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Difference between revisions of "Hybrid input-output algorithm"

From Online Dictionary of Crystallography

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== Definition ==
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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.
 
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.
  
Be <math>\rho^{(n)}</math> a trial scattering density in <math>n^{th}</math> iteration cycle. Be <math>\rho'^{(n)}</math> 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:
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Let <math>\rho^{(n)}</math> be a trial scattering density in the ''n''th 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:
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<br>[[Image:CF_4.png|500px|center]]<br>
  
[[Image:CF_4|600px|center]]
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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 predefined criterion.
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[[Category: Structure determination]]

Latest revision as of 14:00, 15 May 2017

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 nth 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:


CF 4.png

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.