Realspace - Revision history

KevinYager: /* Other */

2020-01-08T15:38:20Z

‎Other

KevinYager: /* Pair Distribution Function (PDF) */

2015-07-06T13:37:20Z

‎Pair Distribution Function (PDF)

KevinYager at 15:47, 20 January 2015

2015-01-20T15:47:05Z

KevinYager at 15:45, 20 January 2015

2015-01-20T15:45:02Z

KevinYager at 14:35, 22 December 2014

2014-12-22T14:35:32Z

KevinYager: /* Indirect Fourier Transform (IFT) */

2014-12-19T20:34:29Z

‎Indirect Fourier Transform (IFT)

KevinYager: /* Realspace functions */

2014-12-19T20:31:33Z

‎Realspace functions

KevinYager: /* Pair Distribution Function, or PDF */

2014-12-19T20:23:27Z

‎Pair Distribution Function, or PDF

KevinYager: /* Realspace functions */

2014-12-19T20:22:10Z

‎Realspace functions

KevinYager at 20:16, 19 December 2014

2014-12-19T20:16:49Z

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 ===Other===
 * Hansen, S. [http://journals.iucr.org/j/issues/2003/05/00/issconts.html Estimation of chord length distributions from small-angle scattering using indirect Fourier transformation] ''J. Appl. Cryst.'' '''2003''', 36, 1190–1196 [http://dx.doi.org/10.1107/S0021889803014262 doi: 10.1107/S0021889803014262]
 * Fritz, G. [http://scitation.aip.org/content/aip/journal/jcp/124/21/10.1063/1.2202325 Determination of pair correlation functions of dense colloidal systems by means of indirect Fourier transformation] ''J. Chem. Phys.'' '''2006''' 124, 214707 [http://dx.doi.org/10.1063/1.2202325 doi: 10.1063/1.2202325]

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 * Billinge, S. J. L. & Thorpe, M. F. [http://link.springer.com/book/10.1007%2Fb119172 Local Structure from Diffraction], edited by S. J. L. Billinge. '''1998''' New York: Plenum Press.
 * P. F. Peterson, M. Gutmann, Th. Proffen and S. J. L. Billinge [http://scripts.iucr.org/cgi-bin/paper?ks0034 PDFgetN: a user-friendly program to extract the total scattering structure factor and the pair distribution function from neutron powder diffraction data] ''J. Appl. Cryst.'' '''2000''', 33, 1192 [http://dx.doi.org/10.1107/S0021889800007123 doi: 10.1107/S0021889800007123]
 ===Autocorrelation Function===

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 [[Image:BCP etch.jpg|thumb|300px|Example realspace image (SEM) of a [[block-copolymer]] pattern etched into [[silicon]].]]
 '''Realspace''' or '''direct-space''' is simply the regular 3D space that we inhabit. In [[scattering]], it is introduced as a term to differentiate from [[reciprocal-space]] (a.k.a. inverse-space). Whereas reciprocal-space refers to the [[Fourier transform]] of the sample's structure, realspace refers to the actual structure: the [[electron-density distribution|electron-density spatial distribution]] (as imaged in SEM, TEM, AFM, STM, etc.).
 ==Realspace functions==

← Older revision		Revision as of 15:45, 20 January 2015
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−	[[Image:BCP etch.jpg\|thumb\|300px\|Example realspace image (SEM) of a [[block-copolymer]] pattern etched into silicon.]]	+	[[Image:BCP etch.jpg\|thumb\|300px\|Example realspace image (SEM) of a [[block-copolymer]] pattern etched into [[silicon]].]]
	'''Realspace''' or '''direct-space''' is simply the regular 3D space that we inhabit. In [[scattering]], it is introduced as a term to differentiate from [[reciprocal-space]] (a.k.a. inverse-space). Whereas reciprocal-space refers to the [[Fourier transform]] of the sample's structure, realspace refers to the actual structure: the [[electron-density distribution\|electron-density spatial distribution]] (as imaged in SEM, TEM, AFM, STM, etc.).		'''Realspace''' or '''direct-space''' is simply the regular 3D space that we inhabit. In [[scattering]], it is introduced as a term to differentiate from [[reciprocal-space]] (a.k.a. inverse-space). Whereas reciprocal-space refers to the [[Fourier transform]] of the sample's structure, realspace refers to the actual structure: the [[electron-density distribution\|electron-density spatial distribution]] (as imaged in SEM, TEM, AFM, STM, etc.).

