Indirect Fourier transform

Characterization of controlled pore glasses by small angle x-ray scattering and evaluation of the scattering data by he indirect Fourier transformation... 

Fitting parameters for the indirect Fourier transformation method. 

An alternative method of analysis is that of indirect Fourier transform This model-independent... 

All measured SAXS data were analyzed by the generalized indirect Fourier transformation (GIFT) technique with the Boltzmann simplex simulated annealing (BSSA) algorithm [34, 35]. The GIFT calculation is based on the analytical or numerical solution of the Ornstein-Zernike (OZ) equation that describes the interplay between the total (h(r)) and direct (c(r)) correlation functions ... 

Use an indirect Fourier transform technique which involves a series of Fourier transforms between the real and the reciprocal space to fit the scattering data. ° It is quite possible, from a mathematical perspective, to get negative size distributions which are difficult to interpret. 

Svergun and coworkers have developed the software GNOM to obtain p r) from an indirect Fourier transform of the scattering profile. Nevertheless, in recent times, the use of p r) displaced by algorithms provide a low-resolution 3D electron density map of the molecule from the ID SAXS profile. 

A typical system composed of EAN/l-hexadecyl-3-methyllmidazolium chloride [Cj mim][Cl]/dodecane at ambient temperature with high thermal stability (stable between 30 and 150°C) was reported by Zech et al. [100]. Inherent properties were characterized by SANS, DLS, generalized indirect Fourier transformation, and Teubner and Strey model. A phase behavioral study with respect to temperature and IL mass fraction of a system comprising water/TX-100/[bmim][PFJ was reported by Anjum et al. [101]. SANS and polarized microscopic techniques revealed the existence of discontinnons-type microemulsion droplets in the system. 

Fritz, G. and Glatter, O. (2006). Structure and interaction in dense coUoidal systems Evaluation of scattering data by the generalized indirect Fourier transformation method. J. Phys-Condens. Mat., 18, S2403-S2419. 

Glatter, O. (1977). Data evaluation in small angle scattering Calculation of the radial electron density distribution by means of indirect Fourier transformation. Acta Phys. Austriaca, 47, 83-102. 

Figure 15.12. The obtained cross-section pair distribution function p R) as obtained by the indirect Fourier transformation method, where the composition of SDS/DTAB was 80 20. The results almost perfectly correlate with the results obtained by the model-dependent method illustrated in Figure 15.11. (see ref. (32) for further details)...

Here, p(r), as obtained by an indirect Fourier transform of the scattering curve, is... 

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