Error evaluation of partial scattering functions obtained from contrast variation small-angle neutron scattering

TL;DR

This paper develops methods to quantitatively estimate the errors in partial scattering functions derived from contrast variation small-angle neutron scattering data, enabling better optimization of contrast conditions.

Contribution

It introduces deterministic and statistical approaches to evaluate error propagation from measurement uncertainties to partial scattering functions in CV-SANS.

Findings

Successfully estimated errors in partial scattering functions for various samples.

Demonstrated error estimation can guide contrast optimization.

Applied methods to both computational and experimental data.

Abstract

Contrast variation small-angle neutron scattering (CV-SANS) is a powerful tool to evaluate the structure of multi-component systems by decomposing scattering intensities $I$ measured with different scattering contrasts into partial scattering functions $S$ of self- and cross-correlations between components. The measured $I$ contains a measurement error, $\Delta I$, and $\Delta I$ results in an uncertainty of partial scattering functions, $\Delta S$. However, the error propagation from $\Delta I$ to $\Delta S$ has not been quantitatively clarified. In this work, we have established deterministic and statistical approaches to determine $\Delta S$ from $\Delta I$. We have applied the two methods to (i) computational data of a core-shell sphere and experimental CV-SANS data of (ii) clay/polyethylene glycol (PEG) aqueous solutions and (iii) polyrotaxane solutions, and have successfully estimated the errors of \(S\). The quantitative error estimation of \(S\) offers us a strategy to optimize the combination of scattering contrasts to minimize error propagation.