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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Indirect Fourier transform ： ウィキペディア英語版 Indirect Fourier transform Indirect Fourier transform (IFT) is a solution of ill-posed given by Fourier transform of noisy data (as from biological small-angle scattering) proposed by Glatter. IFT is used instead of direct Fourier transform of noisy data, since a direct FT would give large systematic errors. Transform is computed by linear fit to a subfamily of functions corresponding to constraints on a reasonable solution. If a result of the transform is distance distribution function, it is common to assume that the function is non-negative, and is zero at ''P''(0) =  0  and ''P''(''D''max)≥;0, where Dmax is a maximum diameter of the particle. It is approximately true, although it disregards inter-particle effects. IFT is also performed in order to regularize noisy data. == Fourier transformation in small angle scattering == see Lindner et al. for a thorough introduction 〔Neutrons, X-rays and Light: Scattering Methds Applied to Soft Condensed Matter by P. Lindner and Th.Zemb (chapter 3 by Olivier Spalla)〕 The intensity ''I'' per unit volume ''V'' is expressed as: : $I(\backslash mathbf)\; =\; \backslash frac\backslash int\_V\backslash int\_V\backslash rho(\backslash mathbf)\backslash rho(\backslash mathbf\text{'})e^-\backslash mathbf\text{'})\}\backslash text\backslash mathbf\backslash text\backslash mathbf\text{'},$ where $\backslash rho(\backslash mathbf)$ is the scattering length density. We introduce the correlation function $\backslash gamma(\backslash mathbf)$ by: :$I(\backslash mathbf)\; =\; \backslash int\_V\backslash gamma(\backslash mathbf)e^\}\backslash text\backslash mathbf$ That is, taking the fourier transformation of the correlation function gives the intensity. The probability of finding, within a particle, a point $i$ at a distance $r$ from a given point $j$ is given by the distance probability function $\backslash gamma\_0(r)$. And the connection between the correlation function $\backslash gamma(r)$ and the distance probability function $\backslash gamma\_0(r)$ is given by: :$\backslash gamma(r)\; =\; b\_i\backslash cdot\; bj\backslash gamma\_0(r)V$, where $b\_k$ is the scattering length of the point $k$. That is, the correlation function is weighted by the scattering length. For X-ray scattering, the scattering length $b$ is directly proportional to the electron density $\backslash rho\_e$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Indirect Fourier transform」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.