Length sensing and control

Length sensing can be seen as the core objective of interferometry, aiming at an as precise as possible measurement of length and length fluctuations. For an interferometric gravitational-wave detector, the quantity containing gravitational-wave information is derived from an ultra-sensitive measurement of differential length fluctuations of the long arms. In this chapter we will describe methods to deduce length signals for advanced gravitational-wave detectors and discuss aspects of length control. We will further look at the non-trivial process of lock acquisition, as well as the readout of the gravitational-wave signal.