Correlation methods for the analysis of X-ray polarimetric signals

TL;DR

This paper introduces two correlation-based tools for analyzing X-ray polarimetric signals, enabling straightforward visualization and estimation of polarization parameters while assessing systematic distortions.

Contribution

The authors develop novel correlation methods that transform angular distributions into visual patterns for improved polarization analysis in X-ray measurements.

Findings

Correlation methods produce clear visual patterns for polarization signals.

Tools effectively distinguish polarized from unpolarized radiation.

Methods help identify systematic distortions in measurements.

Abstract

X-ray polarimetric measurements are based on studying the distribution of the directions of scattered photons or photoelectrons and on the search of a sinusoidal modulation with a period of {\pi}. We developed two tools for investigating these angular distributions based on the correlations between counts in phase bins separated by fixed phase distances. In one case we use the correlation between data separated by half of the bin number (one period) which is expected to give a linear pattern. In the other case, the scatter plot obtained by shifting by 1/8 of the bin number (1/4 of period) transforms the sinusoid in a circular pattern whose radius is equal to the amplitude of the modulation. For unpolarized radiation these plots are reduced to a random point distribution centred at the mean count level. This new methods provide direct visual and simple statistical tools for evaluating the quality of polarization measurements and for estimating the polarization parameters. Furthermore they are useful for investigating distortions due to systematic effects.