  We describe the Zurich Imaging Polarimeter (ZIMPOL), the visual focal plane
subsystem of the SPHERE "VLT planet finder", which pushes the limits of current
AO systems to shorter wavelengths, higher spatial resolution, and much improved
polarimetric performance. We provide new benchmarks for the performance of high
contrast instruments, in particular for polarimetric differential imaging. We
have analyzed SPHERE/ZIMPOL point spread functions and measure the peak surface
brightness, the encircled energy, and the full width half maximum (FWHM) for
different wavelengths, atmospheric conditions, star brightness, and instrument
modes. Coronagraphic images are described and analized and the performance for
different coronagraphs is compared with tests for the binary alpha Hyi with a
separation of 92 mas and a contrast of 6 mag. For the polarimetric mode we made
the instrument calibrations using zero polarization and high polarization
standard stars and here we give a recipe for the absolute calibration of
polarimetric data. The data show a small <1 mas but disturbing differential
polarimetric beam shifts, which can be explained as Goos-H\"ahnchen shifts from
the inclined mirrors, and we discuss how to correct this effect. The
polarimetric sensitivity is investigated with non-coronagraphic and deep,
coronagraphic observations of the dust scattering around the symbiotic Mira
variable R Aqr. SPHERE/ZIMPOL achieves imaging performances in the visual range
with unprecedented characteristics, in particular very high spatial resolution
and very high polarimetric contrast. This instrument opens up many new research
opportunities for the detailed investigation of circumstellar dust, in
scattered and therefore polarized light, for the investigation of faint
companions, and for the mapping of circumstellar Halpha emission.
