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.