Difference between revisions of "Correlation methods"

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Conventional [[x-ray]] [[scattering]] relies on ensemble averaging to yield a robust, high [[signal-to-noise]] image. For instance, scattering data is normally averaged over a certain time duration, to accumulate sufficient statistics. For nominally isotropic samples, the two-dimensional [[detector]] image is collapsed ([[circular average]]) into a one-dimensional curve. This averaging, however, throws away potentially useful information contained within the ''variance'' of the x-ray signal.
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A variety of emerging techniques focus instead on emphasizing and measuring the variations or fluctuations of an x-ray scattering signal (over time, space, angle, etc.). Such an analysis can, most obviously, return information about heterogeneity. However, careful correlation analysis can also extract subtle information about structure (e.g. local packing motifs) that is normally erased in ensemble averaging.
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[[Image:Variance scattering concept01.png|700px]]
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=XCCA=
 
'''X-ray cross-correlation analysis''' ('''XCCA''') is a suite of techniques for analyzing correlations within [[x-ray]] [[scattering]] datasets. In particular, analysis of angular correlations within the 2D detector image can be used to isolate structural information that would be lost in a conventional circular-averaged 1D curve. Thus, even for nominally isotropic materials (powder-like sample), information about local symmetry (and thus packing motifs or [[unit cell]]) can be extracted from the data.
 
'''X-ray cross-correlation analysis''' ('''XCCA''') is a suite of techniques for analyzing correlations within [[x-ray]] [[scattering]] datasets. In particular, analysis of angular correlations within the 2D detector image can be used to isolate structural information that would be lost in a conventional circular-averaged 1D curve. Thus, even for nominally isotropic materials (powder-like sample), information about local symmetry (and thus packing motifs or [[unit cell]]) can be extracted from the data.
  
 
Angular correlation information can also be mined to reconstruct the three-dimensional [[reciprocal-space]] from individual 2D detector snapshots. That is, XCCA methods can be exploited to co-align scattering frames, registering them into the 3D [[scattering]] volume. This is conceptually similar to [[reciprocal-space mapping]], but instead of directly reconstructing reciprocal-space by merging images, this is done in a statistical sense (because the relative alignment of frames is not known).
 
Angular correlation information can also be mined to reconstruct the three-dimensional [[reciprocal-space]] from individual 2D detector snapshots. That is, XCCA methods can be exploited to co-align scattering frames, registering them into the 3D [[scattering]] volume. This is conceptually similar to [[reciprocal-space mapping]], but instead of directly reconstructing reciprocal-space by merging images, this is done in a statistical sense (because the relative alignment of frames is not known).
  
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==References==
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Correlation methods can be combined with coherent scattering effects to amplify the x-ray scattering signal from a weak sample (refer to [[XAmp]]).
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=Fluctuation Scattering=
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'''Fluctuation Scattering''': TBD
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=Variance Scattering=
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The term '''Variance Scattering''' has been used to describe methods that intentionally emphasize, and analyze, variations in x-ray scattering signals.
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* [[Ring graininess]] analysis (to determine grain count, grain size and size-distribution, crystallinity, etc.)
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** [[Yager, K.G.]]; Majewski, P.W. [http://scripts.iucr.org/cgi-bin/paper?S1600576714020822 Metrics of graininess: robust quantification of grain count from the non-uniformity of scattering rings] ''Journal of Applied Crystallography'' '''2014''', 47, 1855–1865. [http://dx.doi.org/10.1107/S1600576714020822 doi: 10.1107/S1600576714020822]
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* Heterogeneity
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** C. J. Gommes [http://scripts.iucr.org/cgi-bin/paper?ge5024 Small-angle scattering and scale-dependent heterogeneity] ''J. Appl. Cryst.'' '''2016''', 49, 1162-1176. [https://doi.org/10.1107/S1600576716007810 doi: 10.1107/S1600576716007810]
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=XPCS=
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'''[[XPCS|X-ray Photon Correlation Spectroscopy (XPCS)]]''' measures the temporal fluctuation of coherent speckle. From the reconstructed time correlation function, one can infer system dynamics.
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=References=
  
 
===XCCA===
 
===XCCA===
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* F. Lehmkühler, G. Grübel and C. Gutt [http://scripts.iucr.org/cgi-bin/paper?S1600576714012424 Detecting orientational order in model systems by X-ray cross-correlation methods] ''J. Appl. Cryst.'' '''2014''', 47, 1315-1323. [https://doi.org/10.1107/S1600576714012424 doi: 10.1107/S1600576714012424]
 
