On the origin of visibility contrast in x-ray Talbot interferometry

The reduction in visibility in x-ray grating interferometry based on the Talbot effect is formulated by the autocorrelation function of spatial fluctuations of a wavefront due to unresolved micron-size structures in samples. The experimental results for microspheres and melamine sponge were successfully explained by this formula with three parameters characterizing the wavefront fluctuations: variance, correlation length, and the Hurst exponent. The ultra-small-angle x-ray scattering of these samples was measured, and the scattering profiles were consistent with the formulation. Furthermore, we discuss the relation between the three parameters and the features of the micron-sized structures. The visibility-reduction contrast observed by x-ray grating interferometry can thus be understood in relation to the structural parameters of the microstructures.