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Difference between revisions of "Charge flipping"

From Online Dictionary of Crystallography

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# The density <math>\rho^{(n)}</math> is calculated by inverse Fourier transform of <math>F^{(n)}</math>.
 
# The density <math>\rho^{(n)}</math> is calculated by inverse Fourier transform of <math>F^{(n)}</math>.
 
# 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>
 
# 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>
#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>
+
#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>
 
#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:
 
#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:
  

Revision as of 14:20, 27 August 2013

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.