Statistically Optimum Optical Data Processing with Automatic Focus Estimation

The problem of optimally processing data with unknown focus is investigated. Optimum data processors are found by the method of maximum likelihood under a variety of assumptions that apply to most of the situations arising in practice. The unknown focus may be either an unknown parameter or an unknown random variable; the signal may be of known form or a random function; it is further assumed that the signal is received in additive, white, Gaussian noise. The problems of jointly estimating other unknown parameters and, in the case of a random signal, jointly estimating the signal, are also treated. The asymptotic variance and correlation of the estimators is discussed. Electrooptical realizations of the maximum likelihood computers are given. An iterative method of solution of the likelihood equation is also discussed. The discussion and results are directly applicable to the processing of synthetic aperture radar data.