Statistics of X-Ray Polarization Measurements

TL;DR

This paper develops methods for simulating and analyzing the angular distribution of electrons ejected by polarized X-ray beams, providing extended analytical tools for a broader range of polarization amplitudes.

Contribution

It introduces new analytical expressions and simulation methods for analyzing X-ray polarization measurements, extending previous work to cover all polarization amplitudes.

Findings

Validated analytical expressions through simulations

Extended the analytical framework to full polarization amplitude range

Confirmed consistency with prior research

Abstract

The polarization of an X-ray beam that produces electrons with velocity components perpendicular to the beam generates an azimuthal distribution of the ejected electrons. We present methods for simulating and for analyzing the angular dependence of electron detections which enable us to derive simple analytical expressions for useful statistical properties of observable data. The derivations are verified by simulations. While we confirm the results of previous work on this topic, we provide an extension needed for analytical treatment of the full range of possible polarization amplitudes.