  The measurement of the linear polarization is one of the hot topics of High
Energy Astrophysics. Gas detectors based on photoelectric effect have paved the
way for the design of sensitive instruments and mission proposals based on them
have been presented in the last few years in the energy range from about 2 keV
to a few tens of keV. As well, a number of polarimeters based on Compton
scattering are approved or discussed for launch on-board balloons or space
satellites at higher energies. These instruments are typically dedicated to
pointed observations with narrow field of view telescopes or collimators, but
there are also projects aimed at the polarimetry of bright transient sources,
like Soft Gamma Repeaters or the prompt emission of Gamma Ray Bursts. Given the
erratic appearance of such events in the sky, these polarimeters have a large
field of view to catch a reasonable number of them and, as a result, photons
may impinge on the detector off-axis. This changes dramatically the response of
the instrument to polarization, regardless if photoabsorption or Compton
scattering is involved. Instead of the simple cosine square dependency expected
for polarized photons which are incident on-axis, the response is never purely
cosinusoidal and a systematic modulation appears also for unpolarized
radiation. We investigate the origin of these differences and present an
analytic treatment which proves that actually such systematic effects are the
natural consequence of how current instruments operate. Our analysis provides
the expected response of photoelectric or Compton polarimeters to photons
impinging with any inclination and state of polarization.
