  In August 2017, Advanced Virgo joined Advanced LIGO for the end of the O2
run, leading to the first gravitational waves detections with the
three-detector network. This paper describes the Advanced Virgo calibration and
the gravitational wave strain h(t) reconstruction during O2. The methods are
the same as the ones developed for the initial Virgo detector and have already
been described in previous publications, this paper summarizes the differences
and emphasis is put on estimating systematic uncertainties. Three versions of
the h(t) signal have been computed for the Virgo O2 run, an online version and
two post-run reprocessed versions with improved detector calibration and
reconstruction algorithm. A photon calibrator has been used to establish the
sign of h(t) and to make an independent partial cross-check of the systematic
uncertainties. The uncertainties reached for the latest h(t) version are 5.1%
in amplitude, 40 mrad in phase and 20 microseconds in timing.
