Estimate of the ultimate sensitivity of multiple-beam interferometers for displacement measurement

The problem of the ultimate sensitivity of a Fabry — Perot interferometer (FPI) used to measure small displacements is considered. A conventional FPI, operating in the transmission mode, is compared with a reflecting interferometer (RI). It is shown that the RI has significant advantages. A detailed analysis is made of a modulation method for obtaining an output signal from the RI. An estimate is obtained of the influence of weak background illumination and of an incorrect choice of the mirror parameters. At the level of the losses currently achieved in mirrors (10^–6). The sensitivity to displacements should be 4 × 10^–23 m Hz^–1/2 for a light source of 1 W power. It is suggested that the RI can be used in gravitational wave detectors, particularly if they are constructed so that there is a small space between the mirrors. This condition makes it possible to reduce the frequency dispersion, which is nearly excluded in a dispersion-free variant of the interferometer.