  We analyze a cavity optomechanical setup, in which position of an oscillator
modulates optical loss. We show that in such setup quantum limited position
measurements can be performed if the external cavity coupling rate matches the
optical loss rate, a condition known as "critical coupling". Additionally,
under this condition the setup exhibits a number of potential benefits for
practical operation including the complete absence of dynamical backaction, and
hence optomechanical instability, and rejection of classical laser noise and
thermal fluctuations of cavity frequency from the measurement record. We
propose two implementations of this scheme: one based on signal-recycled
Michelson-type interferometer and the other on a tilted membrane inside
Fabry-Perot cavity.
