Using the singular value decomposition to extract 2D correlation functions from scattering patterns. Issue 5 (23rd August 2019)

• Record Type: Journal Article
• Authors: Bender, Philipp; Zákutná, Dominika; Disch, Sabrina; Marcano, Lourdes; Alba Venero, Diego; Honecker, Dirk
• Is Part Of: Acta crystallographica. Volume 75:Issue 5(2019:Sep.)
• Page Start: 766
• Page End: 771
• Publication Date: 2019-08-23
• Subjects: small‐angle scattering -- correlation function -- 2D Fourier transform -- anisotropic nanoparticles -- singular value decomposition -- anisotropic structures -- nanoparticles -- noise filtering; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S205327331900891X
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : The truncated singular value decomposition is applied to extract the underlying 2D correlation functions from small‐angle scattering patterns. 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.