Enhanced estimation method for partial scattering functions in contrast variation small‐angle neutron scattering via Gaussian process regression with prior knowledge of smoothness

Contrast variation small‐angle neutron scattering (CV‐SANS) is a powerful tool for evaluating the structure of multi‐component systems. In CV‐SANS, the scattering intensities I ( Q ) measured with different scattering contrasts are decomposed into partial scattering functions S ( Q ) of the self‐ and cross‐correlations between components. Since the measurement has a measurement error, S ( Q ) must be estimated statistically from I ( Q ). If no prior knowledge about S ( Q ) is available, the least‐squares method is best, and this is the most popular estimation method. However, if prior knowledge is available, the estimation can be improved using Bayesian inference in a statistically authorized way. In this paper, we propose a novel method to improve the estimation of S ( Q ), based on Gaussian process regression using prior knowledge about the smoothness and flatness of S ( Q ). We demonstrate the method using synthetic core–shell and experimental polyrotaxane SANS data.