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Difference between revisions of "Charge flipping"

From Online Dictionary of Crystallography

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Charge flipping is a structure solution method from the class of [[dual-space phase retrieval algorithms|dual-space algorithms]]. The key component of the charge flipping algorithm is the charge flipping operation. In this operation, all scattering density pixels with density lower than a small positive threshold delta are multiplied by -1 (flipped). In the classical charge flipping algorithm, this direct-space modification is combined with simple resubstitution of structure-factor amplitudes by experimental values, but other modifications and iteration schemes have been proposed and successfully used.
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== Definition ==
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Charge flipping is a structure solution method from the class of [[dual-space phase retrieval algorithms|dual-space algorithms]]. The key component of the charge flipping algorithm is the charge flipping operation. In this operation, all scattering density pixels with density lower than a small positive threshold δ are multiplied by -1 (flipped). In the classical charge flipping algorithm, this direct-space modification is combined with simple resubstitution of structure-factor amplitudes by experimental values, but other modifications and iteration schemes have been proposed and successfully used.
  
 
Given a trial scattering density <math>\rho</math> sampled on a regular grid, and a set of measured structure-factor amplitudes <math>F^{obs}(\mathbf{H})</math>, the basic charge flipping algorithm follows this scheme:
 
Given a trial scattering density <math>\rho</math> sampled on a regular grid, and a set of measured structure-factor amplitudes <math>F^{obs}(\mathbf{H})</math>, the basic charge flipping algorithm follows this scheme:
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[[Image:CF_1.png|600px|center]]
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[[Image:CF_1.png|600px|center]]<br>
  
 
The iteration cycle then proceeds as follows:
 
The iteration cycle then proceeds as follows:
  
1. The density <math>\rho^{(n)}</math> is calculated by inverse Fourier transform of <math>F^{(n)}</math>.
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# The density <math>\rho^{(n)}</math> is calculated by inverse Fourier transform of <math>F^{(n)}</math>.
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# The modified density <math>g^{(n)}</math> is obtained by flipping the density of all pixels with density values below a certain positive threshold <math>\delta</math> and keeping the rest of the pixels unchanged:[[Image:CF_2.png|300px|center]]<br>
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#Temporary structure factors <math>G^{(n)}(\mathbf{H})=|G^{(n)}(\mathbf{H})|\exp{(i\varphi_{G}(\mathbf{H}))}</math> are calculated by Fourier transform of <math>g^{(n)}</math>.<br>
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#New structure factors <math>F^{(n+1)}</math> are obtained by combining the experimental amplitudes with the phases <math>\varphi_{G}</math> and setting all non-measured structure factors to zero:<br>[[Image:CF_3.png|600px|center]]<br>
  
2. The modified density <math>g^{(n)}</math> is obtained by flipping the density of all pixels with density values below a certain positive threshold <math>\delta</math> and keeping the rest of the pixels unchanged:
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These modified structure factors then enter the next cycle of iteration.
 
 
[[Image:CF_2.png|300px|center]]
 
 
 
3. Temporary structure factors <math>G^{(n)}(\mathbf{H})=|G^{(n)}(\mathbf{H})|\exp{(i\varphi_{G}(\mathbf{H}))}</math> are calculated by Fourier transform of <math>g^{(n)}</math>.
 
  
4. New structure factors <math>F^{(n+1)}</math> are obtained by combining the experimental amplitudes with the phases <math>\varphi_{G}</math> and setting all non-measured structure factors to zero:
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==See also==
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*[[Dual-space phase retrieval algorithms]]
  
[[Image:CF_3.png|600px|center]]
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[[Category: Structure determination]]
 
 
These modified structure factors then enter the next cycle of iteration.
 

Latest revision as of 10:35, 13 May 2017

Definition

Charge flipping is a structure solution method from the class of dual-space algorithms. The key component of the charge flipping algorithm is the charge flipping operation. In this operation, all scattering density pixels with density lower than a small positive threshold δ are multiplied by -1 (flipped). In the classical charge flipping algorithm, this direct-space modification is combined with simple resubstitution of structure-factor amplitudes by experimental values, but other modifications and iteration schemes have been proposed and successfully used.

Given a trial scattering density [math]\rho[/math] sampled on a regular grid, and a set of measured structure-factor amplitudes [math]F^{obs}(\mathbf{H})[/math], the basic charge flipping algorithm follows this scheme:

First, the algorithm is initiated in the zeroth cycle by assigning random starting phases [math]\varphi_{rand}(\mathbf{H})[/math] to all experimental amplitudes and making all unobserved amplitudes equal to zero:


CF 1.png

The iteration cycle then proceeds as follows:

  1. The density [math]\rho^{(n)}[/math] is calculated by inverse Fourier transform of [math]F^{(n)}[/math].
  2. The modified density [math]g^{(n)}[/math] is obtained by flipping the density of all pixels with density values below a certain positive threshold [math]\delta[/math] and keeping the rest of the pixels unchanged:
    CF 2.png

  3. Temporary structure factors [math]G^{(n)}(\mathbf{H})=|G^{(n)}(\mathbf{H})|\exp{(i\varphi_{G}(\mathbf{H}))}[/math] are calculated by Fourier transform of [math]g^{(n)}[/math].
  4. New structure factors [math]F^{(n+1)}[/math] are obtained by combining the experimental amplitudes with the phases [math]\varphi_{G}[/math] and setting all non-measured structure factors to zero:
    CF 3.png

These modified structure factors then enter the next cycle of iteration.

See also