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Geometrical tools for the analysis of x-ray polarimetric signals

X-ray polarimetric measurements are based on the study of distributions of the directions of scattered photons or photoelectrons and the search of a sinusoidal modulation with a period of π. We present a new simple tool based on a scatter plot of the modulation curve in which the counts in each angular bin are reported after a shifting by 1/4 of the period. The sinusoidal pattern is thus transformed in a circular plot whose radius is equal to the amplitude of the modulation, while for a not polarized radiation the scatter plot is reduced to a random point distribution centred at the mean frequency value. The advantage of this tool is that one can easily evaluate the statistical significance of the polarimetric detection and can obtain useful information on the quality of the measurement.