Perturbation perspective of partial coherence discussion on imperfect x-ray optical elements

The rapid development of new-generation synchrotron facilities with excellent coherence demands more accurate evaluation of beamline performance. A perturbation theory based on wave optics is proposed in this work to describe the effect of imperfections on the performance of x-ray optical elements. It shows that the perturbed performance of the non-ideal optical element could be derived from the perfect performance of the ideal optic through a convolution operation. The semi-analytical approach proposed here provides a new way to improve the simulation efficiency for imperfect optical elements. The finite aperture effect on diffraction-limited optics and focal shape distortion by surface height error are treated to show the application of the proposed method.