The baseline design for an Advanced Laser Interferometer Gravitational-Wave Observatory (Advanced LIGO) is a dual-recycled Michelson interferometer with cavities in each of the Michelson interferometer arms. We describe one possible length-sensing and control scheme for such a dual-recycled, cavity-enhanced Michelson interferometer. We discuss the principles of this scheme and derive the first-order sensing signals. We also present a successful experimental verification of our length-sensing system using a prototype tabletop interferometer. Our results demonstrate the robustness of the scheme against deviations from the idealized design. We also identify potential weaknesses and discuss possible improvements. These results as well as other benchtop experiments that we present form the basis for a sensing and control scheme for Advanced LIGO.
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