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

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, Δ I, and Δ I results in an uncertainty of partial scattering functions, Δ S. However, the error propagation from Δ I to Δ S has not been quantitatively clarified. In this work, we have established deterministic and statistical approaches to determine Δ S from Δ I. We have applied the two methods to experimental SANS data of polyrotaxane solutions with different contrasts, 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.