  Calibration of the second-generation LIGO interferometric gravitational-wave
detectors employs a method that uses injected periodic modulations to track and
compensate for slow temporal variations in the differential length response of
the instruments. These detectors utilize feedback control loops to maintain
resonance conditions by suppressing differential arm length variations. We
describe how the sensing and actuation functions of these servo loops are
parameterized and how the slow variations in these parameters are quantified
using the injected modulations. We report the results of applying this method
to the LIGO detectors and show that it significantly reduces systematic errors
in their calibrated outputs.
