Charge flipping - Revision history

BrianMcMahon: Style edits to align with printed edition

2017-05-13T10:35:55Z

Style edits to align with printed edition

MassimoNespolo: + cat

2014-12-04T05:57:44Z

+ cat

GervaisChapuis at 14:22, 27 August 2013

2013-08-27T14:22:49Z

GervaisChapuis at 14:21, 27 August 2013

2013-08-27T14:21:49Z

GervaisChapuis at 14:20, 27 August 2013

2013-08-27T14:20:10Z

GervaisChapuis at 14:19, 27 August 2013

2013-08-27T14:19:26Z

GervaisChapuis at 14:13, 27 August 2013

2013-08-27T14:13:08Z

GervaisChapuis at 14:11, 27 August 2013

2013-08-27T14:11:12Z

GervaisChapuis at 13:49, 27 August 2013

2013-08-27T13:49:54Z

GervaisChapuis at 12:04, 27 August 2013

2013-08-27T12:04:29Z

@@ Line 14: / Line 14: @@
 # 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>
+#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.
 [[Category: Structure determination]]

← Older revision		Revision as of 05:57, 4 December 2014
Line 18:		Line 18:

	These modified structure factors then enter the next cycle of iteration.		These modified structure factors then enter the next cycle of iteration.
		+
		+	[[Category: Structure determination]]

@@ Line 15: / Line 15: @@
 # 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:[[Image:CF_3.png|600px|center]]<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.

@@ Line 15: / Line 15: @@
 # 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:
+#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:[[Image:CF_3.png|600px|center]]<br>
-[[Image:CF_3.png|600px|center]]
+These modified structure factors then enter the next cycle of iteration.

@@ Line 14: / Line 14: @@
 # 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>
+#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:

@@ Line 1: / Line 1: @@
 == 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.
+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:

← Older revision		Revision as of 12:04, 27 August 2013
Line 1:		Line 1:
−	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 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.	+	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:		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: