Unequal-Arms Michelson Interferometers

Michelson interferometers allow phase measurements many orders of magnitude below the phase stability of the laser light injected into their two almost equal-length arms. If, however, the two arms are unequal, the laser fluctuations can not be removed by simply recombining the two beams. This is because the laser jitters experience different time delays in the two arms, and therefore can not cancel at the photo detector. We present here a method for achieving exact laser noise cancellation, even in an unequal-arm interferometer. The method presented in this paper requires a separate readout of the relative phase in each arm, made by interfering the returning beam in each arm with a fraction of the outgoing beam. By linearly combining the two data sets with themselves, after they have been properly time shifted, we show that it is possible to construct a new data set that is free of laser fluctuations. An application of this technique to future planned space-based laser interferometer detector3 of gravitational radiation is discussed.