Young giant exoplanets emit infrared radiation that can be linearly polarized up to several percent. This linear polarization can trace: 1) the presence of atmospheric cloud and haze layers, 2) spatial structure, e.g. cloud bands and rotational flattening, 3) the spin axis orientation and 4) particle sizes and cloud top pressure. We introduce a novel high-contrast imaging scheme that combines angular differential imaging (ADI) and accurate near-infrared polarimetry to characterize self-luminous giant exoplanets. We implemented this technique at VLT/SPHERE-IRDIS and developed the corresponding observing strategies, the polarization calibration and the data-reduction approaches. By combining ADI and polarimetry we can characterize planets that can be directly imaged with a very high signal-to-noise ratio. We use the IRDIS pupil-tracking mode and combine ADI and principal component analysis to reduce speckle noise. We take advantage of IRDIS dual-beam polarimetric mode to eliminate differential effects that severely limit the polarimetric sensitivity (flat-fielding errors, differential aberrations and seeing), and thus further suppress speckle noise. To correct for instrumental polarization effects, we apply a detailed Mueller matrix model that describes the telescope and instrument and that has an absolute polarimetric accuracy $leq0.1%$. Using this technique we have observed the planets of HR 8799 and the (sub-stellar) companion PZ Tel B. Unfortunately, we do not detect a polarization signal in a first analysis. We estimate preliminary $1sigma$ upper limits on the degree of linear polarization of $sim1%$ and $sim0.1%$ for the planets of HR 8799 and PZ Tel B, respectively. The achieved sub-percent sensitivity and accuracy show that our technique has great promise for characterizing exoplanets through direct-imaging polarimetry.
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