CLASSICAL AND QUANTUM PARAMETER ESTIMATION THEORY FOR OPTICAL SPECTROSCOPY AND IMAGING

Abstract

We present three results on parameter estimation theory and its application to optical spectroscopy and imaging. In the first study, we derive analytic expressions for the Cramér-Rao lower bound on the errors for parameter estimation from a noisy optomechanical system, and apply various estimation techniques to experimental data. These results should be valuable to optomechanics experimental designs. Second, we derive analytic expressions for quantum limits to the estimation errors of spectral parameters. We analyze a continuous-optical-phase-estimation experiment and demonstrate that homodyne detection is close to our quantum limit. We further propose a spectral photon counting method that can beat homodyne detection and attain quantum-optimal performance in low signal-to-noise regime. For the last result, we obtain the quantum limit to the estimation of the centroid and separation of two incoherent optical point sources. We propose two measurement schemes that asymptotically attain the quantum limit for both Cartesian components of the separation.