The effects of time-varying measurement noise on transmission matrix acquisition processes are considered for the first time, to our knowledge. Dominant noise sources are discussed, and the noise properties of a typical interferometer system used for characterizing a multimode fiber transmission matrix are quantified. It is demonstrated that an appropriate choice of measurement basis allows a more accurate transmission matrix to be more quickly obtained in the presence of measurement noise. Finally, it is shown that characterizing the noise figure of the experimental system allows the inverse transmission matrix to be constructed with an ideal amount of regularization, which can in turn be used for optimal image acquisition.