chapter  11
22 Pages

IdentifyingaGoodFit

In EXAFS modeling, we are usually fitting either the Fourier transform or the back-transform. According to the Rayleigh criterion (Section 4.5.2 of Chapter 4), we can just barely resolve peaks in the Fourier transform with a spacing of

ΔR k k =

−( ) pi

2 max min (11.1)

If we fit over a range from Rmin to Rmax, that means we could consider there to be a number of independent points given by

N R R

R

k k R R ind =

−( ) =

−( ) −( )max min max min max min Δ

pi (11.2)

This is often known as the Nyquist criterion, due to its relationship to an analysis of the information content of telegraph signals by Harry Nyquist (Nyquist, 1928).