Analysis of neutron scattering data: Visualization and parameter estimation

PDF Version Also Available for Download.

Description

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, ... continued below

Physical Description

41 p.

Creation Information

Beauchamp, J.J.; Fedorov, V.; Hamilton, W.A. & Yethiraj, M. September 1, 1998.

Context

This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided by UNT Libraries Government Documents Department to Digital Library, a digital repository hosted by the UNT Libraries. More information about this report can be viewed below.

Who

People and organizations associated with either the creation of this report or its content.

Sponsor

Publisher

Provided By

UNT Libraries Government Documents Department

Serving as both a federal and a state depository library, the UNT Libraries Government Documents Department maintains millions of items in a variety of formats. The department is a member of the FDLP Content Partnerships Program and an Affiliated Archive of the National Archives.

Contact Us

What

Descriptive information to help identify this report. Follow the links below to find similar items on the Digital Library.

Description

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.

Physical Description

41 p.

Notes

INIS; OSTI as DE00771196

Medium: P; Size: 41 pages

Source

  • Other Information: PBD: 1 Sep 1998

Language

Item Type

Identifier

Unique identifying numbers for this report in the Digital Library or other systems.

  • Report No.: ORNL/TM-13677
  • Report No.: ORNL-13677
  • Grant Number: AC05-96OR22464
  • DOI: 10.2172/771196 | External Link
  • Office of Scientific & Technical Information Report Number: 771196
  • Archival Resource Key: ark:/67531/metadc722654

Collections

This report is part of the following collection of related materials.

Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

What responsibilities do I have when using this report?

When

Dates and time periods associated with this report.

Creation Date

  • September 1, 1998

Added to The UNT Digital Library

  • Sept. 29, 2015, 5:31 a.m.

Description Last Updated

  • April 12, 2017, 3:07 p.m.

Usage Statistics

When was this report last used?

Yesterday: 0
Past 30 days: 0
Total Uses: 10

Interact With This Report

Here are some suggestions for what to do next.

Start Reading

PDF Version Also Available for Download.

International Image Interoperability Framework

IIF Logo

We support the IIIF Presentation API

Beauchamp, J.J.; Fedorov, V.; Hamilton, W.A. & Yethiraj, M. Analysis of neutron scattering data: Visualization and parameter estimation, report, September 1, 1998; Tennessee. (digital.library.unt.edu/ark:/67531/metadc722654/: accessed July 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.