View source for Charge flipping

== Definition ==

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.

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:


[[Image:CF_1.png|600px|center]]<br>

The iteration cycle then proceeds as follows:

# 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>
#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:<br>[[Image:CF_3.png|600px|center]]<br>

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

==See also==
*[[Dual-space phase retrieval algorithms]]

[[Category: Structure determination]]