Ultimate Sensitivity in X-ray Diffraction: Angular Moments vs. Shot Noise

The sensitivity of x-ray diffraction experiments towards Bragg peak parameters constitutes a crucial performance attribute of experimental setups. Frequently, diffraction peaks are characterized by model-free angular moment analysis, which offers a greater versatility compared to traditional model-based peak fitting. Here, we have determined the ultimate sensitivity of angular moments for diffraction data that is limited by photon shot noise. We report experimentally achieved sensitivities of the first moment below $1/1000$th of a detector pixel and below $1\mu$rad. We have demonstrated the validity of our theoretical predictions by an excellent agreement with experimental results from three different setups. The provided formulas for the uncertainties of angular moments allow for the rapid determination of experimentally achieved sensitivities from single diffraction frames.