Optical microresonators constitute the basic building block for numerous precision measurements including single-particle detection, magnetometry, force and position sensing. The ability to resolve a signal of interest is limited however by various noise sources. In this tutorial style paper we provide a matrix formalism to analyze the effect of various modulations upon the optical cavity. The technique can in principle be used to estimate the sensitivity of microresonator based sensors and potentially to identify the optimal detection basis and cavity parameters to optimise the signal to noise ratio
