Describing small-angle scattering profiles by a limited set of intensities.
Describing small-angle scattering profiles by a limited set of intensities.
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DOI：
10.1107/s1600576722006598
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发表时间：
2022-10-01
影响因子：
6.1
通讯作者：
Grant, Thomas D.
中科院分区：
文献类型：
--
作者：
Grant, Thomas D.
提出了一种间接傅里叶变换方法，它描述了从一组约化的强度得到的解的散射分布。用最小二乘法导出方程来拟合实验轮廓，并直接从减少的强度集计算常用的尺寸和形状参数，以及相关的不确定度。导出了使实空间对分布函数正则化的解析方程。提供了方便的软件来执行所有描述的计算。小角散射(SAS)通过分析X射线或中子通过粒子溶液的散射，以低分辨率探测粒子的大小和形状。从SAS数据中提取结构信息的一种方法是间接傅立叶变换(IFT)。IFT方法使用一组基函数对粒子的实空间对分布函数[P(R)]进行参数化，该基函数组同时使用相应的倒数空间基函数来确定散射分布[I(Q)]。本文给出了Moore提出的IFT算法的一个扩展[J.J.Appl.克赖斯特。(1980)，13,168-175]，它使用三角级数来描述基函数，其中实空间基函数和倒数空间基函数是傅里叶配合。给出了摩尔系数与SAS分布在特定位置的强度之间的关系式，以及一系列新的方程，描述了由这组不同的强度值得到的粒子的尺寸和形状参数。推导了一种解析实空间正则化方法，以平滑P(R)曲线并改善串联终止引起的系统偏差。正则化是IFT方法中常用的方法，但在Moore的原始方法中没有描述，它特别容易受到这种影响。该算法以脚本denss.fit_data.py的形式提供，它是用于SAS的DENSS软件包的一部分，该软件包包括命令行和交互式图形界面。使用实验数据的程序结果表明，它与现有工具一样准确，而且往往比现有工具更准确。
An indirect Fourier transform method is presented which describes a solution scattering profile from a reduced set of intensities. Equations are derived to fit the experimental profile using least squares and to calculate commonly used size and shape parameters directly from the reduced set of intensities, along with associated uncertainties. An analytical equation is derived enabling regularization of the real-space pair distribution function. Convenient software is provided to perform all described calculations. Small-angle scattering (SAS) probes the size and shape of particles at low resolution through the analysis of the scattering of X-rays or neutrons passing through a solution of particles. One approach to extracting structural information from SAS data is the indirect Fourier transform (IFT). The IFT approach parameterizes the real-space pair distribution function [P(r)] of a particle using a set of basis functions, which simultaneously determines the scattering profile [I(q)] using corresponding reciprocal-space basis functions. This article presents an extension of an IFT algorithm proposed by Moore [ J. Appl. Cryst. (1980), 13, 168–175] which used a trigonometric series to describe the basis functions, where the real-space and reciprocal-space basis functions are Fourier mates. An equation is presented relating the Moore coefficients to the intensities of the SAS profile at specific positions, as well as a series of new equations that describe the size and shape parameters of a particle from this distinct set of intensity values. An analytical real-space regularizer is derived to smooth the P(r) curve and ameliorate systematic deviations caused by series termination. Regularization is commonly used in IFT methods though not described in Moore’s original approach, which is particularly susceptible to such effects. The algorithm is provided as a script, denss.f it_data.py, as part of the DENSS software package for SAS, which includes both command line and interactive graphical interfaces. Results of the program using experimental data show that it is as accurate as, and often more accurate than, existing tools.