A homodyne Michelson interferometer with sub-picometer resolution

A homodyne interferometer which exploits a multiple reflection arrangement between two quasi parallel mirrors to deliver a multiplication factor is presented. The relative displacement of the two mirrors causes a more than 100-fold increment of the optical path, which is measured by the optoelectronic circuitry. This leads to a proportional reduction of the errors associated with the subdivision of the optical fringes, with the effect of fringe nonlinearities, and with the opto-electronic noise. In particular the reduction of the electronic noise limit to the level of 20 fm Hz(-1/2) has been demonstrated. The exact formula of the gain has been calculated and confirmed experimentally.