  Context. Circumstellar disks and self-luminous giant exoplanets or companion
brown dwarfs can be characterized through direct-imaging polarimetry at
near-infrared wavelengths. SPHERE/IRDIS at the Very Large Telescope has the
capabilities to perform such measurements, but uncalibrated instrumental
polarization effects limit the attainable polarimetric accuracy. Aims. We aim
to characterize and correct the instrumental polarization effects of the
complete optical system, i.e. the telescope and SPHERE/IRDIS. Methods. We
create a detailed Mueller matrix model in the broadband filters Y-, J-, H- and
Ks, and calibrate it using measurements with SPHERE's internal light source and
observations of two unpolarized stars. We develop a data-reduction method that
uses the model to correct for the instrumental polarization effects, and apply
it to observations of the circumstellar disk of T Cha. Results. The
instrumental polarization is almost exclusively produced by the telescope and
SPHERE's first mirror and varies with telescope altitude angle. The crosstalk
primarily originates from the image derotator (K-mirror). At some orientations,
the derotator causes severe loss of signal (>90% loss in H- and Ks-band) and
strongly offsets the angle of linear polarization. With our correction method
we reach in all filters a total polarimetric accuracy of <0.1% in the degree of
linear polarization and an accuracy of a few degrees in angle of linear
polarization. Conclusions. The correction method enables us to accurately
measure the polarized intensity and angle of linear polarization of
circumstellar disks, and is a vital tool for detecting unresolved (inner) disks
and measuring the polarization of substellar companions. We have incorporated
the correction method in a highly-automatic end-to-end data-reduction pipeline
called IRDAP which is publicly available at https://irdap.readthedocs.io.
