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P(r) Inversion Perspective
Description
This tool calculates a realspace distance distribution function, P(r), using the inversion approach (Moore, 1908).
P(r) is set to be equal to an expansion of base functions of the type
bigphi_n(r) = 2.r.sin(pi.n.r/D_max)
The coefficient of each base function in the expansion is found by performing a least square fit with the following fit function
chi^{2} = bigsigma_{i} [ I_{meas}(Q_{i})  I_{th}(Q_{i}) ] ^{2} / (Error) ^{2} + Reg_term
where I_{meas}(Q) is the measured scattering intensity and I_{th}(Q) is the prediction from the Fourier transform of the P(r) expansion.
The Reg_term term is a regularization term set to the second derivative d^{2}P(r) / dr^{2} integrated over r. It is used to produce a smooth P(r) output.
Using the perspective
The user must enter
 Number of terms: the number of base functions in the P(r) expansion.
 Regularization constant: a multiplicative constant to set the size of the regularization term.
 Maximum distance: the maximum distance between any two points in the system.
Reference
P.B. Moore J. Appl. Cryst., 13 (1980) 168175
Note
This help document was last changed by Steve King, 01May2015