6 Interferometric Length Sensing and Control

In this section we introduce interferometers as length sensing devices. In particular, we explain how the Fabry–Pérot interferometer and the Michelson interferometer can be used for high-precision measurements and that both require a careful control of the base length (which is to be measured) in order to yield their large sensitivity. In addition, we briefly introduce the general concepts of error signals and transfer functions, which are used to describe most essential features of length sensing and control.

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Figure 32: Example of an error signal: the top graph shows the electronic interferometer output signal as a function of mirror displacement. The operating point is given as the zero crossing, and the error-signal slope is defined as the slope at the operating point. The right graph shows the magnitude of the transfer function mirror displacement → error signal. The slope of the error signal (left graph) is equal to the low frequency limit of the transfer function magnitude (see Equation (102View Equation)).
 6.1 Error signals and transfer functions
 6.2 Fabry–Pérot length sensing
 6.3 The Pound–Drever–Hall length sensing scheme
 6.4 Michelson length sensing
 6.5 The Schnupp modulation scheme
 6.6 Finesse examples
  6.6.1 Cavity power and slope
  6.6.2 Michelson with Schnupp modulation

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