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X-ray dark-field or ultra-small angle scatter imaging has become increasinglyimportant since the introduction of phase-based x-ray imaging and is havingtransformative impact in fields such as in vivo lung imaging and explosivesdetection. Here we show that dark-field images acquired with theedge-illumination method (either in its traditional double mask or simplifiedsingle mask implementation) provide a direct measurement of the scatteringfunction, which is unaffected by system-specific parameters such as theautocorrelation length. We show that this is a consequence both of the specificmeasurement setup and of the mathematical approach followed to retrieve thedark-field images. We show agreement with theoretical models for datasetsacquired both with synchrotron and laboratory x-ray sources. We also introducea new contrast mechanism, the variance of refraction, which is extracted fromthe same dataset and provides a direct link with the size of the scatteringcentres. We show that this can also be described by the same theoreticalmodels. We study the behaviour of both signals vs. key parameters such as x-rayenergy and scatterer radius. We find this allows quantitative, direct,multi-scale scattering measurements during imaging, with implications in allfields where dark-field imaging is used.

Direct x-ray scattering signal measurements in  edge-illumination/beam-tracking imaging and their interplay with the variance  of the refraction signals