  The polarimetry of gamma rays converting to an $e^+e^-$ pair would open a new
window on the high-energy gamma-ray sky by, among other things, providing
insight into the radiation mechanism in pulsars (curvature or synchrotron) or
deciphering the composition of the gamma-ray emitting jets in blazars (leptonic
or lepto-hadronic). The performance of polarimeters based on homogeneous active
targets (gas detectors (MeV, HARPO) or emulsions (GeV, GRAINE) has been studied
both with simulation and by the analysis of data collected with telescope
prototypes on linearly-polarised gamma-ray beams, and found to be excellent.
The present (Fermi LAT), AGILE and future project (AMEGO, ASTROGAM) gamma-ray
missions, though, are using active targets based on silicon strip detectors
(SSD). No demonstration of a non-zero effective polarisation asymmetry with
SSDs has been published to date, be it only with simulated data, and
sensitivity estimations were obtained from an assumed value of the effective
polarisation asymmetry. I present a characterisation of the potential of
SSD-based active targets for polarimetry with gamma-ray conversions to pairs
and the development of various methods to improve on the sensitivity. This work
could pave the way to providing the polarimetry of the brightest gamma-ray
sources of the sky from the decade of data collected by the Fermi LAT and by
AGILE, and to guiding the design of future missions.
