programs can k-weight the collection time with a power of k, which wlll try to make the counting noise uniform for k^(w) * chi(k) for some k-weight w. That definitely misses important sources of noise, but I think the general observation is that this does actually help for many cases. I don't think there is much work analyzing this process in detail. There is always a preference to reduce noise levels over characterizing noise levels in excuriating detail.
That is definitely not an answer, but I hope it helps,
--Matt