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We perform a quantum theoretical calculation of the noise power spectrum fora phase measurement of the light output from a coherently driven optical cavitywith a freely moving rear mirror. We examine how the noise resulting from thequantum back action appears among the various contributions from other noisesources. We do not assume an ideal (homodyne) phase measurement, but ratherconsider phase modulation detection, which we show has a different shot noiselevel. We also take into account the effects of thermal damping of the mirror,losses within the cavity, and classical laser noise. We relate our theoreticalresults to experimental parameters, so as to make direct comparisons withcurrent experiments simple. We also show that in this situation, the standardBrownian motion master equation is inadequate for describing the thermaldamping of the mirror, as it produces a spurious term in the steady-state phasefluctuation spectrum. The corrected Brownian motion master equation [L. Diosi,Europhys. Lett. {\bf 22}, 1 (1993)] rectifies this inadequacy.Comment: 12 pages revtex, 2 figure

Quantum noise in the position measurement of a cavity mirror undergoing Brownian motion