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.

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


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.


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




Sparse Data


Fluctuation Scattering

Correlated X-ray Scattering (CXS)