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> | + | #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 \rho sampled on a regular grid, and a set of measured structure-factor amplitudes F^{obs}(\mathbf{H}), the basic charge flipping algorithm follows this scheme:
First, the algorithm is initiated in the zeroth cycle by assigning random starting phases \varphi_{rand}(\mathbf{H}) to all experimental amplitudes and making all unobserved amplitudes equal to zero:
The iteration cycle then proceeds as follows:
- The density \rho^{(n)} is calculated by inverse Fourier transform of F^{(n)}.
- The modified density g^{(n)} is obtained by flipping the density of all pixels with density values below a certain positive threshold \delta and keeping the rest of the pixels unchanged:
- Temporary structure factors G^{(n)}(\mathbf{H})=|G^{(n)}(\mathbf{H})|\exp{(i\varphi_{G}(\mathbf{H}))} are calculated by Fourier transform of g^{(n)}
- New structure factors F^{(n+1)} are obtained by combining the experimental amplitudes with the phases \varphi_{G} and setting all non-measured structure factors to zero:
These modified structure factors then enter the next cycle of iteration.