  The development of multi-layer optics which allow to focus photons up to 100
keV and more promises an enormous jump in sensitivity in the hard X-ray energy
band. This technology is already planned to be exploited by future missions
dedicated to spectroscopy and imaging at energies >10 keV, e.g. Astro-H and
NuSTAR. Nevertheless, our understanding of the hard X-ray sky would greatly
benefit from carrying out contemporaneous polarimetric measurements, because
the study of hard spectral tails and of polarized emission often are two
complementary diagnostics of the same non-thermal and acceleration processes.
At energies above a few tens of keV, the preferred technique to detect
polarization involves the determination of photon directions after a Compton
scattering. Many authors have asserted that stacked detectors with imaging
capabilities can be exploited for this purpose. If it is possible to
discriminate those events which initially interact in the first detector by
Compton scattering and are subsequently absorbed by the second layer, the
direction of scattering is singled out from the hit pixels in the two
detectors. In this paper we give the first detailed discussion of the
sensitivity of such a generic design to the X-ray polarization. The efficiency
and the modulation factor are calculated analytically from the geometry of the
instruments and then compared with the performance as derived by means of
Geant4 Monte Carlo simulations.
