Controlling calibration errors in gravitational-wave detectors by precise location of calibration forces

We present results of finite element analysis simulations which could lead to more accurate calibration of interferometric gravitational wave detectors. Calibration and actuation forces applied to the interferometer test masses cause elastic deformation, inducing errors in the calibration. These errors increase with actuation frequency, and can be greater than 50% at frequencies above a few kilohertz. We show that they can be reduced significantly by optimizing the position at which the forces are applied. The Advanced LIGO [1] photon calibrators use a two-beam configuration to reduce the impact of local deformations of the test mass surface. The position of the beams over the test mass can be chosen such both the local and the bulk induced elastic deformation are minimized. Our finite element modeling indicates that with two beams positioned within ±1 mm of their optimal locations, calibration errors due to test mass elastic deformation can be kept below 1% for frequencies up to 3.5 kHz. We thus show that precise control of the location of calibration forces could considerably improve calibration accuracy, especially at high frequencies.