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

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, $\hat{I}”I$, and $\hat{I}”I$ results in an uncertainty of partial scattering functions, $\hat{I}”S$. However, the error propagation from $\hat{I}”I$ to $\hat{I}”S$ has not been quantitatively clarified. In this work, we have established deterministic and statistical approaches to determine $\hat{I}”S$ from $\hat{I}”I$. 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.