← Older revision		Revision as of 14:35, 22 December 2014
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	Two-dimensional scattering data can in principle also be converted into a two-dimensional realspace function. This realspace representation contains the same information, but emphasizes spatial distance correlations.		Two-dimensional scattering data can in principle also be converted into a two-dimensional realspace function. This realspace representation contains the same information, but emphasizes spatial distance correlations.
	* G. Fritz-Popovski [http://scripts.iucr.org/cgi-bin/paper?ks5437 Interpretation of two-dimensional real-space functions obtained from small-angle scattering data of oriented microstructures] ''J. Appl. Cryst.'' '''2015''', 48 [http://dx.doi.org/10.1107/S1600576714024972 doi: 10.1107/S1600576714024972]		* G. Fritz-Popovski [http://scripts.iucr.org/cgi-bin/paper?ks5437 Interpretation of two-dimensional real-space functions obtained from small-angle scattering data of oriented microstructures] ''J. Appl. Cryst.'' '''2015''', 48 [http://dx.doi.org/10.1107/S1600576714024972 doi: 10.1107/S1600576714024972]
		+
		+	==See Also==
		+	* [[Q value]]: Conversion from [[reciprocal-space]] values to realspace distances can be accomplished using <math>\scriptstyle d = 2 \pi / q</math>

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 ===Indirect Fourier Transform (IFT)===
 * Glatter, O. ''Acta Phys. Austriaca,'' '''1977''' 47, 83–102
-* Glatter, O. ''J. Appl. Cryst.'' '''1977''', 10, 415–421
+* Glatter, O. [http://scripts.iucr.org/cgi-bin/paper?S0021889877013879 A new method for the evaluation of small-angle scattering data] ''J. Appl. Cryst.'' '''1977''', 10, 415–421 [http://dx.doi.org/10.1107/S0021889877013879 doi: 10.1107/S0021889877013879]
-* Moore, P. B. ''J. Appl. Cryst.'' '''1980''', 13, 168–175
+* Moore, P. B. [http://scripts.iucr.org/cgi-bin/paper?S002188988001179X Small-angle scattering. Information content and error analysis] ''J. Appl. Cryst.'' '''1980''', 13, 168–175 [http://dx.doi.org/10.1107/S002188988001179X doi: 10.1107/S002188988001179X]
-* Svergun, D. I., Semenyuk, A. V. & Feigin, L. A.  ''Acta Cryst. A'' '''1988''' A44, 244–250
+* Svergun, D. I., Semenyuk, A. V. & Feigin, L. A.  [http://scripts.iucr.org/cgi-bin/paper?S0108767387011255 Small-angle-scattering-data treatment by the regularization method] ''Acta Cryst. A'' '''1988''' A44, 244–250 [http://dx.doi.org/10.1107/S0108767387011255 doi: 10.1107/S0108767387011255]
 ===Pair Distribution Function ([[PDF]])===

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 Scattering data can be converted into a corresponding realspace representation. Normally, scattering data cannot be simply inverted (via [[Fourier transform]]) to recover the exact realspace structure. This is known as the [[Fourier_transform#Phase_problem|phase problem]]: experiments typically record the intensity (but not phase) of scattered radiation, making unambiguous inversion impossible (note that coherent techniques, such as [[CDI]] or [[ptychography]] attempt to work around this). However, the inverse-space data of a scattering experiment can at least be converted into a statistical (or average) realspace representation. Total one-dimensional scattering can be converted into a realspace function that describes the amount of correlation across various distances
-===Pair Distribution Function, or [[PDF]]===
+===Indirect Fourier Transform (IFT)===
 * Porod, G. ''Acta Phys. Austriaca'' '''1948''', 2, 255–292.
 * Billinge, S. J. L. & Thorpe, M. F. [http://link.springer.com/book/10.1007%2Fb119172 Local Structure from Diffraction], edited by S. J. L. Billinge. '''1998''' New York: Plenum Press.
 * P. F. Peterson, M. Gutmann, Th. Proffen and S. J. L. Billinge [http://scripts.iucr.org/cgi-bin/paper?ks0034 PDFgetN: a user-friendly program to extract the total scattering structure factor and the pair distribution function from neutron powder diffraction data] ''J. Appl. Cryst.'' '''2000''', 33, 1192 [http://dx.doi.org/10.1107/S0021889800007123 doi: 10.1107/S0021889800007123]
 ===Two-dimensional===
 Two-dimensional scattering data can in principle also be converted into a two-dimensional realspace function. This realspace representation contains the same information, but emphasizes spatial distance correlations.
 * G. Fritz-Popovski [http://scripts.iucr.org/cgi-bin/paper?ks5437 Interpretation of two-dimensional real-space functions obtained from small-angle scattering data of oriented microstructures] ''J. Appl. Cryst.'' '''2015''', 48 [http://dx.doi.org/10.1107/S1600576714024972 doi: 10.1107/S1600576714024972]