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In a recent article (P.Wochner et al., PNAS (2009)) x-ray scatteringintensity correlations around a ring, in the speckle diffraction pattern of acolloidal glass, were shown to display a remarkable ~ cos(n $\phi$) dependenceon the angular coordinate $\phi$ around the ring, with integer index ndepending on the magnitude of the scattering wavevector. With an analyticalderivation that preserves full generality in the Fraunhofer diffraction limit,we clarify the relationship of this result to previous x-ray studies ofbond-orientation order, and provide a sound basis to the statement that theangular intensity correlations deliver information on local bond arrangementsin a disordered (or partially ordered) system. We present a detailed analysisof the angular cross-correlation function and show its applicability forstudies of wide range of structural properties of disordered systems, fromlocal structure to spatial correlations between distant structural elements.

X-ray cross-correlation analysis and local symmetries of disordered systems. I. General theory