The most sensitive gravitational-wave detectors today are based on large-scale laser interferometers whose optics are suspended from pendulums to decouple the instrument from seismic motion. Complex control systems are required to set and maintain the microscopic position of each mirror at a precisely defined value. Such control systems use the interferometer signals as input signals, and ideally it is designed such that the degrees of freedom (mirror positions) are well decoupled in the interferometer signals. However, this is not always feasible, in particular the mirror alignment control signals in interferometric gravitational wave detectors often show strong couplings between the different degrees of freedom. In this paper we will describe a simple and powerful method to quantify in advance the performances of an alignment control system by analyzing the optical matrix of the proposed read-out system. We will motivate the method using a Fabry-Perot cavity as an example, and we will further present results for the Virgo alignment system where this method was used to characterize and improve the alignment sensing scheme.
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