Using the singular value decomposition to extract 2D correlation functions from scattering patterns,Acta Crystallographica Section A: Foundations and Advances

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Using the singular value decomposition to extract 2D correlation functions from scattering patterns
Acta Crystallographica Section A: Foundations and Advances ( IF 1.9 ) Pub Date : 2019-08-23 , DOI: 10.1107/s205327331900891x
Philipp Bender ₁ , Dominika Zákutná ₂ , Sabrina Disch ₃ , Lourdes Marcano ₄ , Diego Alba Venero ₅ , Dirk Honecker ₂

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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.

中文翻译：

使用奇异值分解从散射图案中提取二维相关函数

应用截断奇异值分解 (TSVD) 从小角度散射模式中提取底层的 2D 相关函数。该方法通过转换椭球粒子的模拟数据进行了测试，结果表明，在各向异性模式的情况下（IE对齐的椭球体）导出的相关函数对应于理论预测的轮廓。此外，TSVD还用于分析磁场存在下赤铁矿纺锤体和趋磁细菌胶体分散体的小角X射线散射图，以验证该方法可以应用于无模型提取的散射剖面。来自噪声数据的各向异性散射体。

更新日期：2019-08-23

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