Analysis of neutron scattering data: Visualization and parameter estimation
Traditionally, small-angle neutron and x-ray scattering (SANS and SAXS) data analysis requires measurements of the signal and corrections due to the empty sample container, detector efficiency and time-dependent background. These corrections are then made on a pixel-by-pixel basis and estimates of relevant parameters (e.g., the radius of gyration) are made using the corrected data. This study was carried out in order to determine whether treatment of the detector efficiency and empty sample cell in a more statistically sound way would significantly reduce the uncertainties in the parameter estimators. Elements of experiment design are shortly discussed in this paper. For instance, we studied the way the time for a measurement should be optimally divided between the counting for signal, background and detector efficiency. In Section 2 we introduce the commonly accepted models for small-angle neutron and x-scattering and confine ourselves to the Guinier and Rayleigh models and their minor generalizations. The traditional approaches of data analysis are discussed only to the extent necessary to allow their comparison with the proposed techniques. Section 3 describes the main stages of the proposed method: visual data exploration, fitting the detector sensitivity function, and fitting a compound model. This model includes three additive terms describing scattering by the sampler, scattering with an empty container and a background noise. We compare a few alternatives for the first term by applying various scatter plots and computing sums of standardized squared residuals. Possible corrections due to smearing effects and randomness of estimated parameters are also shortly discussed. In Section 4 the robustness of the estimators with respect to low and upper bounds imposed on the momentum value is discussed. We show that for the available data set the most accurate and stable estimates are generated by models containing double terms either of Guinier's or Rayleigh's type. The optimal partitioning of the total experimental time between measuring various signals is discussed in Section 5. We applied a straightforward optimization instead of some special experimental techniques because of the numerical simplicity of the corresponding problem. As a criterion of optimality we selected the variance of the gyration radius maximum likelihood estimator. The statistical background of the proposed approach is given in the appendix. The properties of the maximum likelihood estimators and the corresponding iterated estimator together with its possible numerical realization are presented in subsection A.1. In subsection A.2 we prove that the use of a compound model leads to more efficient estimators than a stage-wise analysis of different components entering that model.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- US Department of Energy (US)
- DOE Contract Number:
- AC05-96OR22464
- OSTI ID:
- 771196
- Report Number(s):
- ORNL/TM-13677; ORNL-13677; TRN: US0201042
- Resource Relation:
- Other Information: PBD: 1 Sep 1998
- Country of Publication:
- United States
- Language:
- English
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