| Large interferometers are currently under construction for the detection of gravitational radiation. These will contain a number of optical surfaces at each of which the relative phase of incident beams must be kept strictly controlled in order to achieve high sensitivity.; The type of interferometer considered here consists of two Fabry-Perot cavities illuminated by a laser beam which is split in half by a beam splitter, together with a recycling mirror between the laser and the beam splitter, which reflects light returning from the beam splitter toward the laser back into the interferometer. A scheme for sensing deviations from proper interference has been analyzed and the adequacy of this method for incorporation in a control system has been evaluated. The sensing scheme involves phase modulating the laser light incident on the interferometer, introducing an asymmetry in the distances between the Fabry-Perot cavities and the beam splitter, and demodulating the signals from photodetectors monitoring three optical outputs of the interferometer. These optical outputs are light returning to the laser, light extracted by a pick-off from between the recycling mirror and the beam splitter, and light leaving the interferometer at the beam splitter.; The analysis has shown that the matrix of transfer functions from mirror displacement to demodulated signal is ill-conditioned, that as many as three of the transfer functions may contain right half plane zeros, and that one of these transfer functions can be affected by the modulation depth. The performance of the closed-loop system, however, need not be significantly affected, provided that certain constraints are observed in the optical and electronic design.; A table-top interferometer has been constructed, to demonstrate the feasibility of constructing a control system using this sensing scheme and to compare the response of the interferometer with that predicted by calculations. Good agreement between the experiment and the calculation has been obtained. |
