Unlike conventional x-ray attenuation one of the advantages of phase contrast x-ray imaging is its capability of extracting useful physical properties of the sample. In particular the possibility to obtain information from small angle scattering about unresolvable structures with sub-pixel resolution sensitivity has drawn attention for both medical and material science applications. We report on a novel algorithm for the analyzer based x-ray phase contrast imaging modality, which allows the robust separation of absorption, refraction and scattering effects from three measured x-ray images. This analytical approach is based on a simple Gaussian description of the analyzer transmission function and this method is capable of retrieving refraction and small angle scattering angles in the full angular range typical of biological samples. After a validation of the algorithm with a simulation code, which demonstrated the potential of this highly sensitive method, we have applied this theoretical framework to experimental data on a phantom and biological tissues obtained with synchrotron radiation. Owing to its extended angular acceptance range the algorithm allows precise assessment of local scattering distributions at biocompatible radiation doses, which in turn might yield a quantitative characterization tool with sufficient structural sensitivity on a submicron length scale.
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