Characterization of a Nanometer Displacement Gauge for the Dimensional Control of Large Optomechanical Structures

We present the design, implementation, and characterization of a heterodyne laser interferometer for nanometer displacement metrology. The purpose is to monitor the 3-D shape of a large optomechanical structure planned for future general relativity experiments. Reaching the target 10(-11)-m displacement uncertainty over 7-m distances and many days' integration periods is a challenging task. The solution here investigated consists of a nonpolarizing Mach-Zehnder layout, featuring an optical cancelable circuit and a holey folding mirror. The instrument working principle and the method for online phase reconstruction are presented, as well as the complete hardware configuration used. The several sources of noise are investigated mathematically and, whenever possible, verified experimentally. The displacement gauge was tested up to one day of continuous data acquisition, showing nanometer-level performance down to 100 mHz, while air index variations and mechanical instabilities are currently the main limiting factors at lower frequencies. This experiment has brought into light many technical issues that will constitute precious "lessons learned" for the future improvements of the system.