Accounting for instrument resolution in the pair distribution functions obtained from total scattering data using Hermite functions

Wang, S.; Gao, M.; Qin, Y.; Zhang, S.; Tan, L.; Dove, M.T.

doi:10.1107/S1600576725004340

Figure 4
Demonstration of the reconstruction of the scattering function Qi(Q) and PDF D(r) by accounting for resolution in the fitting of the scattering function with Hermite functions convolved with an appropriate resolution function, equations (24

) and (25

). (a) Three examples of broadened scattering functions Qi(Q) with fitting to the corresponding broadened Hermite functions. The black points representing the synthetic data are entirely overlapped by the red curves, which are the fitted functions. (b) The three reconstructed scattering functions Qi(Q) with the effects of the resolution function removed, showing close agreement in each case. The black points representing the synthetic data prior to the convolution with a resolution function (identical in each case) are overlapped by the red curves, which show the reconstructed scattering functions. (c) The reconstructed PDFs D(r) obtained with the effects of resolution removed (red curves) and compared with the initial data (black, identical in each case). Each plot gives the three values of the Gaussian width parameters, σ, equation (26

). The blue curves in each case give the difference between the fitted or extracted functions and synthetic data.

JOURNAL OF
APPLIED
CRYSTALLOGRAPHY

ISSN: 1600-5767

Volume 58| Part 4| August 2025| Pages 1269-1287

https://doi.org/10.1107/S1600576725004340

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