Carlo said:
However, mesuring for one second per point on, say, a 0.25 eV grid is similar in a counting statistics sense to two measurements of one second per point on a 0.5 eV grid. That counting statistics improvement is not lost in the interpolation of chi(E) to chi(k).
CS> I think that this last sentence is the answer that I was looking CS> for. I wanted to know if the counting statistics improvement is CS> propagated in the transformation to k-space. This is good since CS> it means that we do not have to write our own rebinning or CS> smoothing routines before handing the data off to athena and CS> ifeffit. Hmm.... upon further reflection, I think that what I said is not right. Or, more specifically, it depends upon how the interpolation is done and what the densities are of the starting and ending grids. Suppose you are interpolating ONTO a 1eV grid FROM a 0.5 eV grid using three-point interpolation. Then every point you measure gets used to determine points on the new grid. However, if you do the same interpolation ONTO a 1 eV grid FROM a 0.25 eV interpolation, then 1/2 of the points never get used to determine the new grid. For any polynomial interpolation, this argument will hold for any starting grid that is sufficiently dense compared to the ending grid. I had to reread what Numerical Recipes has to say about cubic spline interpolation (i.e. Ifeffit's splint() function), but it too has this problem of relative densities. Because second derivatives of the starting grid are computed, the splint makes better use of the denser grid. However, the splint may fail to use some of the information provided in the chi(E) to chi(k) conversion -- particularly far above the edge where the k-grid is very sparse compared to the E-grid. As Matt said yesterday, Ifeffit uses a quadratic, i.e. three-point, interpolation to make chi(k) from chi(E) (Source divers: See src/lib/spline.f at line 364) onto a 0.05invAng grid (a hardwired value set in consts.h). Sorry I misled you yesterday. But since the E-grid does not map linearly onto the k-grid, you will need to think hard about how you do any rebinning. Whatever you come up with, you should let us know. It may be something worth putting into either Athena or Ifeffit. B -- Bruce Ravel ----------------------------------- ravel@phys.washington.edu Code 6134, Building 3, Room 222 Naval Research Laboratory phone: (1) 202 767 5947 Washington DC 20375, USA fax: (1) 202 767 1697 NRL Synchrotron Radiation Consortium (NRL-SRC) Beamlines X11a, X11b, X23b, X24c, U4b National Synchrotron Light Source Brookhaven National Laboratory, Upton, NY 11973 My homepage: http://feff.phys.washington.edu/~ravel EXAFS software: http://feff.phys.washington.edu/~ravel/software/exafs/