Direct Fourier transform
The simplest method used to analyze DEER data is direct Fourier transform of the time-
domain data to give a frequency spectrum where the Pake pattern splitting is proportional to l/r3
(where r is the interspin distance). However, this method does not provide a detailed analysis or
distribution profile. Instead, this method only reports on a most probable distance between spins.
A graphical representation of this analysis method is shown in Figure 2-21.
A B C
H ~1/r3
I \ I I
0 1 2 3 -10 -5 0 5 10 20 25 30 35 40 45 50 55
T (Ls) Frequency (MHz) Distance (A)
Figure 2-21. Pictorial representation of the direct Fourier transform method of analysis, A) time
domain spectrum is converted to a B) frequency domain spectrum, where the
singularities in the Pake pattern are proportional to 1/r3, where r is C) the most
probable distance between two spins.
Curve fitting and Monte Carlo analysis
In order to gain more information than the direct Fourier transform method provides, i.e., a
distance distribution profile, a more complex analysis method is required. A common technique,
referred to as curve fitting, can be employed to solve the inverse problem of generating a
distance profile based on known information about the system, and optimize it until the
theoretical and experimental dipolar evolution curves match. In Monte Carlo (MC) analysis, the
scheme for which is shown in Figure 2-22, the distance profile has a pre-determined form (e.g.,
Gaussian) (Fajer 2006). The MC analysis has the advantage of being a fairly easy and expansive