4 Energy Origin, Pre-Edge, and Normalization

   

In addition to fitting the background function , the data must be properly normalized in order to construct the of Eq. (1). Both the normalization process and the conversion from to require a reasonable estimate of the threshold energy . Though both and the normalization constant can be explicitly set by the user, autobk can make adequate estimates of these numbers, as will be described here.

   

The value for found by autobk will rarely be extremely poor, but it can easily be off by a few volts from where you might pick it. By default the value of will be chosen as an energy point in the edge, near where $d\mu/dE$, the derivative of , has a maximum. Numerical derivatives are not very trustworthy and the maximum might find a glitch in the data, so is chosen more safely than simply finding the value of E with the maximum $d\mu/dE$. The initial value of (either entered by the user or found by autobk) will be varied if a standard is used for the background removal, unless the logical flag fixe0 is explicitly set to true. The fitting of isn't very sensitive, because the job of autobk is to get , which doesn't depend much on the . It is rare for to be adjusted more than a few volts. The fitted value of probably shouldn't be trusted very much anyway, and should probably be more carefully determined in the analysis of .

    The normalization in autobk is done by a single constant number, . Because energy-dependences of x-ray detectors are usually comparable in size to the energy-dependence of there is little point in normalizing by a energy-dependent background. In any event, the primary energy-dependences of the detectors and are not difficult to estimate (as with the uwxafs3.0 program atoms), so that these corrections can be later put into the analysis. See the example of pure Cu in the feffit document for how this can be done.

  The constant value of can be set in autobk using the keyword step. If it is not given, this constant will be found by taking the difference in the extrapolation of smooth functional fits to the pre-edge total absorption and post-edge background absorption (after it is found, of course) at the threshold energy, , so that  $$\Delta \mu_{0}(E_0) = \mu^+_0(E_0) - \mu^-(E_0).$$

    The measured absorption below the edge step (the so-called pre-edge region) is fit to a straight line over the energy region between $[E_0 + E_{\rm pre1}, E_0 + E_{\rm pre2}]$. Both $E_{\rm pre1}$ and $E_{\rm pre2}$ can be set by the user with keywords pre1 and pre2, and have default values of -200, and -50 eV, respectively. These two numbers are relative to , so they should be negative numbers that are in the measured pre-edge region of the data. This fitted line is then extrapolated to , giving $\mu^-(E_0)$. The values of the slope and intercept of this pre-edge line will be written to autobk.log.

    The background function (found as discussed in chapter 5) is fit to a quadratic polynomial in E over the energy region between $[E_0 + E_{\rm nor1}, E_0 + E_{\rm nor2}]$. Both $E_{\rm nor1}$ and $E_{\rm nor2}$ can be set by the user with keywords nor1 and nor2, and have default values of 100, and 300 eV, respectively. These two numbers are relative to ,and should be positive numbers that are in the measured region of the data. This fitted polynomial is then extrapolated to ,giving $\mu^+_0(E_0)$.