Difference between revisions of "Hybrid input-output algorithm"
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In crystallography, the support is usually not known <math>\textit{a~priori}</math>, and a dynamical support must be used, <math>\textit{i.e.}</math> the support is newly defined in each iteration cycle based on a predefined criterion. | In crystallography, the support is usually not known <math>\textit{a~priori}</math>, and a dynamical support must be used, <math>\textit{i.e.}</math> the support is newly defined in each iteration cycle based on a predefined criterion. | ||
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Revision as of 05:58, 4 December 2014
Definition
An algorithm proposed by R. Fienup in 1982. The original application of the algorithm was the phase retrieval of diffraction patterns of non-periodic objects. However, the algorithm or its components have been used several times also in crystallography.
Let [math]\rho^{(n)}[/math] be a trial scattering density in the [math]n^{th}[/math] iteration cycle. Let [math]\rho'^{(n)}[/math] be a density obtained from [math]\rho^{(n)}[/math] by Fourier-transforming [math]\rho^{(n)}[/math], replacing all Fourier amplitudes by the experimentally observed amplitudes, and applying inverse Fourier transform. Then the density [math]\rho^{(n+1)}[/math] is defined pixel-wise by the following scheme:
In crystallography, the support is usually not known [math]\textit{a~priori}[/math], and a dynamical support must be used, [math]\textit{i.e.}[/math] the support is newly defined in each iteration cycle based on a predefined criterion.