* F. Lehmkühler, G. Grübel and C. Gutt [http://scripts.iucr.org/cgi-bin/paper?S1600576714012424 Detecting orientational order in model systems by X-ray cross-correlation methods] ''J. Appl. Cryst.'' '''2014''', 47, 1315-1323. [https://doi.org/10.1107/S1600576714012424 doi: 10.1107/S1600576714012424]
 
* Lehmkühler, F.; Fischer, B.; Müller, L.; Ruta B.; Grübel, G. [http://scripts.iucr.org/cgi-bin/paper?zg5001 Structure beyond pair correlations: X-ray cross-correlation from colloidal crystals] ''Journal of Applied Crystallography'' '''2016''', 49, [https://doi.org/10.1107/S1600576716017313 doi: 10.1107/S1600576716017313]
 
* Lehmkühler, F.; Fischer, B.; Müller, L.; Ruta B.; Grübel, G. [http://scripts.iucr.org/cgi-bin/paper?zg5001 Structure beyond pair correlations: X-ray cross-correlation from colloidal crystals] ''Journal of Applied Crystallography'' '''2016''', 49, [https://doi.org/10.1107/S1600576716017313 doi: 10.1107/S1600576716017313]
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*  Julien R. Lhermitte, Cheng Tian, Aaron Stein, Atikur Rahman, Yugang Zhang, Lutz Wiegart, Andrei Fluerasu, Oleg Gang, and [[Kevin G. Yager]] [http://journals.iucr.org/j/issues/2017/03/00/aj5285/index.html Robust X-ray angular correlations for the study of meso-structures] ''J. Appl. Cryst.'' '''2017''', 50(3). [https://doi.org/10.1107/S1600576717003946 doi: 10.1107/S1600576717003946]
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**  Julien R. Lhermitte, Aaron Stein, Cheng Tian,  Yugang Zhang, Lutz Wiegart, Andrei Fluerasu, Oleg Gang, and [[Kevin G. Yager]] [http://journals.iucr.org/m/issues/2017/05/00/it5012/index.html Coherent Amplification of X-ray Scattering from Meso-structures] ''IUCrJ'' '''2017''' 4(5) [https://doi.org/10.1107/S2052252517008107 doi: 10.1107/S2052252517008107]
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*  Felix Lehmkühler, Florian Schulz, Martin A. Schroer, Lara Frenzel, Holger Langeb, and Gerhard Grübel [http://journals.iucr.org/m/issues/2018/03/00/ro5011/index.html Heterogeneous local order in self-assembled nanoparticle films revealed by X-ray cross-correlations] ''IUCrJ'' '''2018''', 5 (3), 354-360. [https://doi.org/10.1107/S2052252518005407 doi: 10.1107/S2052252518005407]
  
 
===Reconstruction===
 
===Reconstruction===
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* Derek Mendez, Herschel Watkins, Shenglan Qiao, Kevin S. Raines, Thomas J. Lane, Gundolf Schenk, Garrett Nelson, Ganesh Subramanian, Kensuke Tono, Yasumasa Joti, Makina Yabashi, Daniel Ratner and Sebastian Doniach [http://journals.iucr.org/m/issues/2016/06/00/cw5011/index.html Angular correlations of photons from solution diffraction at a free-electron laser encode molecular structure] ''IUCrJ'' '''2016''', 3(6), 420-429. [http://dx.doi.org/10.1107/S2052252516013956 doi: 10.1107/S2052252516013956]
 
* Derek Mendez, Herschel Watkins, Shenglan Qiao, Kevin S. Raines, Thomas J. Lane, Gundolf Schenk, Garrett Nelson, Ganesh Subramanian, Kensuke Tono, Yasumasa Joti, Makina Yabashi, Daniel Ratner and Sebastian Doniach [http://journals.iucr.org/m/issues/2016/06/00/cw5011/index.html Angular correlations of photons from solution diffraction at a free-electron laser encode molecular structure] ''IUCrJ'' '''2016''', 3(6), 420-429. [http://dx.doi.org/10.1107/S2052252516013956 doi: 10.1107/S2052252516013956]
  
