# Using the singular value decomposition to extract 2D correlation functions from scattering patterns

## TL;DR

This paper demonstrates how truncated singular value decomposition (SVD) can effectively extract 2D correlation functions from small-angle scattering data, including anisotropic patterns, enabling model-free analysis of complex scattering profiles.

## Contribution

The study introduces a novel application of truncated SVD to derive 2D correlation functions from scattering patterns, even in noisy and anisotropic cases.

## Key findings

- Accurately reconstructs correlation functions from simulated data.
- Successfully applies the method to real experimental scattering data.
- Shows robustness in analyzing anisotropic scattering patterns.

## Abstract

We apply the truncated singular value decomposition (SVD) to extract the underlying 2D correlation functions from small-angle scattering patterns. We test the approach by transforming the simulated data of ellipsoidal particles and show that also in case of anisotropic patterns (i.e. aligned ellipsoids) the derived correlation functions correspond to the theoretically predicted profiles. Furthermore, we use the truncated SVD to analyze the small-angle x-ray scattering patterns of colloidal dispersions of hematite spindles and magnetotactic bacteria in presence of magnetic fields, to verify that this approach can be applied to extract model-free the scattering profiles of anisotropic scatterers from noisy data.