Ultimate sensitivity in X-ray diffraction: angular moments versus shot noise

The sensitivity towards Bragg peak parameters constitutes a crucial performance attribute of X-ray diffraction experiments. Diffraction peaks are frequently characterized by model-free angular moment analysis, which offers greater versatility compared with traditional model-based peak fitting. Here, we have theoretically determined the ultimate limit of the sensitivities of angular moments imposed by photon shot noise. These predictions have been validated by experimental data provided by three different setups. We have observed experimentally achieved sensitivities of the first moment below 1/1000th of a detector pixel and below 1 µrad. The formulae provided for the uncertainties of angular moments can now be used to rapidly determine experimentally achieved sensitivities from a single diffraction frame. Corresponding limitations (<i>i.e.</i> ultra-low photon counts and exceedingly high photon count rates) are identified and discussed.