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==See Also==
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===Fluctuation Scattering===
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* [[X-ray Photon Correlation Spectroscopy]] ([[XPCS]])
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* G. Chen, M. A. Modestino, B. K. Poon, A. Schirotzek, S. Marchesini, R. A. Segalman, A. Hexemer and P. H. Zwart [http://scripts.iucr.org/cgi-bin/paper?S0909049512023801 Structure determination of Pt-coated Au dumbbells via fluctuation X-ray scattering] ''J. Synchrotron Rad.'' '''2012''', 19, 695-700. [https://doi.org/10.1107/S0909049512023801 doi: 10.1107/S0909049512023801]
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* [[Fluctuation X-ray Scattering]] (FXS)
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* Erik Malmerberg, Cheryl A. Kerfeld and Petrus H. Zwart  [https://journals.iucr.org/m/issues/2015/03/00/dc5005/index.html Operational properties of fluctuation X-ray scattering data] ''IUCrJ'' '''2015''', 2(3), 309-316. [http://dx.doi.org/10.1107/S2052252515002535 doi: 10.1107/S2052252515002535]
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* [[Variance Scattering]] (VS)
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* Andrew V. Martin [http://journals.iucr.org/m/issues/2017/01/00/it5008/index.html Orientational order of liquids and glasses via fluctuation diffraction] ''IUCrJ'' '''2016''', 4 (1). [https://doi.org/10.1107/S2052252516016730 doi: 10.1107/S2052252516016730]
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** [[Ring graininess]] analysis (to determine grain count, grain size and size-distribution, crystallinity, etc.)
+
 
−
*** [[Yager, K.G.]]; Majewski, P.W. [http://scripts.iucr.org/cgi-bin/paper?S1600576714020822 Metrics of graininess: robust quantification of grain count from the non-uniformity of scattering rings] ''Journal of Applied Crystallography'' '''2014''', 47, 1855–1865. [http://dx.doi.org/10.1107/S1600576714020822 doi: 10.1107/S1600576714020822]
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===Correlated X-ray Scattering (CXS)===
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** Heterogeneity
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* Derek Mendez, Thomas J. Lane, Jongmin Sung, Jonas Sellberg, Clément Levard, Herschel Watkins, Aina E. Cohen, Michael Soltis, Shirley Sutton, James Spudich, Vijay Pande, Daniel Ratner, Sebastian Doniach [http://rstb.royalsocietypublishing.org/content/369/1647/20130315.short Observation of correlated X-ray scattering at atomic resolution] [http://dx.doi.org/10.1098/rstb.2013.0315 doi: 10.1098/rstb.2013.0315]
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*** C. J. Gommes [http://scripts.iucr.org/cgi-bin/paper?ge5024 Small-angle scattering and scale-dependent heterogeneity] ''J. Appl. Cryst.'' '''2016''', 49, 1162-1176. [https://doi.org/10.1107/S1600576716007810 doi: 10.1107/S1600576716007810]
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** Dataset: Mendez, Derek; Thomas J. Lane; Daniel Ratner; Sebastian Doniach [https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/23244 Correlated x-ray scattering dataset, silver nanoparticles] ''Harvard Dataverse'' '''2013''', V2. [http://dx.doi.org/10.7910/DVN/23244 doi: 10.7910/DVN/23244]

Latest revision as of 13:15, 7 May 2018

Conventional x-ray scattering relies on ensemble averaging to yield a robust, high signal-to-noise image. For instance, scattering data is normally averaged over a certain time duration, to accumulate sufficient statistics. For nominally isotropic samples, the two-dimensional detector image is collapsed (circular average) into a one-dimensional curve. This averaging, however, throws away potentially useful information contained within the variance of the x-ray signal.

A variety of emerging techniques focus instead on emphasizing and measuring the variations or fluctuations of an x-ray scattering signal (over time, space, angle, etc.). Such an analysis can, most obviously, return information about heterogeneity. However, careful correlation analysis can also extract subtle information about structure (e.g. local packing motifs) that is normally erased in ensemble averaging.

Variance scattering concept01.png

XCCA

X-ray cross-correlation analysis (XCCA) is a suite of techniques for analyzing correlations within x-ray scattering datasets. In particular, analysis of angular correlations within the 2D detector image can be used to isolate structural information that would be lost in a conventional circular-averaged 1D curve. Thus, even for nominally isotropic materials (powder-like sample), information about local symmetry (and thus packing motifs or unit cell) can be extracted from the data.

Angular correlation information can also be mined to reconstruct the three-dimensional reciprocal-space from individual 2D detector snapshots. That is, XCCA methods can be exploited to co-align scattering frames, registering them into the 3D scattering volume. This is conceptually similar to reciprocal-space mapping, but instead of directly reconstructing reciprocal-space by merging images, this is done in a statistical sense (because the relative alignment of frames is not known).

Correlation methods can be combined with coherent scattering effects to amplify the x-ray scattering signal from a weak sample (refer to XAmp).

Fluctuation Scattering

Fluctuation Scattering: TBD

Variance Scattering

The term Variance Scattering has been used to describe methods that intentionally emphasize, and analyze, variations in x-ray scattering signals.

XPCS

X-ray Photon Correlation Spectroscopy (XPCS) measures the temporal fluctuation of coherent speckle. From the reconstructed time correlation function, one can infer system dynamics.

References

XCCA

Reconstruction

Sparse Data

XFEL

Fluctuation Scattering

Correlated X-ray Scattering (CXS)

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