  We present a scheme to strongly enhance the readout sensitivity of the
squared displacement of a mobile scatterer placed in a Fabry-P\'erot cavity. We
investigate the largely unexplored regime of cavity electrodynamics in which a
highly reflective element positioned between the end mirrors of a symmetric
Fabry-P\'erot resonator strongly modifies the cavity response function, such
that two longitudinal modes with different spatial parity are brought close to
frequency degeneracy and interfere in the cavity output field. In the case of a
movable middle reflector we show that the interference in this generic "optical
coalescence" phenomenon gives rise to an enhanced frequency shift of the peaks
of the cavity transmission that can be exploited in optomechanics.
