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-Hahnchen 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.
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