Abstract
A maximum entropy method for reducing truncation effects in the three dimensional inverse Fourier transform of S(q) to g(r) is described in detail. The failure of a naive approach, maximizing the entropy of g(r) subject to a chi-square statistic on the S(q) data is demonstrated. Subsequently, a method is described which yields better results, by restricting the spaces on which g(r) and S(q) are defined, and allowing a tail to form beyond the original range of the data. Our algorithm is tested using a PY hard sphere structure factor as model input data. An example using real data on the structure of light and heavy water is presented. It is seen that the maximum entropy method can greatly enhance our ability to distinguish physically meaningful structure from that arising from noise and the truncation effects of traditional Fourier transform methods.
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© 1988 Kluwer Academic Publishers
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Root, J.H., Egelstaff, P.A., Nickel, B.G. (1988). Maximum Entropy Analysis of Liquid Diffraction Data. In: Erickson, G.J., Smith, C.R. (eds) Maximum-Entropy and Bayesian Methods in Science and Engineering. Fundamental Theories of Physics, vol 31-32. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9054-4_24
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DOI: https://doi.org/10.1007/978-94-010-9054-4_24
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-9056-8
Online ISBN: 978-94-010-9054-4
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