Intensity-weighted phase-derivative statistics

It is shown that amplitude weighting can improve the accuracy of measuremen ts of the frequency offset of a signal contaminated by multiplicative Gauss ian noise. The more general non-Gaussian case is investigated through study of the statistics of a simple phase-screen scattering model. Formulas are derived for the low-order moments of the intensity-weighted phase derivativ e. Numerical simulation is tested against these results and is used to gene rate full probability densities that are analytically intractable and to de termine the optimum weighting for the non-Gaussian regime of the model. The results are relevant to a variety of remote-sensing and signal-processing problems. (C) 2001 Optical Society of America.