X-rays are particularly suited to probe the physics of extreme objects.
However, despite the enormous improvements of X-ray Astronomy in imaging,
spectroscopy and timing, polarimetry remains largely unexplored. We propose the
photoelectric polarimeter Gas Pixel Detector (GPD) as an instrument candidate
to fill the gap of more than thirty years of lack of measurements. The GPD, in
the focus of a telescope, will increase the sensitivity of orders of magnitude.
Moreover, since it can measure the energy, the position, the arrival time and
the polarization angle of every single photon, allows to perform polarimetry of
subsets of data singled out from the spectrum, the light curve or the image of
source. The GPD has an intrinsic very fine imaging capability and in this work
we report on the calibration campaign carried out in 2012 at the PANTER X-ray
test facility of the Max-Planck-Institut f\"ur extraterrestrische Physik of
Garching (Germany) in which, for the first time, we coupled it to a JET-X
optics module with a focal length of 3.5 m and an angular resolution of 18
arcsec at 4.5 keV. This configuration was proposed in 2012 aboard the X-ray
Imaging Polarimetry Explorer (XIPE) in response to the ESA call for a small
mission. We derived the imaging and polarimetric performance for extended
sources like Pulsar Wind Nebulae and Supernova Remnants as case studies for the
XIPE configuration, discussing also possible improvements by coupling the
detector with advanced optics, having finer angular resolution and larger
effective area, to study with more details extended objects.Comment: Accepted for publication in The Astrophysical Journal Supplemen
