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The direct spline method

The direct spline method is analogous to standard XAFS analysis. It splines the measured DAFS intensity, subtracts the spline from the data, and normalizes the resulting fine structure signal to the spline. In its simplest form, it produces an effective tex2html_wrap_inline1594 function that contains a mixture of the tex2html_wrap_inline1584, tex2html_wrap_inline1586 and tex2html_wrap_inline1454 components. If the data is divided by the measured absorption correction before it is splined, the tex2html_wrap_inline1594 function will still contain a mixture of tex2html_wrap_inline1584 and tex2html_wrap_inline1586 components. The measured intensity can be related to the theoretical intensity (Eqn. 10) by tex2html_wrap_inline1636, where C(E) accounts for the energy dependent instrument correction factors. The measured intensity is fit with a smooth spline tex2html_wrap_inline1640, and the fine structure is separated from the measured intensity by subtracting the spline from the data. The fine structure is normalized by dividing by tex2html_wrap_inline1642 to yield the effective tex2html_wrap_inline1594 function,
 eqnarray327
Note that the site specific tex2html_wrap_inline1646 and tex2html_wrap_inline1648 signals can be determined from the effective tex2html_wrap_inline1594 function if the real and imaginary parts of the smoothly varying background, tex2html_wrap_inline1588 and tex2html_wrap_inline1590, and the crystallographic weights, tex2html_wrap_inline1526, can be determined.