Bounds of parameter estimation for interference signals.

Parameter estimation, especially frequency estimation, from noisy observations of interference is essential in optical interferometric sensing and metrology. The Cramer-Rao bound (CRB) of such estimation determines measurement sensitivity limit. Unlike the well-studied complex sinusoids in communication theory, an optical interference signal is distinctly different in its model parameters and noise statistics. The connection between these parameters and their estimation bounds has not been well understood. Here we propose a complete, realistic multiparameter interference model corrupted by a combination of shot noise, dark noise, and readout noise. We derive the Fisher information matrix and the CRBs for all model parameters, including intensity, visibility, optical path length (frequency), and initial phase. We show that the CRBs of frequency and phase are coupled but not affected by the knowledge of intensity and visibility. Knowing the initial phase offers significant sensitivity advantage, which is verified by both theoretical derivations and numerical simulations. In addition to the complete model, a shot noise-limited case is studied, permitting the calculation of the CRBs directly from measured data.