  Virgo is a kilometer-length interferometer for gravitational waves detection
located near Pisa. Its first science run, VSR1, occured from May to October
2007. The aims of the calibration are to measure the detector sensitivity and
to reconstruct the time series of the gravitational wave strain h(t). The
absolute length calibration is based on an original non-linear reconstruction
of the differential arm length variations in free swinging Michelson
configurations. It uses the laser wavelength as length standard. This method is
used to calibrate the frequency dependent response of the Virgo mirror
actuators and derive the detector in-loop response and sensitivity within ~5%.
The principle of the strain reconstruction is highlighted and the h(t)
systematic errors are estimated. A photon calibrator is used to check the sign
of h(t). The reconstructed h(t) during VSR1 is valid from 10 Hz up to 10 kHz
with systematic errors estimated to 6% in amplitude. The phase error is
estimated to be 70 mrad below 1.9 kHz and 6 micro-seconds above.
