Tikhonov regularization-based reconstruction of partial scattering functions obtained from contrast variation small-angle neutron scattering

TL;DR

This paper introduces a Tikhonov regularization method to improve the stability of reconstructing partial scattering functions in contrast variation small-angle neutron scattering, addressing issues caused by small absolute values and singular value disparities.

Contribution

It presents a novel application of Tikhonov regularization to enhance the stability and accuracy of partial scattering function reconstruction in CV-SANS experiments.

Findings

Regularization improves reconstruction stability.

Enhanced accuracy in partial scattering functions.

Addresses instability caused by small singular values.

Abstract

Contrast variation small-angle neutron scattering (CV-SANS) has been widely employed for nano structural analysis of multicomponent systems. In CV-SANS experiments, scattering intensities of samples with different scattering co\ ntrasts are decomposed into partial scattering functions, corresponding to structure of each component and cross-correlation between different components, by singular value decomposition (SVD). However, the estimation of partial scattering functions with small absolute values often suffers from instability due to the significant differences in the singular values. In this paper, we propose a remedy for this instability by introducing the Tikhonov regularization, which ensures more stable reconstruction of the partial scattering functions.