A two-step optimized measurement for the phase-shift

A two-step detection strategy is suggested for the precise measurement of the optical phase-shift. In the first step an unsharp, however, unbiased joint measurement of the phase and photon number is performed by heterodyning the signal field. Information coming from this step is then used for suitable squeezing of the probe mode to obtain a sharp phase distribution. Application to squeezed states leads to a phase sensitivity scaling as $\Delta\phi\simeq N^{-1}$ relative to the total number of photons impinged into the apparatus. Numerical simulations of the whole detection strategy are also also presented.