Based on the unified theory of coherence and polarization, the changes in the polarization state of random electromagnetic beams which propagate in free space or random medium have been studied in previous works. In this paper, inspired by the grating-based differential phase-contrast imaging method, we study the spectral degree of polarization of random electromagnetic beams generated by Gaussian Schell-model source which propagate in XTI. We derive the formula of spectral degree of polarization in the detector plane and give the definition of polarization-stepping visibility. Numerical simulation result implies that XTI has a potential to study the internal structure of the object by using the measured spectral degree of polarization, and differential phase-contrast imaging can be performed with the same settings.