A systematic error in X-ray grating interferometry due to asymmetric scattering distributions

The high sensitivity provided by x-ray grating interferometry is one of the distinct characteristics of this phase contrast imaging technique. Up to now, several contributions to the uncertainty of the determined phase signal are known, which can be addressed by adapting total acquisition time or improving the mechanics of the experimental setup. Here, we demonstrate the occurrence of an additional systematic error, which is intrinsic to the physics of the contrast formation process. Based on a recently established scattering-based description of grating interferometry, we demonstrate analytically that asymmetric scattering distributions lead to a systematic error in the determined phase signal.