In search of the third dimension in Compton X-ray polarimeters

Compton polarimeters are typically designed to be sensitive only to the azimuthal angle of the scattered photon, ignoring the scattering angle. Such a 2-dimensional reconstruction of the event is pursued for both simplicity and because the polarization of the incident photon influences only the azimuthal response of the instrument. While this is true for on-axis sources, when the source starts to be off-axis of several degrees the azimuthal response of the instrument is effectively a convolution of the azimuthal and polar scattering angles: measuring the latter would provide a better sensitivity and smaller systematic effects. In this contribution, we will present a design which allows to estimate the scattering angle in a Compton polarimeter through the read-out of the light signal at the two ends of scintillator bars. Such a design is being tested with a representative set-up and first results on the performance are presented.