Phase Estimation Techniques for Active Optics Systems Used in Real-Time Wavefront Reconstruction

摘要

Two analyses ae presented, which involve estimation of constant phase from single detector and detector array measurements. The single detector analysis is carried out in a discrete mode to obtain algorithms based on photon counting. The method used follows the Maximum A Posteriori and Maximum Likelihood estimation theories. Both white Gaussian noise and Poisson Shot noise limited conditions are considered. Simulation results show that signal-to-noise ratios of 17 dB or better are needed to produce adequate estimates. Estimate improvement is obtained as more photon counts are performed. In this sense, photon counting seems to be inferior to current measuring, but the error variance is only 1.65 dB larger in the worst case, where three photon counts are performed. An extension of the single detector analysis is made, using only the Gaussian noise assumption, to derive an algorithm that jointly estimates the phase distribution over an optical wavefront. The procedure is based on a parametric dependence between the measurements performed by adjacent detectors, and on the a priori knowledge available through a covariance matrix. An algorithm for processing continuous waveform measurements is developed, but no computer simulation is included due to difficulties encountered in solving the feedback system equations.