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P(r) Inversion Perspective

Description

This tool calculates a real-space 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 [ Imeas(Qi) - Ith(Qi) ] 2 / (Error) 2 + Reg_term

where Imeas(Q) is the measured scattering intensity and Ith(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 d2P(r) / dr2 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) 168-175

Note

This help document was last changed by Steve King, 01May2015

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