Hybrid input-output algorithm - Revision history

BrianMcMahon: Style edits to align with printed edition

2017-05-15T14:00:29Z

Style edits to align with printed edition

MassimoNespolo: + cat

2014-12-04T05:58:50Z

+ cat

BrianMcMahon at 12:30, 19 May 2014

2014-05-19T12:30:14Z

GervaisChapuis at 14:16, 27 August 2013

2013-08-27T14:16:24Z

GervaisChapuis at 13:52, 27 August 2013

2013-08-27T13:52:43Z

GervaisChapuis at 11:57, 27 August 2013

2013-08-27T11:57:00Z

GervaisChapuis at 11:45, 27 August 2013

2013-08-27T11:45:24Z

GervaisChapuis: Created page with "An algorithm proposed by R. Fienup in 1982. The original application of the algorithm was the phase retrieval of diffraction patterns of non-periodic objects. However, the algori..."

2013-08-27T11:43:32Z

Created page with "An algorithm proposed by R. Fienup in 1982. The original application of the algorithm was the phase retrieval of diffraction patterns of non-periodic objects. However, the algori..."

New page

An algorithm proposed by R. Fienup in 1982. The original application of the algorithm was the phase retrieval of diffraction patterns of non-periodic objects. However, the algorithm or its components have been used several times also in crystallography.

Be <math>\rho^{(n)}</math> a trial scattering density in <math>n^{th}</math> iteration cycle. Be <math>\rho'^{(n)}</math> a density obtained from <math>\rho^{(n)}</math> by Fourier-transforming <math>\rho^{(n)}</math>, replacing all Fourier amplitudes by the experimentally observed amplitudes, and applying inverse Fourier transform. Then the density <math>\rho^{(n+1)}</math> is defined pixel-wise by the following scheme:

[[Image:CF_4.png]]

In crystallography, the support is usually not known <math>\textit{a~priori}</math>, and a dynamical support must be used, <math>\textit{i.e.}</math> the support is newly defined in each iteration cycle based on predefined criterion.

@@ Line 3: / Line 3: @@
 An algorithm proposed by R. Fienup in 1982. The original application of the algorithm was the phase retrieval of diffraction patterns of non-periodic objects. However, the algorithm or its components have been used several times also in crystallography.
-Let <math>\rho^{(n)}</math> be a trial scattering density in the <math>n^{th}</math> iteration cycle. Let <math>\rho'^{(n)}</math> be a density obtained from <math>\rho^{(n)}</math> by Fourier-transforming <math>\rho^{(n)}</math>, replacing all Fourier amplitudes by the experimentally observed amplitudes, and applying inverse Fourier transform. Then the density <math>\rho^{(n+1)}</math> is defined pixel-wise by the following scheme:
+Let <math>\rho^{(n)}</math> be a trial scattering density in the ''n''th iteration cycle. Let <math>\rho'^{(n)}</math> be a density obtained from <math>\rho^{(n)}</math> by Fourier-transforming <math>\rho^{(n)}</math>, replacing all Fourier amplitudes by the experimentally observed amplitudes, and applying inverse Fourier transform. Then the density <math>\rho^{(n+1)}</math> is defined pixel-wise by the following scheme:
 <br>[[Image:CF_4.png|500px|center]]<br>

← Older revision		Revision as of 05:58, 4 December 2014
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	In crystallography, the support is usually not known <math>\textit{a~priori}</math>, and a dynamical support must be used, <math>\textit{i.e.}</math> the support is newly defined in each iteration cycle based on a predefined criterion.		In crystallography, the support is usually not known <math>\textit{a~priori}</math>, and a dynamical support must be used, <math>\textit{i.e.}</math> the support is newly defined in each iteration cycle based on a predefined criterion.
		+
		+	[[Category: Structure determination]]

@@ Line 3: / Line 3: @@
 An algorithm proposed by R. Fienup in 1982. The original application of the algorithm was the phase retrieval of diffraction patterns of non-periodic objects. However, the algorithm or its components have been used several times also in crystallography.
-Be <math>\rho^{(n)}</math> a trial scattering density in <math>n^{th}</math> iteration cycle. Be <math>\rho'^{(n)}</math> a density obtained from <math>\rho^{(n)}</math> by Fourier-transforming <math>\rho^{(n)}</math>, replacing all Fourier amplitudes by the experimentally observed amplitudes, and applying inverse Fourier transform. Then the density <math>\rho^{(n+1)}</math> is defined pixel-wise by the following scheme:
+Let <math>\rho^{(n)}</math> be a trial scattering density in the <math>n^{th}</math> iteration cycle. Let <math>\rho'^{(n)}</math> be a density obtained from <math>\rho^{(n)}</math> by Fourier-transforming <math>\rho^{(n)}</math>, replacing all Fourier amplitudes by the experimentally observed amplitudes, and applying inverse Fourier transform. Then the density <math>\rho^{(n+1)}</math> is defined pixel-wise by the following scheme:
 <br>[[Image:CF_4.png|500px|center]]<br>
-In crystallography, the support is usually not known <math>\textit{a~priori}</math>, and a dynamical support must be used, <math>\textit{i.e.}</math> the support is newly defined in each iteration cycle based on predefined criterion.
+In crystallography, the support is usually not known <math>\textit{a~priori}</math>, and a dynamical support must be used, <math>\textit{i.e.}</math> the support is newly defined in each iteration cycle based on a predefined criterion.

@@ Line 5: / Line 5: @@
 Be <math>\rho^{(n)}</math> a trial scattering density in <math>n^{th}</math> iteration cycle. Be <math>\rho'^{(n)}</math> a density obtained from <math>\rho^{(n)}</math> by Fourier-transforming <math>\rho^{(n)}</math>, replacing all Fourier amplitudes by the experimentally observed amplitudes, and applying inverse Fourier transform. Then the density <math>\rho^{(n+1)}</math> is defined pixel-wise by the following scheme:
-[[Image:CF_4.png|500px|center]]
+<br>[[Image:CF_4.png|500px|center]]<br>
 In crystallography, the support is usually not known <math>\textit{a~priori}</math>, and a dynamical support must be used, <math>\textit{i.e.}</math> the support is newly defined in each iteration cycle based on predefined criterion.

← Older revision		Revision as of 13:52, 27 August 2013
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		+	== Definition ==
		+
	An algorithm proposed by R. Fienup in 1982. The original application of the algorithm was the phase retrieval of diffraction patterns of non-periodic objects. However, the algorithm or its components have been used several times also in crystallography.		An algorithm proposed by R. Fienup in 1982. The original application of the algorithm was the phase retrieval of diffraction patterns of non-periodic objects. However, the algorithm or its components have been used several times also in crystallography.