We present a first feasible scheme for detecting the phase of a single
mode of radiation with ideal RMS sensitivity delta phi similar to (n)
over bar(-1) versus the average number of photons (n) over bar. It in
volves pairs of alternate independent homodyne measurements of two con
jugated quadratures on a weakly squeezed state at the input. Nonunit q
uantum efficiency eta of photodetectors degrades phase sensitivity lea
ding to a power law delta phi similar to (n) over bar-(gamma(eta)), wi
th gamma increasingversus eta.