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

TL;DR

This paper establishes the ultimate sensitivity limits of angular moment analysis in x-ray diffraction under shot noise, demonstrating experimental achievements surpassing traditional resolution and validating theoretical predictions across multiple setups.

Contribution

It introduces theoretical formulas for sensitivity limits of angular moments in x-ray diffraction and validates them with experimental data from three different setups.

Findings

Achieved sensitivity of first angular moment below 1/1000th of a pixel

Sensitivity below 1 microradian demonstrated

Excellent agreement between theory and experiment across setups

Abstract

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.