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In Advanced LIGO, detection and astrophysical source parameter estimation ofthe binary black hole merger GW150914 requires a calibrated estimate of thegravitational-wave strain sensed by the detectors. Producing an estimate fromeach detector's differential arm length control loop readout signals requiresapplying time domain filters, which are designed from a frequency domain modelof the detector's gravitational-wave response. The gravitational-wave responsemodel is determined by the detector's opto-mechanical response and theproperties of its feedback control system. The measurements used to validatethe model and characterize its uncertainty are derived primarily from adedicated photon radiation pressure actuator, with cross-checks provided byoptical and radio frequency references. We describe how the gravitational-wavereadout signal is calibrated into equivalent gravitational-wave-induced strainand how the statistical uncertainties and systematic errors are assessed.Detector data collected over 38 calendar days, from September 12 to October 20,2015, contain the event GW150914 and approximately 16 of coincident data usedto estimate the event false alarm probability. The calibration uncertainty isless than 10% in magnitude and 10 degrees in phase across the relevantfrequency band 20 Hz to 1 kHz.

Calibration of the Advanced LIGO detectors for the discovery of the binary black-hole merger GW150914