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Updated: Jan 20, 2026
Singularity Functions for Shear
Using the singular value decomposition to extract 2D correlation functions from scattering patterns
Philipp Bender1, Dominika Zákutná2, Sabrina Disch3
1Physics and Materials Science Research Unit, University of Luxembourg, 162A Avenue de la Faïencerie, L-1511 Luxembourg, Grand Duchy of Luxembourg.
Abstract:
The truncated singular value decomposition (TSVD) is applied to extract the underlying 2D correlation functions from small-angle scattering patterns. The approach is tested by transforming the simulated data of ellipsoidal particles and it is shown that also in the case of anisotropic patterns (i.e. aligned ellipsoids) the derived correlation functions correspond to the theoretically predicted profiles. Furthermore, the TSVD is used to analyze the small-angle X-ray scattering patterns of colloidal dispersions of hematite spindles and magnetotactic bacteria in the 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.
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