The two LIGO (Laser Interferometer Gravitational-wave Observatory) detectors have successfully completed three observing runs in recent years and, together with the Virgo detector, have directly observed transient gravitational waves from binary systems of neutron stars and black holes.  

The time series of dimensionless strain, defined by the differential changes in the length of the two orthogonal arms divided by the averaged full arm length (∼4 km in the two LIGO detectors), is used to determine the detection of a gravitational wave signal and to infer the properties of the astrophysical source. A conceptual diagram of the optical configuration of the LIGO interferometers is shown in Fig 1. 

FIG. 1: Conceptual diagram of the optical configuration of the LIGO interferometers. The X and Y arms are 4km-long, Fabry-Perot cavities formed by the highly reflective end test masses and partially transmissive input test masses. Inset: one of the full quadruple pendulum suspension systems and its actuators. Credit: Ref. [1]. 

Due to the presence of noise, and the desire to maintain the resonance condition of the optical cavities, the detectors do not directly measure the strain. The differential arm displacement is suppressed by the control force allocated to the test masses. The residual differential arm displacement in the control loop is converted into digitised photodetector output signals. Therefore, the strain is reconstructed from the raw digitised electrical output of each detector, with an accurate and precise model of the detector response to the strain. This reconstruction process is referred to as the calibration of the detectors. The accuracy and precision of the estimated detector response, and hence the reconstructed strain data, are important for detecting gravitational wave signals and crucial for estimating their astrophysical parameters. 

As the global gravitational-wave detector network sensitivity increases, detector calibration accuracy and precision will play an increasingly important role. Research and development of new techniques are being conducted at the Centre for Gravitational Astrophysics, to further improve the level of accuracy and precision in detector calibration, as well as better integrate the calibration bias and uncertainty into astrophysical analyses.  

[1] Sun et al., Class. Quant. Grav. 37, 225008 (2020)